Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #3744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#63645 |
| Sylow | C33 ⋊ #107 |
304 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 304 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) = 288 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589115, C3×#10589118, C3×#10589139, … |
| maximal normal subgroup of | C3×#10589115, C3×#10589118, C3×#10589139, … |
| maximal quotient of | C3×#10589324, C3×#10589371, C3×#10589370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2114);