Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of C3⋊D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic99 |
| unambiguous semidirect product | C9⋊Dic33 |
| unambiguous semidirect product | C11⋊(C3⋊Dic9) |
| derived, Hall | C3×C9×C11 ⋊ C4 |
| Sylow | C3×C9 ⋊ Dic11 |
| Sylow | C11 ⋊ C3⋊Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D99 |
| commutator, hypocenter | C3×C9×C11 | C4 |
| Frattini | C2×C3 | C3⋊D33 |
| Fitting, cosocle | C2×C3×C9×C11 | C2 |
| socle, prime radical | C2×C32×C11 | D3 |
| LCS | G ▷ C3×C9×C11 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1188 |
Polycyclic presentation:
2^2,3^2,11,3|a^2=b,d^3=f,c^a=c^2,d^a=d^2f^2,e^a=e^10,f^a=f^2300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 24);