Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D99 |
| unambiguous semidirect product | (C2×C11)⋊(C3×D9) |
| Fitting | C2×C3×C9×C11 ⋊ C2 |
| derived | C9×C11 ⋊ C22×C3 |
| Hall | C3×C9×C11 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C3×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D99 |
| commutator, cosocle, hypocenter | C9×C11 | C22×C3 |
| Frattini | C3 | C2×C3×D33 |
| Fitting | C2×C3×C9×C11 | C2 |
| socle | C2×C32×C11 | D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C2×C3 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 56);