Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#124 ⋊ C4 |
| Sylow | C5 ⋊ #2337 |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^2,c^b=ce,h^b=h^3,h^g=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #13020260, #13020261, #13020264, … |
| maximal normal subgroup of | #13020260, #13020261, #13020264, … |
| maximal quotient of | #13027957, #13027972, #13027976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19407);