Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×C8×Q8 ⋊ C2 |
| Sylow | C5 ⋊ #2986 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,h^a=h^4,c^b=ceg,d^b=dg,h^d=h^4130 conjugacy classes — view the full character table.
| maximal subgroup of | #12070475, #12070478, #12070512, … |
| maximal normal subgroup of | #12070475, #12070478, #12070512, … |
| maximal quotient of | #12098058, #12098065, #12098352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13736);