Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of D63 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D63 |
| Fitting, Hall | C7×C92 ⋊ C2 |
| derived | C7×C9 ⋊ C2×C9 |
| Sylow | C92 ⋊ D7 |
| Sylow | C7 ⋊ C9×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D63 |
| commutator, hypocenter | C7×C9 | C2×C9 |
| Frattini | C32 | C3×D21 |
| Fitting | C7×C92 | C2 |
| socle | C32×C7 | C3×D3 |
| prime radical | C3×D63 | C3 |
| cosocle | C3×C7×C9 | C2×C3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C9 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72229930, C9×ΓL(1,𝔽8)⋊D9, #72229948, … |
| maximal normal subgroup of | #72229930, C9×ΓL(1,𝔽8)⋊D9, #72229948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 101);