Finite Group DatabasebetaFinite Group Databasebeta| order | 7625 |
| automorphism | ? |
| homology | Abelianization (H1) = C125 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C61⋊C125 |
| derived, Sylow | C61 ⋊ C125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C25 | C61⋊C5 |
| commutator, hypocenter | C61 | C125 |
| Fitting | C25×C61 | C5 |
| socle | C5×C61 | C25 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C25 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
5^3,61|a^5=b,b^5=c,d^a=d^9425 conjugacy classes — view the full character table.
| maximal subgroup of | C125×C61⋊C5, C5×C61⋊C125, #49185657, … |
| maximal normal subgroup of | C125×C61⋊C5, C5×C61⋊C125, #49185657, … |
| maximal quotient of | C61⋊C625, C5×C61⋊C125 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7625, 6);