Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3×Q8×C3⋊D3 |
| Fitting | C2×C33×Q8 ⋊ C2 |
| Sylow | C33 ⋊ C22×Q8 |
1088 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 1088 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) = 288 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10591552, C3×#10591562, C3×#10591592, … |
| maximal normal subgroup of | C3×#10591552, C3×#10591562, C3×#10591592, … |
| maximal quotient of | C2×C3×#64096, C2×C3×#64105, C2×C3×#64097, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4632);