Finite Group Databasebeta

← Group #296772

Character table — Group #296772

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444444444444422444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-111-1-11-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-1-1-111-11
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11-111-1-111-11
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11-11111-1-11-1
χ91111111111111111-1-1-1-11111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1111-1
χ1722222222222-2-2-2-22222222-2-2-2-222-2-22200-2-2-2-2000000000000000000000000000000
χ1822222222222-2-2-2-222222-2-22222-2-2-2-2-2-200-2-222000000000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-222-2-2-2-222-2-2-2-2002222000000000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-22222-2-2-2-2220022-2-2000000000000000000000000000000
χ2122222222-2-2-22222-2000022-2-222-2-2-2-20022000022000000000000000000-2-200000000
χ2222222222-2-2-22222-2000022-2-222-2-2-2-200-2-20000-2-20000000000000000002200000000
χ2322222222-2-2-22222-20000-2-222-2-222-2-200220000-2-20000000000000000002-200000000
χ2422222222-2-2-22222-20000-2-222-2-222-2-200-2-2000022000000000000000000-2200000000
χ2522222222-2-2-2-2-2-2-2-200002222-2-2-2-222000000000000000000000000002-2002-2000000
χ2622222222-2-2-2-2-2-2-2-200002222-2-2-2-22200000000000000000000000000-2200-22000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2-2-2222222000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2-2-222222200000000000000000000000000-22002-2000000
χ29222-2-2-2-222-2-20000222-2-22-200002-2002-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ30222-2-2-2-222-2-20000222-2-22-200002-2002-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ31222-2-2-2-222-2-20000222-2-2-220000-2200-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ32222-2-2-2-222-2-20000222-2-2-220000-2200-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ33222-2-2-2-222-2-200002-2-2222-200002-200-2200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ34222-2-2-2-222-2-200002-2-2222-200002-200-2200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ35222-2-2-2-222-2-200002-2-222-220000-22002-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ36222-2-2-2-222-2-200002-2-222-220000-22002-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ3722-22-22-2-2-22-2000022i−2i2i−2i002-22-200000000002i−2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ3822-22-22-2-2-22-2000022i−2i2i−2i002-22-200000000002i−2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-22-22-2-2-22-2000022i−2i2i−2i00-22-220000000000−2i2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ4022-22-22-2-2-22-2000022i−2i2i−2i00-22-220000000000−2i2i00−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ4122-22-22-2-2-22-200002−2i2i−2i2i002-22-20000000000−2i2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ4222-22-22-2-2-22-200002−2i2i−2i2i002-22-20000000000−2i2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ4322-22-22-2-2-22-200002−2i2i−2i2i00-22-2200000000002i−2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ4422-22-22-2-2-22-200002−2i2i−2i2i00-22-2200000000002i−2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ4522-2-22-22-2-2-222-22-222i−2i−2i2i000000002-200002i−2i000000002i−2i−2i2i0000-222-2000000000000
χ4622-2-22-22-2-2-222-22-222i−2i−2i2i000000002-200002i−2i00000000−2i2i2i−2i00002-2-22000000000000
χ4722-2-22-22-2-2-222-22-22−2i2i2i−2i000000002-20000−2i2i000000002i−2i−2i2i00002-2-22000000000000
χ4822-2-22-22-2-2-222-22-22−2i2i2i−2i000000002-20000−2i2i00000000−2i2i2i−2i0000-222-2000000000000
χ4922-2-22-22-2-2-22-22-2222i−2i−2i2i00000000-220000−2i2i00002i−2i−2i2i0000-222-20000000000000000
χ5022-2-22-22-2-2-22-22-2222i−2i−2i2i00000000-220000−2i2i0000−2i2i2i−2i00002-2-220000000000000000
χ5122-2-22-22-2-2-22-22-222−2i2i2i−2i00000000-2200002i−2i00002i−2i−2i2i00002-2-220000000000000000
χ5222-2-22-22-2-2-22-22-222−2i2i2i−2i00000000-2200002i−2i0000−2i2i2i−2i0000-222-20000000000000000
χ53444-4-4-4-44-4440000-400004-40000-440000000000000000000000000000000000000000
χ54444-4-4-4-44-4440000-40000-4400004-40000000000000000000000000000000000000000
χ5544-44-44-4-44-440000-40000004-4-44000000000000000000000000000000000000000000
χ5644-44-44-4-44-440000-4000000-444-4000000000000000000000000000000000000000000
χ5744-4-44-44-444-44-44-4-4000000000000-4400000000000000000000000000000000000000
χ5844-4-44-44-444-4-44-44-40000000000004-400000000000000000000000000000000000000
χ594-44-4-444-40004-4-4400000000000000000000000000000000000000000000000002i2−2i200
χ604-44-4-444-40004-4-440000000000000000000000000000000000000000000000000−2i22i200
χ614-44-4-444-4000-444-4000000000000000000000000000000000000000000000002i2−2i20000
χ624-44-4-444-4000-444-400000000000000000000000000000000000000000000000−2i22i20000
χ634-4-44-4-44400044-4-4000000000000000004i−4i0000000000000000000000000000000000
χ644-4-44-4-44400044-4-400000000000000000−4i4i0000000000000000000000000000000000
χ654-4-44-4-444000-4-444000000000000000000000004-40000000000000000000000000000
χ664-4-44-4-444000-4-44400000000000000000000000-440000000000000000000000000000
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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