Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #64868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#64868 |
| Fitting | C2×C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ C2×#327 |
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | #13017019, C4×#64868, #13017029, … |
| maximal normal subgroup of | #13017019, C4×#64868, #13017029, … |
| maximal quotient of | C2×#10598712, C2×#10598713, #13014638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6338);