Finite Group DatabasebetaFinite Group Databasebeta| order | 30450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D609 |
| unambiguous semidirect product | C3⋊(C25×D203) |
| unambiguous semidirect product | C7⋊(C25×D87) |
| unambiguous semidirect product | C29⋊(C25×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D609 |
| commutator, hypocenter | C3×C7×C29 | C2×C25 |
| Frattini | C5 | C5×D609 |
| Fitting | C3×C7×C25×C29 | C2 |
| socle, cosocle | C3×C5×C7×C29 | C2×C5 |
| prime radical | C5×D609 | C5 |
| LCS | G ▷ C3×C7×C29 | |
| UCS | C1 ◁ C25 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15225 |
7650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30450, 14);