Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C112 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D112 |
| commutator, Fitting, socle, cosocle | C2×C112 | C22 |
| hypocenter | C112 | D4 |
| LCS | G ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C2 | |
57 conjugacy classes of subgroups.
| transitive degree | μt(G) = 44 |
Polycyclic presentation:
2^3,11^2|b^2=c,b^a=bc,e^a=e^10,d^b=d^1095 conjugacy classes — view the full character table.
| maximal subgroup of | #14515525, #14515527, #14515528, … |
| maximal normal subgroup of | #14515525, #14515527, #14515528, … |
| maximal quotient of | #14515458, #14515460, #14515461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 20);