Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C3×#3757 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
1328 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 346 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589187, C3×#10589186, #13145690, … |
| maximal normal subgroup of | C3×#10589187, C3×#10589186, #13145690, … |
| maximal quotient of | C2×C3×#63657, C3×#10592906, C2×C3×#63658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3874);