Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×C4⋊C4×D9 |
| Fitting | C3×C9×C4⋊C4 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×C4⋊C4 |
302 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 120 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 | #13137589, #13137591, #13137601, … |
| maximal normal subgroup of | #13137589, #13137591, #13137601, … |
| maximal quotient of | C3×#10588347, C3×#10588329, C3×#10588330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1412);