Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#26044451 |
| Fitting, socle | C2×C292 ⋊ D7 |
| derived, Hall | #19154637 ⋊ C22 |
| Sylow | C292 ⋊ C2×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #26044451 |
| commutator, cosocle, hypocenter | #19154637 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C292 | D7 |
| LCS | G ▷ #19154637 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 116 |
214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 76);