Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ #2873 |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,e^2=g,d^a=dg,c^b=cg,h^c=h^4148 conjugacy classes — view the full character table.
| maximal subgroup of | #11996632, #11996634, #11996637, … |
| maximal normal subgroup of | #11996632, #11996634, #11996637, … |
| maximal quotient of | #12064882, #12064906, #12064932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12327);