Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#485 ⋊ C2 |
| Sylow | C5 ⋊ #3196 |
414 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^4,c^b=ceg,h^b=h^4,f^c=fg,h^d=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3196, C2×#10613254, #12969936, … |
| maximal normal subgroup of | D5×#3196, C2×#10613254, #12969936, … |
| maximal quotient of | #12108379, #12108388, #12109591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15336);