Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×Q32 ⋊ C4 |
| Sylow | C5 ⋊ #1418 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^4,h^d=h^437 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#1418, C2×#10598683, #13027778, … |
| maximal normal subgroup of | D5⋊#1418, C2×#10598683, #13027778, … |
| maximal quotient of | #13014192, #13014193, #13014272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 765);