Finite Group DatabasebetaFinite Group Databasebeta| order | 6651 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C739 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C739⋊C3 |
| commutator, hypocenter | C739 | C9 |
| Fitting, socle | C3×C739 | C3 |
| LCS | G ▷ C739 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,739|a^3=b,c^a=c^320747 conjugacy classes — view the full character table.
| maximal subgroup of | #20268985⋊C2, C2×#20268985, C9×C739⋊C3, … |
| maximal normal subgroup of | #20268985⋊C2, C2×#20268985, C9×C739⋊C3, … |
| maximal quotient of | C2×#20268985, #34093132, C3×#20268985, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6651, 1);