Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1291 |
138 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 138 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,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=efg,h^a=h^4,d^b=dg112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1291, C2×#10598161, #11989214, … |
| maximal normal subgroup of | D5×#1291, C2×#10598161, #11989214, … |
| maximal quotient of | #11985836, #11985840, #11985843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 243);