Finite Group DatabasebetaFinite Group Databasebeta| order | 30450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C29⋊#3874) |
| unambiguous semidirect product | C29⋊(C7⋊#3874) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C29×C52⋊C3 | C2 |
| Fitting, socle | C52×C7×C29 | D3 |
| LCS | G ▷ C7×C29×C52⋊C3 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3045 |
Polycyclic presentation:
2,3,7,29,5^2|b^a=b^2,c^a=c^6,d^a=d^28,f^a=f^4,e^b=e^2f^4,f^b=e^2f^21124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30450, 61);