Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#4075 |
| Fitting | C24×C4×C5 ⋊ C2 |
| Sylow | C5 ⋊ C22×#123 |
1968 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 645 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 | #11990646, #12005794, #12005914, … |
| maximal normal subgroup of | #11990646, #12005794, #12005914, … |
| maximal quotient of | C22×#65500, C22×#65499, C22×#65502, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21205);