Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×C8×D4 ⋊ C2 |
| Sylow | C5 ⋊ #2972 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,b^a=be,d^a=de,c^b=ce,h^d=h^4148 conjugacy classes — view the full character table.
| maximal subgroup of | #12068731, #12068733, #12068735, … |
| maximal normal subgroup of | #12068731, #12068733, #12068735, … |
| maximal quotient of | #12097970, #12098028, #12098185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13239);