Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D121 |
| unambiguous semidirect product | C121⋊C23 |
| unambiguous semidirect product | (C2×C121)⋊C22 |
| Fitting | C22×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D121 |
| commutator, cosocle, hypocenter | C121 | C23 |
| Frattini | C11 | C22×D11 |
| Fitting | C22×C121 | C2 |
| socle | C22×C11 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C22 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 484 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D121)⋊C4, C2×C4×D121, C2×D484, … |
| maximal normal subgroup of | (C2×D121)⋊C4, C2×C4×D121, C2×D484, … |
| maximal quotient of | C2×Dic242, C2×C4×D121, C2×D484, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 11);