Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#3950 |
| Sylow | C5 ⋊ C22×#107 |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #12005198, #12005200, #12005202, … |
| maximal normal subgroup of | #12005198, #12005200, #12005202, … |
| maximal quotient of | C22×#64678, C2×#10600524, C2×#10601543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17543);