Finite Group DatabasebetaFinite Group Databasebeta| order | 1548 |
| isoclinism | isoclinic class of C3⋊(D43⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C43⋊C3)⋊C4) |
| unambiguous semidirect product | (C43⋊C3)⋊Dic3 |
| unambiguous semidirect product | Dic129⋊C3 |
| derived | C3×C43 ⋊ C3×C4 |
| Hall | C3×C43⋊C3 ⋊ C4 |
| Sylow | C43 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D43⋊C3) |
| commutator, hypocenter | C3×C43 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C43 | C2×C3 |
| prime radical | C2×C3×C43⋊C3 | C2 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 516 |
Polycyclic presentation:
2,3,2,3,43|a^2=c,d^a=d^2,e^a=e^42,e^b=e^660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1548, 18);