Finite Group DatabasebetaFinite Group Databasebeta| order | 32025 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊#13046197 |
| Fitting, socle, derived, Hall | C52×C7×C61 ⋊ C3 |
| Hall | C52×C61 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C61 ⋊ C52⋊C3 |
| Hall | C52×C7 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ C7⋊(C52⋊C3) |
| Sylow | C52 ⋊ #13046197 |
| Sylow | C7 ⋊ C52⋊(C61⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C61 | C3 |
| LCS | G ▷ C52×C7×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6405 |
Polycyclic presentation:
3,5^2,7,61|b^a=bc,c^a=b^2c^3,d^a=d^2,e^a=e^473561 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32025, 21);