Finite Group DatabasebetaFinite Group Databasebeta| order | 15796 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×D359 |
| unambiguous semidirect product | C359⋊(C22×C11) |
| unambiguous semidirect product | (C2×C359)⋊(C2×C11) |
| Fitting, socle | C2×C11×C359 ⋊ C2 |
| derived, Sylow | C359 ⋊ C22×C11 |
| Hall | C11×C359 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D359 |
| commutator, cosocle, hypocenter | C359 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C359 | C2 |
| LCS | G ▷ C359 | |
| UCS | C1 ◁ C2×C11 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7898 |
3982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15796, 9);