Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | (C37⋊C3)⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C5⋊(C5⋊(D37⋊C3)))⋊C3 |
| unambiguous semidirect product | #19149851⋊C3 |
| unambiguous semidirect product | #19149853⋊C3 |
| Fitting, socle, derived, Hall | C52×C37 ⋊ C2×C32 |
| Hall | C52⋊C3×C37⋊C3 ⋊ C2 |
| Hall | C5⋊D185 ⋊ C32 |
| Sylow | C37 ⋊ C3×(C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C3×D37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C37 | C2×C32 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 555 |
Polycyclic presentation:
2,3^2,5^2,37|d^a=d^4,e^a=e^4,f^a=f^36,f^b=f^26,d^c=de,e^c=d^2e^396 conjugacy classes — view the full character table.
| maximal subgroup of | (C5⋊D5)⋊C3×D37⋊C3, #26012846⋊C3, #26012816⋊C3, … |
| maximal normal subgroup of | (C5⋊D5)⋊C3×D37⋊C3, #26012846⋊C3, #26012816⋊C3, … |
| maximal quotient of | #26012784⋊C3, C2×(C37⋊C3)⋊((C5⋊D5)⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 75);