Finite Group Databasebeta

← Group #318739

Character table — Group #318739

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888844444444448888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ121111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222-2-2-2-22222-2-22200000000-2-222-2-222-2-20000000000000000000000000000
χ182222222222-2-2-2-22222-2-22200000000-2-2-2-222-2-2220000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2000000002222-2-2-2-2220000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-20000000022-2-22222-2-20000000000000000000000000000
χ2122222222-2-22222-2-222-2-2-2-22222-2-2-2-22-20000000022-2-2000000000000000000000000
χ2222222222-2-22222-2-222-2-2-2-2-2-2-2-222222-200000000-2-222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2222222-2-2-2-2-2200000000-2-222000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-222-2-2-2-22222-220000000022-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000-220000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000-22000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000002-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222000000002-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-22-2-22222-2-2-2-2002-20022-2-222-2-200000000000000000000002-22-2000000000000
χ30222-2-22-2-22222-2-2-2-2002-20022-2-222-2-20000000000000000000000-22-22000000000000
χ31222-2-22-2-22222-2-2-2-2002-200-2-222-2-22200000000000000000000002-2-22000000000000
χ32222-2-22-2-22222-2-2-2-2002-200-2-222-2-2220000000000000000000000-222-2000000000000
χ33222-2-22-2-2-2-222-2-22200-220022-2-2-2-222000000000000000000000000002i−2i2i−2i00000000
χ34222-2-22-2-2-2-222-2-22200-220022-2-2-2-22200000000000000000000000000−2i2i−2i2i00000000
χ35222-2-22-2-2-2-222-2-22200-2200-2-22222-2-2000000000000000000000000002i−2i−2i2i00000000
χ36222-2-22-2-2-2-222-2-22200-2200-2-22222-2-200000000000000000000000000−2i2i2i−2i00000000
χ3722-22-2-22-22-200002-22i−2i002i−2ii2−i2i2−i2i2−i2i2−i200002i−2i002-22−22−22−22−2i2−i2i2−i20000000000000000
χ3822-22-2-22-22-200002-22i−2i002i−2ii2−i2i2−i2i2−i2i2−i20000−2i2i00-222−22−2−22−22−i2i2−i2i20000000000000000
χ3922-22-2-22-22-200002-22i−2i002i−2i−i2i2−i2i2−i2i2−i2i200002i−2i002-2−22−22−22−22−i2i2−i2i20000000000000000
χ4022-22-2-22-22-200002-22i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000−2i2i00-22−22−222−22−2i2−i2i2−i20000000000000000
χ4122-22-2-22-22-200002-2−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i200002i−2i00-22−22−222−22−2−i2i2−i2i20000000000000000
χ4222-22-2-22-22-200002-2−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000−2i2i002-2−22−22−22−22i2−i2i2−i20000000000000000
χ4322-22-2-22-22-200002-2−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i200002i−2i00-222−22−2−22−22i2−i2i2−i20000000000000000
χ4422-22-2-22-22-200002-2−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i20000−2i2i002-22−22−22−22−2−i2i2−i2i20000000000000000
χ4522-22-2-22-2-220000-222i−2i00−2i2ii2−i2i2−i2−i2i2−i2i2002-2002i−2i002−2−22i2−i2−i2i2−222−20000000000000000
χ4622-22-2-22-2-220000-222i−2i00−2i2ii2−i2i2−i2−i2i2−i2i200-2200−2i2i002−2−22−i2i2i2−i22−2−220000000000000000
χ4722-22-2-22-2-220000-222i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2002-2002i−2i00−222−2−i2i2i2−i22−2−220000000000000000
χ4822-22-2-22-2-220000-222i−2i00−2i2i−i2i2−i2i2i2−i2i2−i200-2200−2i2i00−222−2i2−i2−i2i2−222−20000000000000000
χ4922-22-2-22-2-220000-22−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2002-200−2i2i00−222−2i2−i2−i2i22−2−220000000000000000
χ5022-22-2-22-2-220000-22−2i2i002i−2ii2−i2i2−i2−i2i2−i2i200-22002i−2i00−222−2−i2i2i2−i2−222−20000000000000000
χ5122-22-2-22-2-220000-22−2i2i002i−2i−i2i2−i2i2i2−i2i2−i2002-200−2i2i002−2−22−i2i2i2−i2−222−20000000000000000
χ5222-22-2-22-2-220000-22−2i2i002i−2i−i2i2−i2i2i2−i2i2−i200-22002i−2i002−2−22i2−i2−i2i22−2−220000000000000000
χ53444-4-44-4-444-4-444-4-400-44000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-4-4-4-44444004-4000000000000000000000000000000000000000000000000
χ5544-4-44-4-444-40000-440000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5644-4-44-4-444-40000-44000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5744-4-44-4-44-4400004-40000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5844-4-44-4-44-4400004-4000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ594-4444-4-4-4004-44-40000000000000000000000000000000000000000000000000022−2200
χ604-4444-4-4-4004-44-400000000000000000000000000000000000000000000000000−222200
χ614-4444-4-4-400-44-44000000000000000000000000000000000000000000000000000022−22
χ624-4444-4-4-400-44-440000000000000000000000000000000000000000000000000000−2222
χ634-44-4-4-444004-4-44000000000000000000000000000000000000000000000022−22000000
χ644-44-4-4-444004-4-440000000000000000000000000000000000000000000000−2222000000
χ654-44-4-4-44400-444-400000000000000000000000000000000000000000000000022−220000
χ664-44-4-4-44400-444-4000000000000000000000000000000000000000000000000−22220000
χ678-8-88-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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