Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of SU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#88592 |
| Sylow | H(3,𝔽3) ⋊ C2×C4⋊C4 |
170 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #13146183, C4×#88592, #13146727, … |
| maximal normal subgroup of | #13146183, C4×#88592, #13146727, … |
| maximal quotient of | #13146716, C2×#11720708, #13146718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2287);