Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of D11×D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D27 |
| unambiguous semidirect product | (C11×D27)⋊C2 |
| unambiguous semidirect product | (D11×C27)⋊C2 |
| unambiguous semidirect product | D297⋊C2 |
| Fitting, derived, Hall | C11×C27 ⋊ C22 |
| Sylow | C27 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C27 | C22 |
| Frattini | C9 | D3×D11 |
| socle | C3×C11 | C2×D9 |
| LCS | G ▷ C11×C27 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 297 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 5);