Finite Group DatabasebetaFinite Group Databasebeta| order | 7625 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C25 · Schur multiplier (H2) = C5 |
| direct product | C5×C61⋊C25 |
| unambiguous semidirect product | (C5×C61)⋊C25 |
| derived, Sylow | C61 ⋊ C5×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C61⋊C5 |
| commutator, hypocenter | C61 | C5×C25 |
| Frattini | C5 | C5×C61⋊C5 |
| Fitting, socle | C52×C61 | C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C52 | |
28 conjugacy classes of subgroups.
425 conjugacy classes — view the full character table.
| maximal subgroup of | C25×C61⋊C25, (C5×C61⋊C5)⋊C25, C52⋊(C61⋊C25), … |
| maximal normal subgroup of | C25×C61⋊C25, (C5×C61⋊C5)⋊C25, C52⋊(C61⋊C25), … |
| maximal quotient of | C25×C61⋊C25, C52⋊(C61⋊C25), #49185651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7625, 8);