Finite Group DatabasebetaFinite Group Databasebeta| order | 22785 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊#3862 |
| unambiguous semidirect product | (C31⋊#3862)⋊C5 |
| Fitting, socle, derived, Hall | C72×C31 ⋊ C3×C5 |
| Hall | C72×ΓL(1,𝔽32) ⋊ C3 |
| Hall | C31⋊#3862 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ #3862 |
| Sylow | C72 ⋊ (C31⋊C3)⋊C5 |
| Sylow | C31 ⋊ C5×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C31 | C3×C5 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 651 |
Polycyclic presentation:
3,5,7^2,31|c^a=c^2,d^a=d^4,e^a=e^5,e^b=e^16193 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22785, 19);