Finite Group DatabasebetaFinite Group Databasebeta| order | 8325 |
| isoclinism | isoclinic class of #66526 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#66526 |
| Fitting, Hall | C25×C37 ⋊ C9 |
| derived, Sylow | C37 ⋊ C9×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #66526 |
| commutator, hypocenter | C37 | C9×C25 |
| Frattini | C5 | C5×#66526 |
| Fitting | C25×C37 | C9 |
| socle | C5×C37 | C5×C9 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C25 | |
18 conjugacy classes of subgroups.
325 conjugacy classes — view the full character table.
| maximal subgroup of | C25×#66526⋊C2, C25⋊(#66526⋊C2), D25×#66526, … |
| maximal normal subgroup of | C25×#66526⋊C2, C25⋊(#66526⋊C2), D25×#66526, … |
| maximal quotient of | C2×C25×#66526, C25×C22⋊#66526 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8325, 4);