Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6189 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#6194 |
| Sylow | C3×C9 ⋊ C4×D4 |
312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#6194, #13138440, #13138441, … |
| maximal normal subgroup of | C8×#6194, #13138440, #13138441, … |
| maximal quotient of | C4×#88421, #13137222, C4×#88423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 994);