Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C9⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C9 |
| direct product | C7×C9⋊D9 |
| unambiguous semidirect product | C9⋊(C7×D9) |
| Fitting, Hall | C7×C92 ⋊ C2 |
| derived, Sylow | C92 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C9⋊D9 |
| commutator, cosocle, hypocenter | C92 | C2×C7 |
| Frattini | C32 | C7×C3⋊D3 |
| Fitting | C7×C92 | C2 |
| socle | C32×C7 | C3⋊D3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C7 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#92314, ΓL(1,𝔽8)×C9⋊D9, #72229838, … |
| maximal normal subgroup of | C7×#92314, ΓL(1,𝔽8)×C9⋊D9, #72229838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 114);