Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic20 |
| Sylow | C5 ⋊ C23×Q16 |
1464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #12006110, #12006112, #12006136, … |
| maximal normal subgroup of | #12006110, #12006112, #12006136, … |
| maximal quotient of | C23×#3948, C23×#3950, C22×C4×Dic20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21134);