Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#358 ⋊ C2 |
| Sylow | C5 ⋊ #2141 |
220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=g,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,d^b=df,f^b=fg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2141, C2×#10600015, #12252201, … |
| maximal normal subgroup of | D5×#2141, C2×#10600015, #12252201, … |
| maximal quotient of | #12009051, #12009295, #12009347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2097);