Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6189 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#6189 |
| Sylow | C3×C9 ⋊ C4×Q8 |
240 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 240 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×#6189, #13138112, #13138113, … |
| maximal normal subgroup of | C8×#6189, #13138112, #13138113, … |
| maximal quotient of | C8×#6189, #13138115, #13138116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 935);