Finite Group DatabasebetaFinite Group Databasebeta| order | 22785 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C5×C72×C31⋊C3 |
| unambiguous semidirect product | (C5×C31)⋊(C3×C72) |
| Fitting, socle, Hall | C5×C72×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C5×C72 |
| Hall | C72×C31 ⋊ C3×C5 |
| Hall | C5×C31 ⋊ C3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C72 | C31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C3×C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C31 | C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C72 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7595 |
3185 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22785, 22);