Finite Group DatabasebetaFinite Group Databasebeta| order | 1116 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D31 |
| Fitting | C2×C9×C31 ⋊ C2 |
| derived, Sylow | C31 ⋊ C22×C9 |
| Hall | C9×C31 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D31 |
| commutator, hypocenter | C31 | C22×C9 |
| Frattini | C3 | C2×C3×D31 |
| Fitting | C2×C9×C31 | C2 |
| socle | C2×C3×C31 | C2×C3 |
| prime radical | C2×C3×D31 | C3 |
| cosocle | C3×C31 | C22×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C9 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 558 |
306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D11×D31, C2×C9×C11×D31, C2×C9×D341, … |
| maximal normal subgroup of | C2×C9×C11×D31, C2×C9×C13×D31, C2×C9×C17×D31, … |
| maximal quotient of | C9×D11×D31, C2×C9×C11×D31, C2×C9×D341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1116, 12);