Finite Group DatabasebetaFinite Group Databasebeta| order | 22365 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C7×C71⋊C5 |
| unambiguous semidirect product | (C32×C7×C71)⋊C5 |
| Fitting, socle, Hall | C32×C7×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C32×C5×C7 |
| Hall | C32×C71 ⋊ C5×C7 |
| Hall | C7×C71 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | C71⋊C5 |
| commutator, cosocle, hypocenter | C71 | C32×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C71 | C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C32×C7 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4473 |
1197 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22365, 11);