Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of #4174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#4174 |
| Fitting, Hall | C7×AΣL(1,𝔽27) ⋊ C2 |
| derived | H(3,𝔽3) ⋊ C2×C3×C7 |
| Sylow | AΣL(1,𝔽27) ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3×C7 | (C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C3×C7 |
| Frattini | C32 | C3×D3×C7 |
| Fitting | C7×AΣL(1,𝔽27) | C2 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C3×C7 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 63 |
154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 95);