genus 2: order 16: 1 listed actions; orders, element orders 2,4,8 and G.1 = G.2 G.3: OK; kernels pairwise different (also up to reflection): True; reflexible (computed) [True] (listed [True]); normal in (2,3,8): [True] (orders of the extension quotients [48]); (2,3,8) actions of order 48 listed: 1
   => surfaces with a group of order 16 and signature (2,4,8): 1; of these with full automorphism group of order 16: 0
genus 3: order 32: 2 listed actions; orders, element orders 2,4,8 and G.1 = G.2 G.3: OK; kernels pairwise different (also up to reflection): True; reflexible (computed) [True, True] (listed [True, True]); normal in (2,3,8): [True, False] (orders of the extension quotients [96, 48]); (2,3,8) actions of order 96 listed: 1
   => surfaces with a group of order 32 and signature (2,4,8): 2; of these with full automorphism group of order 32: 1
genus 5: order 64: 2 listed actions; orders, element orders 2,4,8 and G.1 = G.2 G.3: OK; kernels pairwise different (also up to reflection): True; reflexible (computed) [True, True] (listed [True, True]); normal in (2,3,8): [False, True] (orders of the extension quotients [24, 192]); (2,3,8) actions of order 192 listed: 1
   => surfaces with a group of order 64 and signature (2,4,8): 2; of these with full automorphism group of order 64: 1
genus 9: order 128: 4 listed actions; orders, element orders 2,4,8 and G.1 = G.2 G.3: OK; kernels pairwise different (also up to reflection): True; reflexible (computed) [True, True, True, True] (listed [True, True, True, True]); normal in (2,3,8): [False, False, False, False] (orders of the extension quotients [24, 24, 192, 24]); (2,3,8) actions of order 384 listed: 0
   => surfaces with a group of order 128 and signature (2,4,8): 4; of these with full automorphism group of order 128: 4
genus 17: order 256: 4 listed actions; orders, element orders 2,4,8 and G.1 = G.2 G.3: OK; kernels pairwise different (also up to reflection): True; reflexible (computed) [True, True, True, True] (listed [True, True, True, True]); normal in (2,3,8): [False, True, False, False] (orders of the extension quotients [192, 768, 192, 24]); (2,3,8) actions of order 768 listed: 1
   => surfaces with a group of order 256 and signature (2,4,8): 4; of these with full automorphism group of order 256: 3
genus 33: order 512: 8 listed actions; orders, element orders 2,4,8 and G.1 = G.2 G.3: OK; kernels pairwise different (also up to reflection): True; reflexible (computed) [True, True, True, True, True, True, True, True] (listed [True, True, True, True, True, True, True, True]); normal in (2,3,8): [False, False, False, False, True, False, False, False] (orders of the extension quotients [192, 192, 768, 768, 1536, 192, 192, 24]); (2,3,8) actions of order 1536 listed: 1
   => surfaces with a group of order 512 and signature (2,4,8): 8; of these with full automorphism group of order 512: 7
genus 65: order 1024: 14 listed actions; orders, element orders 2,4,8 and G.1 = G.2 G.3: OK; kernels pairwise different (also up to reflection): True; reflexible (computed) [False, False, True, True, True, True, True, True, True, True, True, True, True, True] (listed [False, False, True, True, True, True, True, True, True, True, True, True, True, True]); normal in (2,3,8): [False, False, False, False, False, False, False, False, False, False, False, True, False, False] (orders of the extension quotients [192, 1536, 192, 192, 768, 768, 1536, 768, 768, 768, 768, 3072, 768, 24]); (2,3,8) actions of order 3072 listed: 1
   => surfaces with a group of order 1024 and signature (2,4,8): 16; of these with full automorphism group of order 1024: 15
{2: (1, 1, 0), 3: (2, 2, 1), 5: (2, 2, 1), 9: (4, 4, 4), 17: (4, 4, 3), 33: (8, 8, 7), 65: (14, 16, 15)}
