Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C3⋊D3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C36 |
| direct product | C7×C3⋊(C3⋊(C3⋊D3)) |
| unambiguous semidirect product | C3⋊(C7×C3⋊(C3⋊D3)) |
| Fitting, socle, Hall | C34×C7 ⋊ C2 |
| derived, Sylow | C34 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊(C3⋊(C3⋊D3)) |
| commutator, cosocle, hypocenter | C34 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C34×C7 | C2 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C7 | |
848 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 252);