Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C33 |
| direct product | SD16×C3⋊(C3⋊D3) |
| Fitting | C33×SD16 ⋊ C2 |
| Sylow | C33 ⋊ C2×SD16 |
952 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×SD16×C3⋊D3, #13176734, #13176737, … |
| maximal normal subgroup of | D3×SD16×C3⋊D3, #13176734, #13176737, … |
| maximal quotient of | #13163398, #13163399, #13163400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3921);