Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C22×C11×D11 |
| unambiguous semidirect product | C11⋊(C23×C11) |
| unambiguous semidirect product | (C2×C11)⋊(C22×C11) |
| Fitting, socle | C22×C112 ⋊ C2 |
| derived | C11 ⋊ C23×C11 |
| Sylow | C112 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C11 | D11 |
| commutator, cosocle, hypocenter | C11 | C23×C11 |
| Frattini | C1 | G |
| Fitting, socle | C22×C112 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C22×C11 | |
89 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 40);