Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #2373 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,c^2=e,d^2=ef,b^a=be,c^a=cf,d^b=de,h^c=h^4130 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2373, C2×#10605396, #12258998, … |
| maximal normal subgroup of | D5×#2373, C2×#10605396, #12258998, … |
| maximal quotient of | #12020755, #12020819, #12020832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7478);