Finite Group DatabasebetaFinite Group Databasebeta| order | 7625 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C25×C61 ⋊ C5 |
| Sylow | C61 ⋊ 5−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C5×C61⋊C5 |
| commutator, socle | C5×C61 | C52 |
| Fitting | C25×C61 | C5 |
| hypercenter | C25 | C61⋊C5 |
| hypocenter | C61 | 5−1+2 |
| LCS | G ▷ C5×C61 ▷ C61 | |
| UCS | C1 ◁ C5 ◁ C25 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
5^3,61|a^5=c,b^a=bc,d^b=d^9329 conjugacy classes — view the full character table.
| maximal subgroup of | 5−1+2×C61⋊C5, C5×#21439342, #49185687, … |
| maximal normal subgroup of | 5−1+2×C61⋊C5, C5×#21439342, #49185687, … |
| maximal quotient of | (C5×C61⋊C5)⋊C25, (C61⋊C25)⋊C25, #49185654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7625, 10);