Finite Group DatabasebetaFinite Group Databasebeta| order | 30450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D75×C29⋊C7 |
| unambiguous semidirect product | C3⋊(D25×C29⋊C7) |
| unambiguous semidirect product | C25⋊(D3×C29⋊C7) |
| unambiguous semidirect product | (C29×D75)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C25×C29 | C2×C7 |
| Frattini | C5 | D15×C29⋊C7 |
| socle | C3×C5×C29 | C7×D5 |
| LCS | G ▷ C3×C25×C29 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2175 |
429 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30450, 24);