Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1404 |
112 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 25 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,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^4,c^b=cg,d^b=de,e^b=eg,f^b=fg,d^c=dfg,e^c=eg,e^d=eg49 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1404, C2×#10598262, #12019549, … |
| maximal normal subgroup of | D5×#1404, C2×#10598262, #12019549, … |
| maximal quotient of | #11986662, #11986729, #11986825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 344);