Finite Group DatabasebetaFinite Group Databasebeta| order | 32025 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C61⋊C25 |
| unambiguous semidirect product | (C3×C61)⋊(C7×C25) |
| unambiguous semidirect product | (C3×C7×C61)⋊C25 |
| derived, Sylow | C61 ⋊ C3×C7×C25 |
| Hall | C3×C7×C61 ⋊ C25 |
| Hall | C7×C61 ⋊ C3×C25 |
| Hall | C3×C61 ⋊ C7×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C7 | C61⋊C5 |
| commutator, hypocenter | C61 | C3×C7×C25 |
| Frattini | C5 | C3×C7×C61⋊C5 |
| Fitting, socle, prime radical | C3×C5×C7×C61 | C5 |
| cosocle | C5×C61 | C3×C5×C7 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C5×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32025 |
1785 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32025, 2);