Finite Group DatabasebetaFinite Group Databasebeta| order | 15596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D557 |
| unambiguous semidirect product | C557⋊(C22×C7) |
| unambiguous semidirect product | (C2×C557)⋊(C2×C7) |
| Fitting, socle | C2×C7×C557 ⋊ C2 |
| derived, Sylow | C557 ⋊ C22×C7 |
| Hall | C7×C557 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D557 |
| commutator, cosocle, hypocenter | C557 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C557 | C2 |
| LCS | G ▷ C557 | |
| UCS | C1 ◁ C2×C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7798 |
3920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15596, 11);