Finite Group DatabasebetaFinite Group Databasebeta| order | 8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊#66526 |
| Fitting, socle, derived, Hall | C52×C37 ⋊ C9 |
| Sylow | C37 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ #66526 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C37 | C9 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,5^2,37|a^3=b,c^a=cd^2,d^a=cd^3,e^a=e^16,e^b=e^26133 conjugacy classes — view the full character table.
| maximal subgroup of | #30659271, (C5⋊D5)⋊#66526, #30659275, … |
| maximal normal subgroup of | #30659271, (C5⋊D5)⋊#66526, #30659275, … |
| maximal quotient of | C2×C52⋊#66526, C22⋊(C52⋊#66526) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8325, 12);