Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#688 |
| Fitting | C23×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ C23×SD16 |
1720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #12006101, #12006105, #12006128, … |
| maximal normal subgroup of | #12006101, #12006105, #12006128, … |
| maximal quotient of | C23×#3941, C23×#3967, C23×#3940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21223);