Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C3⋊D3×#217 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
928 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #13154848, #13154850, #13156974, … |
| maximal normal subgroup of | #13154848, #13154850, #13156974, … |
| maximal quotient of | #13160450, #13160475, #13160512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3587);