Finite Group DatabasebetaFinite Group Databasebeta| order | 22785 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #17986945⋊C5 |
| Fitting, derived, Hall | C31×C49 ⋊ C3×C5 |
| Hall | C49×ΓL(1,𝔽32) ⋊ C3 |
| Hall | #17986945 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C49⋊C3 |
| Sylow | C49 ⋊ (C31⋊C3)⋊C5 |
| Sylow | C31 ⋊ C5×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C31×C49 | C3×C5 |
| Frattini | C7 | #10620252⋊C5 |
| socle | C7×C31 | C5×ΓL(1,𝔽8) |
| LCS | G ▷ C31×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1519 |
Polycyclic presentation:
3,5,7,31,7|c^7=e^2,c^a=c^2e,d^a=d^5,e^a=e^2,d^b=d^16193 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22785, 10);