Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of C11⋊#1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C11⋊#1113 |
| Fitting, socle, derived, Hall | C33×C11 ⋊ C22 |
| Sylow | C33 ⋊ C2×D11 |
| Sylow | C11 ⋊ #1113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C11 | C22 |
| LCS | G ▷ C33×C11 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
Polycyclic presentation:
2^2,3^3,11|c^a=c^2,d^a=d^2,f^a=f^10,c^b=c^2,e^b=e^2105 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1113, D32×D33, D3×(C3⋊D3)⋊D11, … |
| maximal normal subgroup of | D11×#1113, D32×D33, D3×(C3⋊D3)⋊D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 90);