Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×D841⋊C7 |
| unambiguous semidirect product | D841⋊(C2×C7) |
| unambiguous semidirect product | (C2×D841)⋊C7 |
| unambiguous semidirect product | (C841⋊C7)⋊C22 |
| unambiguous semidirect product | (C2×C841⋊C7)⋊C2 |
| Fitting | C2×C841 ⋊ C2×C7 |
| derived, Sylow | C841 ⋊ C22×C7 |
| Hall | C841⋊C7 ⋊ C22 |
| Hall | C2×D841 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D841⋊C7 |
| commutator, cosocle, hypocenter | C841 | C22×C7 |
| Frattini | C29 | C2×D29⋊C7 |
| Fitting | C2×C841 | C2×C7 |
| socle | C2×C29 | D29⋊C7 |
| LCS | G ▷ C841 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1682 |
148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 9);