Finite Group DatabasebetaFinite Group Databasebeta| order | 24563 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×C29⋊C7 |
| unambiguous semidirect product | C29⋊(C7×C121) |
| unambiguous semidirect product | (C29×C121)⋊C7 |
| Fitting, Hall | C29×C121 ⋊ C7 |
| derived, Sylow | C29 ⋊ C7×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | C29⋊C7 |
| commutator, hypocenter | C29 | C7×C121 |
| Frattini | C11 | C11×C29⋊C7 |
| Fitting | C29×C121 | C7 |
| socle, cosocle | C11×C29 | C7×C11 |
| prime radical | C11×C29⋊C7 | C11 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C121 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3509 |
1331 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24563, 2);