Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×C22⋊Q8 ⋊ C4 |
| Sylow | C5 ⋊ #2362 |
576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,c^2=e,d^2=e,b^a=be,c^a=cf,h^a=h^2,d^b=de,h^b=h^3,h^g=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13041018, #13041023, #13041026, … |
| maximal normal subgroup of | #13041018, #13041023, #13041026, … |
| maximal quotient of | #13028001, #13028027, #13028031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19368);