Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#344 ⋊ C2 |
| Sylow | C5 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 101 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,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,d^b=dg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1757, C2×#10599807, #12097002, … |
| maximal normal subgroup of | D5×#1757, C2×#10599807, #12097002, … |
| maximal quotient of | #11989827, #11989831, #11989835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1889);