Finite Group Databasebeta

← Group #103970

Character table — Group #103970

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444444444888888888888888816161616161616161616161632323232
order12222222444444444444444488888888888888884444888888884444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ9222222222222222-2-2-2-2-2-2-22-20000000000000000000022-2-200000000
χ10222222222222222-2-2-2-2-2-2-22-200000000000000000000-2-22200000000
χ11222222222222-2-2-2222-2-2-2-2-22000000000000000022-2-2000000000000
χ12222222222222-2-2-2222-2-2-2-2-220000000000000000-2-222000000000000
χ13222222222222-2-2-2-2-2-22222-2-200000000000000000000000000002-200
χ14222222222222-2-2-2-2-2-22222-2-20000000000000000000000000000-2200
χ1522222222-2-2-2-222-222-222-2-2-2-20000000000000000000000002i2i−2i−2i0000
χ1622222222-2-2-2-222-222-222-2-2-2-2000000000000000000000000−2i−2i2i2i0000
χ1722222222-2-2-2-222-2-2-22-2-222-220000000000000000000000000000002-2
χ1822222222-2-2-2-222-2-2-22-2-222-22000000000000000000000000000000-22
χ1922222222-2-2-2-2-2-2222-2-2-2222-22222-2-2-2-2000000000000000000000000
χ2022222222-2-2-2-2-2-2222-2-2-2222-2-2-2-2-22222000000000000000000000000
χ2122222222-2-2-2-2-2-22-2-2222-2-222000000002222-2-2-2-20000000000000000
χ2222222222-2-2-2-2-2-22-2-2222-2-22200000000-2-2-2-222220000000000000000
χ2322-222-2-2-22-22-22-2-200000002022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000002i−2i00000000
χ2422-222-2-2-22-22-22-2-200000002022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000−2i2i00000000
χ2522-222-2-2-22-22-22-2-2000000020−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000−2i2i00000000
χ2622-222-2-2-22-22-22-2-2000000020−2−222−2−222−i2−i2i2i2−i2−i2i2i20000002i−2i00000000
χ2722-222-2-2-2-22-22-22-200000002022−2−2−2−222i2i2−i2−i2−i2−i2i2i200002i−2i0000000000
χ2822-222-2-2-2-22-22-22-200000002022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000−2i2i0000000000
χ2922-222-2-2-2-22-22-22-2000000020−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000−2i2i0000000000
χ3022-222-2-2-2-22-22-22-2000000020−2−22222−2−2−i2−i2i2i2i2i2−i2−i200002i−2i0000000000
χ312-2-22-222-222-2-20002-2-2000002i2−i2i2−i2i2−i2i2−i200000000002i−2i00002−22−20000
χ322-2-22-222-222-2-20002-2-2000002i2−i2i2−i2i2−i2i2−i20000000000−2i2i0000−22−220000
χ332-2-22-222-222-2-20002-2-2000002−i2i2−i2i2−i2i2−i2i200000000002i−2i0000−22−220000
χ342-2-22-222-222-2-20002-2-2000002−i2i2−i2i2−i2i2−i2i20000000000−2i2i00002−22−20000
χ352-2-22-222-2-2-2220002-2200000-2i2−i2i2−i2−i2i2−i2i2000000002-2000000i2−i2−i2i20000
χ362-2-22-222-2-2-2220002-2200000-2i2−i2i2−i2−i2i2−i2i200000000-22000000−i2i2i2−i20000
χ372-2-22-222-2-2-2220002-2200000-2−i2i2−i2i2i2−i2i2−i2000000002-2000000−i2i2i2−i20000
χ382-2-22-222-2-2-2220002-2200000-2−i2i2−i2i2i2−i2i2−i200000000-22000000i2−i2−i2i20000
χ39444-4-44-4-40000000000004-400000000002-22-22-22-20000000000000000
χ40444-4-44-4-40000000000004-40000000000-22-22-22-220000000000000000
χ41444-4-44-4-4000000000000-4400000000002-22-2-22-220000000000000000
χ42444-4-44-4-4000000000000-440000000000-22-222-22-20000000000000000
χ4344-444-4-4-44-44-4-4440000000-4000000000000000000000000000000000
χ4444-444-4-4-4-44-444-440000000-4000000000000000000000000000000000
χ4544-4-4-4-44400000000004-400000000000000002i2−2i2−2i22i20000000000000000
χ4644-4-4-4-44400000000004-40000000000000000−2i22i22i2−2i20000000000000000
χ4744-4-4-4-4440000000000-440000000000002i2−2i2−2i22i200000000000000000000
χ4844-4-4-4-4440000000000-44000000000000−2i22i22i2−2i200000000000000000000
χ494-444-4-4-444-4-440000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ504-444-4-4-444-4-44000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ514-444-4-4-44-444-40000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ524-444-4-4-44-444-4000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ534-4-44-444-444-4-4000-44400000-400000000000000000000000000000000
χ544-4-44-444-4-4-444000-44-400000400000000000000000000000000000000
χ558-88-88-88-8000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).