Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C5×#354 ⋊ C2 |
| Sylow | C5 ⋊ #1406 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cf,d^b=defg,e^b=eg,h^b=h^4,d^c=dfg,e^d=eg40 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1406, C2×#10598035, #12019586, … |
| maximal normal subgroup of | D5×#1406, C2×#10598035, #12019586, … |
| maximal quotient of | #11986678, #11986720, #11986806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 117);