Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C29 · Schur multiplier (H2) = C2 |
| direct product | C22×C29×C29⋊C7 |
| unambiguous semidirect product | (C22×C29)⋊(C7×C29) |
| Fitting, socle, Hall | C22×C292 ⋊ C7 |
| derived | C29 ⋊ C22×C7×C29 |
| Sylow | C292 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C29 | C29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C22×C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C22×C292 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C22×C29 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 812 |
1276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 90);