Finite Group DatabasebetaFinite Group Databasebeta| order | 5766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C312 ⋊ C2×C3 |
| Hall | #15668333 ⋊ C2 |
| Hall | C31×D31 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C312 | C2×C3 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
21 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,31^2|c^a=c^30,c^b=c^5,d^b=d^25181 conjugacy classes — view the full character table.
| maximal subgroup of | #19153446⋊C2, C2×#19153446, C31⋊C3×D31⋊C3, … |
| maximal normal subgroup of | #19153446⋊C2, C2×#19153446, C31⋊C3×D31⋊C3, … |
| maximal quotient of | #26040338, C2×#19153446, #31772347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5766, 12);