Finite Group DatabasebetaFinite Group Databasebeta| order | 31264 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#21463100 |
| unambiguous semidirect product | (C2×#21463100)⋊C2 |
| Fitting | C22×C977 ⋊ C8 |
| Sylow | C977 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3908 |
Polycyclic presentation:
2^5,977|a^2=d,d^2=e,b^a=bc,f^a=f^439,f^d=f^252,f^e=f^976508 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31264, 238);