S1 |G| : 768
S2 |B|, B el.ab. : (8, True)
S2 B normal in G : True
S2 |W|, B∩W : (96, 1)
S3 |E|, E el.ab., E normal in W : (8, True, True)
S3 |A4|, E∩A4 : (12, 1)
S3 |V|, V el.ab., V normal in A4, V∩C3, |C3| : (4, True, True, 1, 3)
S4 stabilisers of nontrivial mu : [{'a': (0, 0, 1), 'order': 24, 'involutions': 1, 'order4': 6, 'normal_Q8': True, 'derived_order': 8, 'orders': [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6]}, {'a': (0, 1, 0), 'order': 24, 'involutions': 1, 'order4': 6, 'normal_Q8': True, 'derived_order': 8, 'orders': [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6]}, {'a': (0, 1, 1), 'order': 32}, {'a': (1, 0, 0), 'order': 24, 'involutions': 1, 'order4': 6, 'normal_Q8': True, 'derived_order': 8, 'orders': [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6]}, {'a': (1, 0, 1), 'order': 32}, {'a': (1, 1, 0), 'order': 32}, {'a': (1, 1, 1), 'order': 24, 'involutions': 1, 'order4': 6, 'normal_Q8': True, 'derived_order': 8, 'orders': [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6]}]
ALL STRUCTURAL CHECKS PASSED
