Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | Q16×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (Q16×C3⋊D3)⋊C3 |
| Fitting | Q16×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×Q16 |
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #13139283, #13139285, #13139287, … |
| maximal normal subgroup of | #13139283, #13139285, #13139287, … |
| maximal quotient of | #10592491⋊C3, #10592492⋊C3, #10592494⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1530);