Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#322 ⋊ C2 |
| Sylow | C5 ⋊ #1722 |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^4,c^b=cf106 conjugacy classes — view the full character table.
| maximal subgroup of | #12012720, D5×#1722, C2×#10598891, … |
| maximal normal subgroup of | #12012720, D5×#1722, C2×#10598891, … |
| maximal quotient of | #11993089, #11999100, #11999107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 973);