Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C5×C37 ⋊ C4 |
| Hall | C32×C37 ⋊ AGL(1,𝔽5) |
| Hall | C5×C37 ⋊ #157 |
| Hall | C32×C5 ⋊ #3866 |
| Sylow | C37 ⋊ #4380 |
| Sylow | C32 ⋊ #10625191 |
| Sylow | C5 ⋊ #13050652 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C37 | C4 |
| LCS | G ▷ C32×C5×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,37|a^2=b,c^a=cd,d^a=cd^2,e^a=e^2,f^a=f^31,c^b=c^2,d^b=d^2,e^b=e^4,f^b=f^36420 conjugacy classes — view the full character table.
| maximal subgroup of | #45685917, C5×#20269165, #45686370, … |
| maximal normal subgroup of | C5×#20269165 |
| maximal quotient of | #45685917, C5×#20269165, #45686370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 162);