Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C3 |
| direct product | C3×C11×#157 |
| Fitting, socle, Hall | C33×C11 ⋊ C4 |
| derived | C32 ⋊ C3×C4×C11 |
| Sylow | C33 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | #157 |
| commutator, hypocenter | C32 | C3×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C33×C11 | C4 |
| prime radical | C3×C11×C3⋊D3 | C2 |
| cosocle | C3⋊D3 | C2×C3×C11 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C3×C11 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 75);