Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#117 ⋊ C4 |
| Sylow | C5 ⋊ #1740 |
420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=g,b^a=bd,d^a=dg,e^b=eg,h^b=h^2,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13021626, #13021627, #13021828, … |
| maximal normal subgroup of | #13021626, #13021627, #13021828, … |
| maximal quotient of | #13015524, #13015530, #13015536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6466);