Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C3⋊D63 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊D63 |
| unambiguous semidirect product | C3⋊(C3×D63) |
| Fitting, Hall | C32×C7×C9 ⋊ C2 |
| derived | C3×C7×C9 ⋊ C2×C3 |
| Sylow | C32×C9 ⋊ D7 |
| Sylow | C7 ⋊ C3×C3⋊D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊D63 |
| commutator, cosocle, hypocenter | C3×C7×C9 | C2×C3 |
| Frattini | C3 | C3×C3⋊D21 |
| Fitting | C32×C7×C9 | C2 |
| socle | C33×C7 | D3 |
| LCS | G ▷ C3×C7×C9 | |
| UCS | C1 ◁ C3 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 378 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 222);