Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2962 |
356 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,h^a=h^4,d^c=dg130 conjugacy classes — view the full character table.
| maximal subgroup of | #11993780, #11993784, #11993794, … |
| maximal normal subgroup of | #11993780, #11993784, #11993794, … |
| maximal quotient of | #12097282, #12097299, #12097943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12321);