Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#3953 |
| Fitting | C23×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #12004863, #12004867, #12005561, … |
| maximal normal subgroup of | #12004863, #12004867, #12005561, … |
| maximal quotient of | C22×#64679, C2×#10601555, C2×#10601551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17551);