Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#63659 |
| Sylow | C33 ⋊ #102 |
516 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#832, C3×#10591413, C3×#10591414, … |
| maximal normal subgroup of | C3×D3×#832, C3×#10591413, C3×#10591414, … |
| maximal quotient of | C3×#10589395, C3×D4⋊(C3⋊(C3⋊C8)), C3×#10589403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2128);