Finite Group DatabasebetaFinite Group Databasebeta| order | 24297 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×#63270 |
| Fitting, socle, Hall | C7×C13×C89 ⋊ C3 |
| derived, Hall | C7×C13 ⋊ C3×C89 |
| Hall | C13×C89 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C89 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×C89 |
| Sylow | C7 ⋊ C13⋊C3×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | #63270 |
| commutator, cosocle, hypocenter | C7×C13 | C3×C89 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C89 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C89 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8099 |
2937 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24297, 4);