Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #3126 |
382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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|c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3126, C2×#10615170, #12967661, … |
| maximal normal subgroup of | D5×#3126, C2×#10615170, #12967661, … |
| maximal quotient of | #12099395, #12102415, #12102452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17252);