Finite Group DatabasebetaFinite Group Databasebeta| order | 22592 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#15667734)⋊C4 |
| Fitting | C2×C4×C353 ⋊ C8 |
| Sylow | C353 ⋊ #336 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2824 |
Polycyclic presentation:
2^6,353|a^2=d,b^2=e,d^2=f,b^a=bc,g^a=g^283,g^d=g^311,g^f=g^352392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22592, 1640);