Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #3383 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=e,c^2=g,d^2=eg,f^2=g,b^a=beg,c^a=cf,f^a=fg,d^b=deg,f^c=fg,h^d=h^473 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3383, C2×#10612953, #12979761, … |
| maximal normal subgroup of | D5×#3383, C2×#10612953, #12979761, … |
| maximal quotient of | #12115909, #12115917, #12117728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15035);