Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C37 ⋊ C2×C9 |
| Hall | C52⋊#66526 ⋊ C2 |
| Hall | C5⋊D185 ⋊ C9 |
| Sylow | C37 ⋊ (C5⋊D5)⋊C9 |
| Sylow | C52 ⋊ #66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C37 | C2×C9 |
| prime radical | C5⋊(C5⋊(D37⋊C3)) | C3 |
| cosocle | C52×C37⋊C3 | C2×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 555 |
Polycyclic presentation:
2,3^2,5^2,37|b^3=c,d^a=d^4,e^a=e^4,f^a=f^36,d^b=de,e^b=d^2e^3,f^b=f^9,f^c=f^2680 conjugacy classes — view the full character table.
| maximal subgroup of | #30659271⋊C2, #45686151, #45686152, … |
| maximal normal subgroup of | #30659271⋊C2, #45686151, #45686152, … |
| maximal quotient of | #45686081, C2×#30659271 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 73);