Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic99 |
| unambiguous semidirect product | C11⋊(C3×Dic9) |
| derived | C9×C11 ⋊ C3×C4 |
| Hall | C3×C9×C11 ⋊ C4 |
| Sylow | C3×C9 ⋊ Dic11 |
| Sylow | C11 ⋊ C3×Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D99 |
| commutator, hypocenter | C9×C11 | C3×C4 |
| Frattini | C2×C3 | C3×D33 |
| Fitting | C2×C3×C9×C11 | C2 |
| socle, prime radical | C2×C32×C11 | D3 |
| cosocle | C2×C9×C11 | C2×C3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C2×C3 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| 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, 18);