Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #3091 |
420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^c=h^494 conjugacy classes — view the full character table.
| maximal subgroup of | #11994414, #11994416, #12071457, … |
| maximal normal subgroup of | #11994414, #11994416, #12071457, … |
| maximal quotient of | #12099089, #12100025, #12100522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16726);