Finite Group DatabasebetaFinite Group Databasebeta| order | 15652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D559 |
| unambiguous semidirect product | (C13×D7)⋊D43 |
| unambiguous semidirect product | (D7×C43)⋊D13 |
| Fitting, socle, derived, Hall | C7×C13×C43 ⋊ C22 |
| Hall | C13×C43 ⋊ C2×D7 |
| Hall | C7×C43 ⋊ C2×D13 |
| Hall | C7×C13 ⋊ C2×D43 |
| Sylow | C43 ⋊ D7×D13 |
| Sylow | C13 ⋊ D7×D43 |
| Sylow | C7 ⋊ C2×D559 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C43 | C22 |
| LCS | G ▷ C7×C13×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3913 |
1405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15652, 30);