Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×Q82 ⋊ C2 |
| Sylow | C5 ⋊ #2205 |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|b^2=g,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^4,c^b=cg,d^b=dg,e^b=efg,d^c=df,e^c=eg,e^d=eg70 conjugacy classes — view the full character table.
| maximal subgroup of | #12020067, #12020068, #12020072, … |
| maximal normal subgroup of | #12020067, #12020068, #12020072, … |
| maximal quotient of | #12011392, #12011557, #12011666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4817);