Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C11×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (C2×C3⋊D3)⋊(C3×C11) |
| unambiguous semidirect product | (C2×C11×C3⋊D3)⋊C3 |
| Fitting | C2×C11×H(3,𝔽3) ⋊ C2 |
| derived | C32 ⋊ C22×C3×C11 |
| Hall | C11×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C22×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | (C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | C32 | C22×C3×C11 |
| Frattini | C3 | C2×C3×D3×C11 |
| Fitting | C2×C11×H(3,𝔽3) | C2 |
| socle | C2×C3×C11 | C3×D3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C11 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 54);