Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#689 |
| Sylow | C5 ⋊ C23×Q16 |
1464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #12006108, #12006109, #12006135, … |
| maximal normal subgroup of | #12006108, #12006109, #12006135, … |
| maximal quotient of | C23×#3942, C23×#3967, C23×#3939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21225);