Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #64849 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#64850 |
| unambiguous semidirect product | D5⋊#367 |
| Fitting | C2×C5×C16 ⋊ C4 |
| Sylow | C5 ⋊ C2×#367 |
168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13014394, #13014395, #13014400, … |
| maximal normal subgroup of | #13014394, #13014395, #13014400, … |
| maximal quotient of | C2×#10598646, D5⋊#1372, C2×#10598647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6188);