Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1746 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^4,c^b=cg136 conjugacy classes — view the full character table.
| maximal subgroup of | #11989754, #11989759, #11990343, … |
| maximal normal subgroup of | #11989754, #11989759, #11990343, … |
| maximal quotient of | #11989727, #11989730, #11989732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2310);