Finite Group DatabasebetaFinite Group Databasebeta| order | 24378 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×D239⋊C17 |
| unambiguous semidirect product | D239⋊(C3×C17) |
| unambiguous semidirect product | (C3×D239)⋊C17 |
| unambiguous semidirect product | (C239⋊C17)⋊(C2×C3) |
| Fitting, socle, Hall | C3×C239 ⋊ C2×C17 |
| derived, Sylow | C239 ⋊ C2×C3×C17 |
| Hall | C3×C239⋊C17 ⋊ C2 |
| Hall | C239⋊C17 ⋊ C2×C3 |
| Hall | C3×D239 ⋊ C17 |
| Hall | D239 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D239⋊C17 |
| commutator, cosocle, hypocenter | C239 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C239 | C2×C17 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 717 |
123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24378, 10);