Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#482 ⋊ C2 |
| Sylow | C5 ⋊ #3324 |
448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,h^b=h^4,f^c=fg,h^c=h^467 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3324, C2×#10613134, #12976253, … |
| maximal normal subgroup of | D5×#3324, C2×#10613134, #12976253, … |
| maximal quotient of | #12114913, #12115764, #12116552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15216);