Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#3964 |
| Sylow | C5 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 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 | #12004864, #12004866, #12005562, … |
| maximal normal subgroup of | #12004864, #12004866, #12005562, … |
| maximal quotient of | C22×D4⋊#168, C2×#10602391, C2×#10602593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17847);