Finite Group DatabasebetaFinite Group Databasebeta| order | 774 |
| isoclinism | isoclinic class of D43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D43⋊C9 |
| unambiguous semidirect product | (C43⋊C9)⋊C2 |
| derived, Sylow | C43 ⋊ C2×C9 |
| Hall | C43⋊C9 ⋊ C2 |
| Hall | D43 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D43⋊C3 |
| commutator, hypocenter | C43 | C2×C9 |
| Fitting, socle, cosocle | C3×C43 | C2×C3 |
| prime radical | C3×D43 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 387 |
Polycyclic presentation:
2,3^2,43|b^3=c,d^a=d^42,d^b=d^3639 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D43⋊C9, C5×D43⋊C9, C5⋊(D43⋊C9), … |
| maximal normal subgroup of | C2×D43⋊C9, C5×D43⋊C9, C17×D43⋊C9, … |
| maximal quotient of | Dic43⋊C9, C2×D43⋊C9, C5×D43⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(774, 1);