Finite Group DatabasebetaFinite Group Databasebeta| order | 24174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C3 |
| direct product | C17×C3⋊D237 |
| unambiguous semidirect product | C3⋊(C17×D237) |
| unambiguous semidirect product | C79⋊(C17×C3⋊D3) |
| Fitting, socle, Hall | C32×C17×C79 ⋊ C2 |
| derived, Hall | C32×C79 ⋊ C2×C17 |
| Hall | C17×C79 ⋊ C3⋊D3 |
| Hall | C32×C17 ⋊ D79 |
| Sylow | C79 ⋊ C17×C3⋊D3 |
| Sylow | C32 ⋊ C17×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C3⋊D237 |
| commutator, cosocle, hypocenter | C32×C79 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C79 | C2 |
| LCS | G ▷ C32×C79 | |
| UCS | C1 ◁ C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12087 |
6069 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24174, 30);