Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3⋊D3×ΓL(1,𝔽25) |
| Fitting | C33×C8 ⋊ C22 |
| Sylow | C33 ⋊ C2×M16 |
488 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #157×ΓL(1,𝔽25), #13166238, #13166240, … |
| maximal normal subgroup of | #157×ΓL(1,𝔽25), #13166238, #13166240, … |
| maximal quotient of | C3⋊D3×Dic3⋊C8, #13159506, #13159510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3278);