Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D841 |
| unambiguous semidirect product | (D7×C841)⋊C2 |
| unambiguous semidirect product | (C7×D841)⋊C2 |
| unambiguous semidirect product | D5887⋊C2 |
| Fitting, derived, Hall | C7×C841 ⋊ C22 |
| Sylow | C841 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D841 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C841 | C22 |
| Frattini | C29 | D7×D29 |
| socle | C7×C29 | C2×D29 |
| LCS | G ▷ C7×C841 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5887 |
2110 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 13);