Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C3×#638 |
| Fitting | C24×C33 ⋊ C2 |
| Sylow | C33 ⋊ C22×D4 |
1952 conjugacy classes of subgroups; only the 426 normal subgroups are shown.
This group has 1952 conjugacy classes of subgroups — too many to draw. Only its 426 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 | C2×C3×#63581, C3×#10591711, C3×#10591704, … |
| maximal normal subgroup of | C2×C3×#63581, C3×#10591711, C3×#10591704, … |
| maximal quotient of | C22×C3×#3750, C2×C3×#64133, C22×C3×#3752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4639);