Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#64735 |
| Fitting | C2×C5×M32 ⋊ C2 |
| Sylow | C5 ⋊ C2×#350 |
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #12014347, C4×#64735, #12014352, … |
| maximal normal subgroup of | #12014347, C4×#64735, #12014352, … |
| maximal quotient of | C2×#10598014, #12008376, C2×#10598016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4311);