Finite Group DatabasebetaFinite Group Databasebeta| order | 23534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D287 |
| unambiguous semidirect product | C7⋊(C41×D41) |
| unambiguous semidirect product | C41⋊(D7×C41) |
| Fitting, socle, Hall | C7×C412 ⋊ C2 |
| derived | C7×C41 ⋊ C2×C41 |
| Sylow | C412 ⋊ D7 |
| Sylow | C7 ⋊ C41×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D287 |
| commutator, cosocle, hypocenter | C7×C41 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C7×C412 | C2 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 ◁ C41 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 574 |
5945 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23534, 12);