Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D11×Dic11 |
| unambiguous semidirect product | (C11×D11)⋊C4 |
| derived, Sylow | C112 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D112 |
| commutator, hypocenter | C112 | C2×C4 |
| Fitting, socle, cosocle | C2×C112 | C22 |
| prime radical | C2×C11×D11 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2 | |
47 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | D11×Dic22, #14515524, #14515525, … |
| maximal normal subgroup of | D11×Dic22, #14515524, #14515525, … |
| maximal quotient of | D11×C11⋊C8, #14515455, Dic112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 17);