Finite Group DatabasebetaFinite Group Databasebeta| order | 22365 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| derived, Hall | C7×C71 ⋊ C5×C9 |
| Hall | C7⋊C9×C71 ⋊ C5 |
| Hall | C7×C71⋊C5 ⋊ C9 |
| Sylow | C71 ⋊ C5×C7⋊C9 |
| Sylow | C7 ⋊ C9×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×C71⋊C5 |
| commutator, hypocenter | C7×C71 | C5×C9 |
| Fitting, socle, cosocle | C3×C7×C71 | C3×C5 |
| prime radical | C3×C7×C71⋊C5 | C3 |
| LCS | G ▷ C7×C71 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4473 |
285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22365, 6);