Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1290 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^2,d^b=dg,h^d=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13013352, #13013353, #13013354, … |
| maximal normal subgroup of | #13013352, #13013353, #13013354, … |
| maximal quotient of | #13013218, #13013226, #13013267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 858);