Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #2132 |
250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=g,d^2=g,e^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,d^b=dg,e^b=efg,h^b=h^4,e^d=eg,h^e=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #13014477, #13014478, #13014490, … |
| maximal normal subgroup of | #13014477, #13014478, #13014490, … |
| maximal quotient of | #13023125, #13023173, #13023277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6227);