Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D112 |
| unambiguous semidirect product | (C11×D11)⋊C22 |
| unambiguous semidirect product | (C11⋊D11)⋊C22 |
| Fitting, socle | C2×C112 ⋊ C22 |
| derived, Sylow | C112 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D112 |
| commutator, cosocle, hypocenter | C112 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112 | C22 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2 | |
89 conjugacy classes of subgroups.
| transitive degree | μt(G) = 44 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | D112⋊C4, C4×D112, D11×D44, … |
| maximal normal subgroup of | D112⋊C4, C4×D112, D11×D44, … |
| maximal quotient of | D11×Dic22, #14515524, #14515525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 39);