Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×#272 |
| Fitting, Hall | C3×C7×H(3,𝔽3) ⋊ C2 |
| derived | H(3,𝔽3) ⋊ C2×C3×C7 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C32×C7 | C3⋊D3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C3×C7 |
| Frattini | C3 | C3×C7×C3⋊D3 |
| Fitting | C3×C7×H(3,𝔽3) | C2 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C32×C7 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#92338, C3×ΓL(1,𝔽8)×#272, C3×D7×#272 |
| maximal normal subgroup of | C3×ΓL(1,𝔽8)×#272, C3×D7×#272 |
| maximal quotient of | C3×C7×#4183, C7×#92300, C7×#4183⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 218);