Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#63831 |
| Sylow | C33 ⋊ #137 |
354 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | #13155936, #13155937, #13155944, … |
| maximal normal subgroup of | #13155936, #13155937, #13155944, … |
| maximal quotient of | C3×#10590272, C3×#10590276, C3×#10590301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3123);