Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C3⋊(C3⋊AGL(1,𝔽7)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| direct product | C3×C3⋊(C3⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | C3⋊(C3×C3⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3×C3⋊D3) |
| Fitting, socle | C33×C7 ⋊ C2×C3 |
| derived | C32×C7 ⋊ C2×C32 |
| Hall | C33×ΓL(1,𝔽8) ⋊ C2 |
| Sylow | C7 ⋊ C32×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C3⋊AGL(1,𝔽7)) |
| commutator, cosocle, hypocenter | C32×C7 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C33×C7 | C2×C3 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C3 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 241);