Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #1729 |
416 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,e^2=g,b^a=bd,h^a=h^4,c^b=cg,h^b=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #11986268, #11986272, #12004651, … |
| maximal normal subgroup of | #11986268, #11986272, #12004651, … |
| maximal quotient of | #11988681, #11988686, #11988689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4855);