Finite Group DatabasebetaFinite Group Databasebeta| order | 24706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C1123⋊C11 |
| unambiguous semidirect product | (C2×C1123)⋊C11 |
| Fitting, socle, Hall | C2×C1123 ⋊ C11 |
| derived, Sylow | C1123 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C1123⋊C11 |
| commutator, cosocle, hypocenter | C1123 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1123 | C11 |
| LCS | G ▷ C1123 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2246 |
226 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24706, 2);