Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C121⋊C8 |
| derived, Sylow | C121 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D121 |
| commutator, hypocenter | C121 | C8 |
| Frattini | C4×C11 | D11 |
| Fitting, cosocle | C4×C121 | C2 |
| socle, prime radical | C2×C11 | Dic11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 968 |
Polycyclic presentation:
2^3,11^2|a^2=b,b^2=c,d^11=e,d^a=d^10e^10,e^a=e^10248 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D121, #14515411, C2×C121⋊C8, … |
| maximal normal subgroup of | C8×D121, #14515411, C2×C121⋊C8, … |
| maximal quotient of | C121⋊C16, C2×C121⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 1);