Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^2,c^b=ce,h^b=h^4,h^d=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊(Q8⋊C16), C2×#10598581, #13023735, … |
| maximal normal subgroup of | D5⋊(Q8⋊C16), C2×#10598581, #13023735, … |
| maximal quotient of | #13013426, #13013446, #13013560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 663);