Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| isoclinism | isoclinic class of SU(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C1 |
| special unitary | SU(3,𝔽3) |
| projective special unitary | PSU(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Permutation generators:
(2,4)(3,6)(5,9)(7,12)(8,13)(10,17)(14,19)(15,20)(16,21)(18,24)(22,26)(23,27);(1,2,5,10,7,3)(4,8,14,12,11,6)(9,15,19,21,22,16)(13,17,23,28,25,18)(24,26,27)14 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SU(3,𝔽3) |
| maximal normal subgroup of | C2×SU(3,𝔽3) |
| maximal quotient of | C2×SU(3,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((2,4)(3,6)(5,9)(7,12)(8,13)(10,17)(14,19)(15,20)(16,21)(18,24)(22,26)(23,27), (1,2,5,10,7,3)(4,8,14,12,11,6)(9,15,19,21,22,16)(13,17,23,28,25,18)(24,26,27));