Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #2977 |
422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,b^a=be,d^a=de,c^b=ceg,d^b=dg,h^b=h^4130 conjugacy classes — view the full character table.
| maximal subgroup of | #11995772, #11995774, #11995776, … |
| maximal normal subgroup of | #11995772, #11995774, #11995776, … |
| maximal quotient of | #12098001, #12098008, #12098066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12418);