Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#11923883⋊C3 |
| unambiguous semidirect product | #11923883⋊(C3×C7) |
| Fitting, socle, Hall | C7×C172 ⋊ C3×C4 |
| derived, Sylow | C172 ⋊ C3×C4×C7 |
| Hall | C7×#11923883 ⋊ C3 |
| Hall | C7×C172⋊C3 ⋊ C4 |
| Hall | #11923883 ⋊ C3×C7 |
| Hall | C172⋊C3 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11923883⋊C3 |
| commutator, hypocenter | C172 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C172 | C3×C4 |
| prime radical | C7×(C17⋊D17)⋊C3 | C2 |
| cosocle | C17⋊D17 | C2×C3×C7 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 357 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 72);