Finite Group DatabasebetaFinite Group Databasebeta| order | 5766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C312 ⋊ D3 |
| derived, Hall | #15668333 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | #15668333 | C2 |
| Fitting, socle | C312 | D3 |
| LCS | G ▷ #15668333 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,31^2|b^a=b^2,c^a=d,d^a=c,c^b=c^5,d^b=d^25208 conjugacy classes — view the full character table.
| maximal subgroup of | #19153449⋊C2, C2×#19153449, #19153449⋊C3, … |
| maximal normal subgroup of | #19153449⋊C2, C2×#19153449, #19153449⋊C3, … |
| maximal quotient of | #26040341, C2×#19153449, #31772350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5766, 15);