Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#368 ⋊ C2 |
| Sylow | C5 ⋊ #2161 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #12020258, #12020261, #12020263, … |
| maximal normal subgroup of | #12020258, #12020261, #12020263, … |
| maximal quotient of | #12010886, #12010888, #12010950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2235);