Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C5×C8 ⋊ C4 |
| Sylow | C5 ⋊ #1835 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=e,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ceg,d^a=dg,e^a=eg,h^a=h^2,h^f=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13013737, #13013738, #13013746, … |
| maximal normal subgroup of | #13013737, #13013738, #13013746, … |
| maximal quotient of | #13018739, #13018740, #13018741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 5928);