Finite Group DatabasebetaFinite Group Databasebeta| order | 1116 |
| isoclinism | isoclinic class of D93 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D93 |
| unambiguous semidirect product | (C2×C3)⋊(C3×D31) |
| Fitting, socle | C2×C32×C31 ⋊ C2 |
| derived | C3×C31 ⋊ C22×C3 |
| Hall | C32×C31 ⋊ C22 |
| Sylow | C31 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ C2×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D93 |
| commutator, cosocle, hypocenter | C3×C31 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C31 | C2 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C2×C3 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 372 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D93, C2×C3×D1023, C2×C3×C11×D93, … |
| maximal normal subgroup of | C2×C3×C11×D93, C2×C3×C13×D93, C2×C3×C17×D93, … |
| maximal quotient of | C3×D11×D93, C2×C3×D1023, C2×C3×C11×D93, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1116, 43);