Finite Group DatabasebetaFinite Group Databasebeta| order | 1116 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D32×C31 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C31) |
| unambiguous semidirect product | (C3⋊D3)⋊(C2×C31) |
| Fitting, socle, Hall | C32×C31 ⋊ C22 |
| derived, Sylow | C32 ⋊ C22×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D32 |
| commutator, cosocle, hypocenter | C32 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C31 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C31 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 186 |
279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D32×C11×C31, D3×C31×D33, C31×(C3⋊D3)⋊D11, … |
| maximal normal subgroup of | D32×C11×C31, D32×C13×C31, D32×C17×C31, … |
| maximal quotient of | D32×C11×C31, D3×C31×D33, C31×(C3⋊D3)⋊D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1116, 35);