Finite Group DatabasebetaFinite Group Databasebeta| order | 23541 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×#87705 |
| Fitting, socle, Hall | C7×C19×C59 ⋊ C3 |
| derived, Hall | C7×C19 ⋊ C3×C59 |
| Hall | C19×C59 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C59 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×C59 |
| Sylow | C7 ⋊ C19⋊C3×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | #87705 |
| commutator, cosocle, hypocenter | C7×C19 | C3×C59 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C59 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C59 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7847 |
2773 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23541, 5);