Finite Group DatabasebetaFinite Group Databasebeta| order | 15652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic43⋊C7 |
| unambiguous semidirect product | Dic43⋊(C7×C13) |
| unambiguous semidirect product | (C43⋊C7)⋊(C4×C13) |
| unambiguous semidirect product | (C13×Dic43)⋊C7 |
| derived, Sylow | C43 ⋊ C4×C7×C13 |
| Hall | C13×C43⋊C7 ⋊ C4 |
| Hall | C13×Dic43 ⋊ C7 |
| Hall | C13×C43 ⋊ C4×C7 |
| Hall | C43⋊C7 ⋊ C4×C13 |
| Hall | Dic43 ⋊ C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D43⋊C7 |
| commutator, hypocenter | C43 | C4×C7×C13 |
| Frattini | C2 | C13×D43⋊C7 |
| Fitting, socle | C2×C13×C43 | C2×C7 |
| prime radical | C2×C13×C43⋊C7 | C2 |
| cosocle | C2×C43 | C2×C7×C13 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2236 |
442 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15652, 10);