Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C5×Q8 ⋊ C4 |
| Sylow | C5 ⋊ #2295 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=f,c^2=fg,d^2=e,b^a=be,c^a=cfg,h^a=h^2,h^b=h^3,h^f=h^4,h^g=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13016856, #13016862, #13016868, … |
| maximal normal subgroup of | #13016856, #13016862, #13016868, … |
| maximal quotient of | #13027904, #13027912, C4×#65711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19291);