Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of C3⋊D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊Dic33 |
| unambiguous semidirect product | C3⋊(C3×Dic33) |
| unambiguous semidirect product | C11⋊(C3×C3⋊Dic3) |
| derived | C32×C11 ⋊ C3×C4 |
| Hall | C33×C11 ⋊ C4 |
| Sylow | C33 ⋊ Dic11 |
| Sylow | C11 ⋊ C3×C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊D33 |
| commutator, hypocenter | C32×C11 | C3×C4 |
| Frattini | C2 | C3×C3⋊D33 |
| Fitting, socle, prime radical | C2×C33×C11 | C2 |
| cosocle | C2×C32×C11 | C2×C3 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C2×C3 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 71);