Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of #11757263 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C11 |
No aliases for this group.
| Fitting, socle, Sylow | C112 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, prime radical, cosocle | C11⋊D11 | C22 |
| Fitting, socle, hypocenter | C112 | Q8 |
| LCS | G ▷ C11⋊D11 ▷ C112 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 44 |
Polycyclic presentation:
2^3,11^2|a^2=c,b^2=c,b^a=bc,d^a=d^5e^7,e^a=de^6,d^b=d^9e^4,e^b=d^7e^2,d^c=d^10,e^c=e^1020 conjugacy classes — view the full character table.
| maximal subgroup of | #11757261⋊C2, C2×#11757263, #72209674, … |
| maximal normal subgroup of | #11757261⋊C2, C2×#11757263, #72209674, … |
| maximal quotient of | #14515515, C2×#11757263 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 37);