Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#353 ⋊ C2 |
| Sylow | C5 ⋊ #1402 |
122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 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,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,d^b=deg,e^b=eg,f^b=fg,h^b=h^4,d^c=dfg,e^c=eg,e^d=eg43 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1402, C2×#10598029, #12019517, … |
| maximal normal subgroup of | D5×#1402, C2×#10598029, #12019517, … |
| maximal quotient of | #11986658, #11986725, #11986824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 111);