Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#360 ⋊ C2 |
| Sylow | C5 ⋊ #2145 |
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=g,d^2=f,f^2=g,b^a=bd,d^a=df,f^a=fg,d^b=dfg,e^b=eg,f^b=fg,h^c=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2145, C2×#10600044, #12252244, … |
| maximal normal subgroup of | D5×#2145, C2×#10600044, #12252244, … |
| maximal quotient of | #12009063, #12009065, #12009073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2126);