Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#63664 |
| Sylow | C33 ⋊ #104 |
424 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 114 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×#837, C3×#10591670, C3×#10591673, … |
| maximal normal subgroup of | C3×D3×#837, C3×#10591670, C3×#10591673, … |
| maximal quotient of | C3×#10589398, C3×D4⋊(C3⋊(C3⋊C8)), C3×#10589401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2133);