Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C7×D289 |
| unambiguous semidirect product | C289⋊(C22×C3×C7) |
| unambiguous semidirect product | (C2×C289)⋊(C2×C3×C7) |
| Fitting | C2×C3×C7×C289 ⋊ C2 |
| derived, Sylow | C289 ⋊ C22×C3×C7 |
| Hall | C3×C7×C289 ⋊ C22 |
| Hall | C7×C289 ⋊ C22×C3 |
| Hall | C3×C289 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | D289 |
| commutator, cosocle, hypocenter | C289 | C22×C3×C7 |
| Frattini | C17 | C2×C3×C7×D17 |
| Fitting | C2×C3×C7×C289 | C2 |
| socle | C2×C3×C7×C17 | D17 |
| LCS | G ▷ C289 | |
| UCS | C1 ◁ C2×C3×C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12138 |
6132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 34);