Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C17 |
| direct product | C4×C7⋊(C172⋊C3) |
| unambiguous semidirect product | (C4×C7)⋊(C172⋊C3) |
| unambiguous semidirect product | (C4×C172)⋊ΓL(1,𝔽8) |
| Fitting, Hall | C4×C7×C172 ⋊ C3 |
| derived, Hall | C7×C172 ⋊ C3×C4 |
| Hall | C4×C172 ⋊ ΓL(1,𝔽8) |
| Sylow | C172 ⋊ C4×ΓL(1,𝔽8) |
| Hall | C4×C7 ⋊ C172⋊C3 |
| Sylow | C7 ⋊ C4×C172⋊C3 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1428 |
2708 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 55);