Finite Group DatabasebetaFinite Group Databasebeta| order | 30450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C29⋊C7)⋊#3874 |
| unambiguous semidirect product | (C29⋊#3874)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C29×C52⋊C3 | C2×C7 |
| Fitting, socle | C52×C29 | D3×C7 |
| LCS | G ▷ C29×C52⋊C3 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 435 |
Polycyclic presentation:
2,7,3,29,5^2|c^a=c^2,d^a=d^28,e^a=ef^2,f^a=f^4,d^b=d^16,e^c=e^3f^3,f^c=e^4f113 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30450, 35);