Finite Group DatabasebetaFinite Group Databasebeta| order | 32025 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13046197⋊C25 |
| derived, Hall | C7×C61 ⋊ C3×C25 |
| Hall | C7×C61⋊C25 ⋊ C3 |
| Hall | C61⋊C25 ⋊ ΓL(1,𝔽8) |
| Hall | #13046197 ⋊ C25 |
| Sylow | C61 ⋊ ΓL(1,𝔽8)×C25 |
| Sylow | C7 ⋊ (C61⋊C3)⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #13046197⋊C5 |
| commutator, hypocenter | C7×C61 | C3×C25 |
| Fitting, socle, cosocle | C5×C7×C61 | C3×C5 |
| prime radical | C5×#13046197 | C5 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10675 |
Polycyclic presentation:
3,5,7,61,5|b^5=e,c^a=c^2,d^a=d^47,d^b=d^9265 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32025, 9);