Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×#272 |
| Fitting, derived | C7×H(3,𝔽3) ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×H(3,𝔽3) ⋊ C2 |
| Sylow | C7 ⋊ C3×#272 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊D3×ΓL(1,𝔽8) |
| commutator, Fitting, cosocle, hypocenter | C7×H(3,𝔽3) | C2×C3 |
| socle | C3×C7 | C3×C3⋊D3 |
| LCS | G ▷ C7×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 63 |
50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 177);