Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#3954 |
| Sylow | C5 ⋊ C22×#108 |
480 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 269 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 | #12005183, #12005185, #12005188, … |
| maximal normal subgroup of | #12005183, #12005185, #12005188, … |
| maximal quotient of | C22×#64700, C22×#64699, C2×#10601538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17566);