Finite Group DatabasebetaFinite Group Databasebeta| order | 8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊#66524 |
| derived, Hall | C52×C37 ⋊ C9 |
| Sylow | C37 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ #66524 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C52⋊(C37⋊C3) |
| commutator, hypocenter | C52×C37 | C9 |
| Fitting, socle | C3×C52×C37 | C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C3 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
3,5^2,37,3|a^3=e,b^a=bc^2,c^a=bc^3,d^a=d^26933 conjugacy classes — view the full character table.
| maximal subgroup of | #30659244, (C5⋊D5)⋊#66524, #30659247, … |
| maximal normal subgroup of | #30659244, (C5⋊D5)⋊#66524, #30659247, … |
| maximal quotient of | C2×C52⋊#66524, C22⋊(C52⋊#66524) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8325, 9);