Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1416 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=g,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^4,c^b=ce,e^b=ef,f^b=fg,h^b=h^4166 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1416, C2×#10598088, #12019731, … |
| maximal normal subgroup of | D5×#1416, C2×#10598088, #12019731, … |
| maximal quotient of | #11986754, #11986859, #11986937, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 170);