Finite Group DatabasebetaFinite Group Databasebeta| order | 9030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C5⋊(D43⋊C7)) |
| unambiguous semidirect product | C5⋊(C3⋊(D43⋊C7)) |
| unambiguous semidirect product | (C43⋊C7)⋊D15 |
| unambiguous semidirect product | D645⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C43 | C2×C7 |
| LCS | G ▷ C3×C5×C43 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,43|b^a=b^2,c^a=c^4,e^a=e^42,e^d=e^41108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9030, 29);