Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#4093 |
| Fitting | C23×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ C22×#124 |
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 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 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #11991935, #12005841, #12005844, … |
| maximal normal subgroup of | #11991935, #12005841, #12005844, … |
| maximal quotient of | C22×#65266, C22×#65279, C22×#65277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21228);