Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| unambiguous semidirect product | C22⋊(C11⋊D11) |
| Fitting | C22×C112 ⋊ C2 |
| Sylow | C112 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C11⋊D11 |
| commutator, socle, cosocle | C2×C112 | C22 |
| Fitting | C22×C112 | C2 |
| hypercenter | C22 | C11⋊D11 |
| hypocenter | C112 | D4 |
| LCS | G ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C2 ◁ C22 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 484 |
Polycyclic presentation:
2^3,11^2|b^a=bc,d^a=d^10,e^a=e^10245 conjugacy classes — view the full character table.
| maximal subgroup of | #14515533, D11×C22⋊D11, #14515554, … |
| maximal normal subgroup of | #14515533, D11×C22⋊D11, #14515554, … |
| maximal quotient of | #14515493, #14515495, #14515496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 31);