Finite Group DatabasebetaFinite Group Databasebeta| order | 24521 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C113⋊C7 |
| unambiguous semidirect product | C113⋊(C7×C31) |
| unambiguous semidirect product | (C31×C113)⋊C7 |
| Fitting, socle, Hall | C31×C113 ⋊ C7 |
| derived, Sylow | C113 ⋊ C7×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C113⋊C7 |
| commutator, cosocle, hypocenter | C113 | C7×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C113 | C7 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3503 |
713 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24521, 1);