Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C32 |
| direct product | C32×C7×C3⋊D3 |
| unambiguous semidirect product | C3⋊(C32×D3×C7) |
| Fitting, socle, Hall | C34×C7 ⋊ C2 |
| derived | C32 ⋊ C2×C32×C7 |
| Sylow | C34 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C34×C7 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C32×C7 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#92338, C3×C7×#4183, C7×#92300, … |
| maximal normal subgroup of | C32×C3⋊D3×ΓL(1,𝔽8), C32×D7×C3⋊D3 |
| maximal quotient of | C7×#4207⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 248);