Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1307 |
130 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 57 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=d,b^2=e,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^4,c^b=cg,d^b=df82 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1307, C2×#10598249, #11989683, … |
| maximal normal subgroup of | D5×#1307, C2×#10598249, #11989683, … |
| maximal quotient of | #11985872, #11985873, #11985875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 331);