Finite Group DatabasebetaFinite Group Databasebeta| order | 6651 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C739 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C739 | C9 |
| LCS | G ▷ C739 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,739|a^3=b,c^a=c^381,c^b=c^32091 conjugacy classes — view the full character table.
| maximal subgroup of | #20268987⋊C2, C2×#20268987, C3×#20268987, … |
| maximal normal subgroup of | #20268987⋊C2, C2×#20268987, C3×#20268987, … |
| maximal quotient of | C2×#20268987, #34093140, C3×#20268987, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6651, 3);