Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×#3712 |
| Sylow | C33 ⋊ C2×M16 |
386 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590047, C3×#10590051, C3×#10590052, … |
| maximal normal subgroup of | C3×#10590047, C3×#10590051, C3×#10590052, … |
| maximal quotient of | C3×#10590296, C3×#10590260, C3×#10590297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3112);