Finite Group DatabasebetaFinite Group Databasebeta| order | 24747 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C113 · Schur multiplier (H2) = C1 |
| direct product | C113×C73⋊C3 |
| unambiguous semidirect product | C73⋊(C3×C113) |
| unambiguous semidirect product | (C73×C113)⋊C3 |
| Fitting, socle, Hall | C73×C113 ⋊ C3 |
| derived, Sylow | C73 ⋊ C3×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | C73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C3×C113 |
| Frattini | C1 | G |
| Fitting, socle | C73×C113 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C113 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8249 |
3051 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24747, 1);