Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | D3×#3743 |
| Fitting | C33×C8 ⋊ C22 |
| Sylow | C33 ⋊ C2×M16 |
488 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D32×ΓL(1,𝔽25), D3×#63798, D3×#63804, … |
| maximal normal subgroup of | D32×ΓL(1,𝔽25), D3×#63798, D3×#63804, … |
| maximal quotient of | #13159503, D3×#63641, #13159511, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3277);