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 ⋊ #3200 |
410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^4,f^c=fg,h^c=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3200, C2×#10613274, #12970024, … |
| maximal normal subgroup of | D5×#3200, C2×#10613274, #12970024, … |
| maximal quotient of | #12108397, #12108405, #12109606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15356);