Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1405 |
106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,c^2=g,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=cg,d^b=de,e^b=eg,f^b=fg,h^b=h^4,d^c=dfg,e^c=eg,e^d=eg,h^d=h^428 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#1405, C2×#10598576, #13027603, … |
| maximal normal subgroup of | D5⋊#1405, C2×#10598576, #13027603, … |
| maximal quotient of | #13014106, #13014173, #13014246, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 658);