Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of SU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×SU(3,𝔽2) |
| Fitting | C4×H(3,𝔽3) ⋊ Q8 |
| Sylow | H(3,𝔽3) ⋊ C4×Q8 |
121 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | SU(3,𝔽2)⋊C8, C8×SU(3,𝔽2), #13146710, … |
| maximal normal subgroup of | SU(3,𝔽2)⋊C8, C8×SU(3,𝔽2), #13146710, … |
| maximal quotient of | C8×SU(3,𝔽2), #13146710, C4×#88592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2285);