Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of #92150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C11 |
| direct product | C2×#92150 |
| Fitting, socle | C2×C112 ⋊ C4 |
| derived, Sylow | C112 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92150 |
| commutator, hypocenter | C112 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112 | C4 |
| prime radical | C2×C11⋊D11 | C2 |
| cosocle | C11⋊D11 | C22 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 44 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | D112⋊C4, #14515511, #14515515, … |
| maximal normal subgroup of | D112⋊C4, #14515511, #14515515, … |
| maximal quotient of | #14515516, #14515517, C4×#92150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 38);