Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2095 |
254 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=deg,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ceg,c^b=cf,d^b=dg,e^b=eg,h^b=h^4,d^c=dg,e^c=eg,h^c=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #11988565, #11988566, #11988602, … |
| maximal normal subgroup of | #11988565, #11988566, #11988602, … |
| maximal quotient of | #12004287, #12004321, #12004353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1566);