Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C5×#405 ⋊ C2 |
| Sylow | C5 ⋊ C4×#131 |
572 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,e^2=g,h^b=h^4,d^c=dg,h^c=h^4160 conjugacy classes — view the full character table.
| maximal subgroup of | #12014347, #12014352, #12015236, … |
| maximal normal subgroup of | #12014347, #12014352, #12015236, … |
| maximal quotient of | #12064887, C8×#4053, #12064911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12362);