Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D121 |
| Fitting | C22×C121 ⋊ C2 |
| Sylow | C121 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D121 |
| commutator, cosocle | C2×C121 | C22 |
| Frattini, socle | C2×C11 | C2×D11 |
| Fitting | C22×C121 | C2 |
| hypercenter | C22 | D121 |
| hypocenter | C121 | D4 |
| LCS | G ▷ C2×C121 ▷ C121 | |
| UCS | C1 ◁ C2 ◁ C22 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 484 |
Polycyclic presentation:
2^3,11^2|d^11=e,b^a=bc,d^a=d^10e^10,e^a=e^10245 conjugacy classes — view the full character table.
| maximal subgroup of | #14515436, D4×D121, #14515438, … |
| maximal normal subgroup of | #14515436, D4×D121, #14515438, … |
| maximal quotient of | Dic121⋊C4, (C2×D121)⋊C4, #14515420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 7);