Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#346 ⋊ C2 |
| Sylow | C5 ⋊ #2177 |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^4,d^b=df,f^b=fg,h^b=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #11986770, #11986772, #12011184, … |
| maximal normal subgroup of | #11986770, #11986772, #12011184, … |
| maximal quotient of | #12011052, #12011225, #12011309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1953);