Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of C3⋊(C3⋊D33) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C3⋊(C3⋊Dic33) |
| unambiguous semidirect product | C11⋊(C3⋊(C3⋊Dic3)) |
| derived, Hall | C33×C11 ⋊ C4 |
| Sylow | C33 ⋊ Dic11 |
| Sylow | C11 ⋊ C3⋊(C3⋊Dic3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊D33) |
| commutator, hypocenter | C33×C11 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C33×C11 | C2 |
| LCS | G ▷ C33×C11 | |
| UCS | C1 ◁ C2 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1188 |
Polycyclic presentation:
2^2,3^3,11|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^10300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 73);