Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #64847 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×ΓL(1,𝔽81) |
| Fitting | C2×C5×C16 ⋊ C4 |
| Sylow | C5 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | C4×ΓL(1,𝔽81), #13026027, #13026051, … |
| maximal normal subgroup of | C4×ΓL(1,𝔽81), #13026027, #13026051, … |
| maximal quotient of | C2×#10598642, C2×#10598643, #13025046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6185);