Finite Group DatabasebetaFinite Group Databasebeta| order | 2709 |
| isoclinism | isoclinic class of (C43⋊C3)⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C43 ⋊ C3×C7 |
| derived, Sylow | C43 ⋊ C32×C7 |
| Hall | C3×C43⋊C3 ⋊ C7 |
| Hall | C43⋊C7 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C43⋊C3)⋊C7 |
| commutator, cosocle, hypocenter | C43 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C43 | C3×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 129 |
69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2709, 9);