Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D292 |
| Fitting, socle, Hall | C7×C292 ⋊ C22 |
| derived, Sylow | C292 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D292 |
| commutator, cosocle, hypocenter | C292 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C292 | C22 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C7 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 406 |
1792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 97);