Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D44 |
| unambiguous semidirect product | C4⋊(C11×D11) |
| Fitting | C4×C112 ⋊ C2 |
| Sylow | C112 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C11 | C2×D11 |
| commutator, cosocle | C2×C11 | C22×C11 |
| Frattini | C2 | C2×C11×D11 |
| Fitting | C4×C112 | C2 |
| socle | C2×C112 | C22 |
| hypercenter | C4×C11 | D11 |
| hypocenter | C11 | D4×C11 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C11 ◁ C4×C11 | |
47 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14515457, #14515458, #14515459, … |
| maximal normal subgroup of | #14515457, #14515458, #14515459, … |
| maximal quotient of | C11×#4314, C11×D88, C11×Dic44, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 24);