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×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #2989 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^4,c^b=ce,h^c=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #11993196, #11993200, #11993203, … |
| maximal normal subgroup of | #11993196, #11993200, #11993203, … |
| maximal quotient of | #12098119, #12098132, #12098197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12827);