Finite Group DatabasebetaFinite Group Databasebeta| order | 24514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C7×D103⋊C17 |
| unambiguous semidirect product | D103⋊(C7×C17) |
| unambiguous semidirect product | (C7×D103)⋊C17 |
| unambiguous semidirect product | (C103⋊C17)⋊(C2×C7) |
| Fitting, socle, Hall | C7×C103 ⋊ C2×C17 |
| derived, Sylow | C103 ⋊ C2×C7×C17 |
| Hall | C7×C103⋊C17 ⋊ C2 |
| Hall | C103⋊C17 ⋊ C2×C7 |
| Hall | C7×D103 ⋊ C17 |
| Hall | D103 ⋊ C7×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D103⋊C17 |
| commutator, cosocle, hypocenter | C103 | C2×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C103 | C2×C17 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 721 |
259 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24514, 10);