Finite Group DatabasebetaFinite Group Databasebeta| order | 18270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C9⋊(D29⋊C7)) |
| unambiguous semidirect product | C9⋊(C5⋊(D29⋊C7)) |
| unambiguous semidirect product | (C29⋊C7)⋊D45 |
| unambiguous semidirect product | D1305⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C29 | C2×C7 |
| Frattini | C3 | C3⋊(C5⋊(D29⋊C7)) |
| socle | C3×C5×C29 | D3×C7 |
| LCS | G ▷ C5×C9×C29 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1305 |
Polycyclic presentation:
2,3,5,7,29,3|b^3=f^2,b^a=b^2f,c^a=c^4,e^a=e^28,f^a=f^2,e^d=e^16258 conjugacy classes — view the full character table.
| maximal subgroup of | D45×D29⋊C7, D5×C9⋊(D29⋊C7), D9×C5⋊(D29⋊C7), … |
| maximal normal subgroup of | D45×D29⋊C7, D5×C9⋊(D29⋊C7), D9×C5⋊(D29⋊C7), … |
| maximal quotient of | C9⋊(Dic145⋊C7), C2×C5⋊(C9⋊(D29⋊C7)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18270, 25);