Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of (C3⋊D9)⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D9)⋊D11 |
| unambiguous semidirect product | D33⋊D9 |
| unambiguous semidirect product | D99⋊D3 |
| Fitting, derived, Hall | C3×C9×C11 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×D11 |
| Sylow | C11 ⋊ D3×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C9×C11 | C22 |
| Frattini | C3 | (C3⋊D3)⋊D11 |
| socle | C32×C11 | C2×D3 |
| LCS | G ▷ C3×C9×C11 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 198 |
Polycyclic presentation:
2^2,3^2,11,3|d^3=f^2,c^a=c^2,e^a=e^10,c^b=c^2,d^b=d^2f,f^b=f^293 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 42);