Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C4×C11×D11 |
| Fitting | C4×C112 ⋊ C2 |
| derived | C11 ⋊ C2×C4×C11 |
| Sylow | C112 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C11 | D11 |
| commutator, hypocenter | C11 | C2×C4×C11 |
| Frattini | C2 | C2×C11×D11 |
| Fitting | C4×C112 | C2 |
| socle | C2×C112 | C22 |
| prime radical | C2×C11×D11 | C2 |
| cosocle | C2×C11 | C22×C11 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C4×C11 | |
47 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×C11⋊C8, #14515455, C8×C11×D11, … |
| maximal normal subgroup of | D11×C11⋊C8, #14515455, C8×C11×D11, … |
| maximal quotient of | C8×C11×D11, C11×#4313, C4×C11×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 23);