Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #2073 |
258 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 81 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,c^2=d,f^2=g,b^a=bd,c^a=ceg,c^b=cf,f^b=fg,f^c=fg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11986836, #11986838, D5×#2073, … |
| maximal normal subgroup of | #11986836, #11986838, D5×#2073, … |
| maximal quotient of | #12004034, #12004039, #12004054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2516);