Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ C4⋊#95 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=g,c^2=e,b^a=bd,c^a=ce,h^b=h^2,h^g=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13013631, #13021852, #13021853, … |
| maximal normal subgroup of | #13013631, #13021852, #13021853, … |
| maximal quotient of | (C2×AGL(1,𝔽5))⋊#95, #13014610, #13014611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6424);