Finite Group DatabasebetaFinite Group Databasebeta| order | 30450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C29⋊(D7⋊(C52⋊C3)) |
| unambiguous semidirect product | D203⋊(C52⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C29 | C2×C3 |
| LCS | G ▷ C52×C7×C29 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3045 |
Polycyclic presentation:
2,3,5^2,7,29|e^a=e^6,f^a=f^28,c^b=c^4d^4,d^b=c,e^b=e^2901 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30450, 54);