Finite Group DatabasebetaFinite Group Databasebeta| order | 1116 |
| isoclinism | isoclinic class of D9×D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D31 |
| unambiguous semidirect product | (D9×C31)⋊C2 |
| unambiguous semidirect product | (C9×D31)⋊C2 |
| unambiguous semidirect product | D279⋊C2 |
| Fitting, derived, Hall | C9×C31 ⋊ C22 |
| Sylow | C31 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C31 | C22 |
| Frattini | C3 | D3×D31 |
| socle | C3×C31 | C2×D3 |
| LCS | G ▷ C9×C31 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 279 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C11×D9×D31, D31×D99, D9×D341, … |
| maximal normal subgroup of | C11×D9×D31, C13×D9×D31, C17×D9×D31, … |
| maximal quotient of | C11×D9×D31, D31×D99, D9×D341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1116, 8);