Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×((C3⋊D3)⋊C3)⋊C2 |
| Fitting | Q8×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C22×Q8 |
584 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
55 conjugacy classes — view the full character table.
| maximal subgroup of | #13146654, #13146656, SD16×((C3⋊D3)⋊C3)⋊C2, … |
| maximal normal subgroup of | #13146654, #13146656, SD16×((C3⋊D3)⋊C3)⋊C2, … |
| maximal quotient of | #13149391, #13149392, #13149394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2485);