Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#63918 |
| Sylow | C33 ⋊ C4⋊Q8 |
370 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 370 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) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13156266, #13156267, #13156270, … |
| maximal normal subgroup of | #13156266, #13156267, #13156270, … |
| maximal quotient of | C3×#10590871, C3×#10590873, C3×#10590889, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3210);