Finite Group DatabasebetaFinite Group Databasebeta| order | 30075 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×#23756635 |
| Fitting, socle, Hall | C3×C401 ⋊ C25 |
| derived, Sylow | C401 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #23756635 |
| commutator, hypocenter | C401 | C3×C25 |
| Frattini | C1 | G |
| Fitting, socle | C3×C401 | C25 |
| prime radical | C3×C401⋊C5 | C5 |
| cosocle | C401⋊C5 | C3×C5 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1203 |
123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30075, 4);