Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)×C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| direct product | ΓL(1,𝔽8)×C3⋊D9 |
| unambiguous semidirect product | C3⋊(D9×ΓL(1,𝔽8)) |
| Fitting, derived | C3×C7×C9 ⋊ C2×C3 |
| Hall | C3×C9×ΓL(1,𝔽8) ⋊ C2 |
| Sylow | C7 ⋊ C3×C3⋊D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C9 | C2×C3 |
| Frattini | C3 | C3⋊D3×ΓL(1,𝔽8) |
| socle | C32×C7 | C3×D3 |
| LCS | G ▷ C3×C7×C9 | |
| UCS | C1 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
75 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 172);