Finite Group Databasebeta

← Group #296752

Character table — Group #296752

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
χ311111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-111-11
χ111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-111-11
χ121111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1111-1
χ1722222222222-2-2-2-2222222222-2-2-2-2-2-2220000-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-222222222-2-2-2-20000-2-2220000000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-2-22222-2-222000022-2-20000000000000000000000000000
χ2122222222-2-2-22222-222-2-20000-2-222-2-20022-2-200000000000000000000-220000000000
χ2222222222-2-2-22222-222-2-20000-2-222-2-200-2-222000000000000000000002-20000000000
χ2322222222-2-2-22222-2-2-222000022-2-2-2-200222200000000000000000000-2-20000000000
χ2422222222-2-2-22222-2-2-222000022-2-2-2-200-2-2-2-200000000000000000000220000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2000022-2-22200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-2000022-2-2220000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2220000-2-2222200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2220000-2-222220000000000000000000000000000-222-2000000
χ292222-2-2-2-222-20000-22-22-222-2-20000002-20000000022−2−222−2−222−2−222−2−2000000000000
χ302222-2-2-2-222-20000-22-22-222-2-20000002-200000000−2−222−2−222−2−222−2−222000000000000
χ312222-2-2-2-222-20000-22-22-2-2-222000000-220000000022−2−222−2−2−2−222−2−222000000000000
χ322222-2-2-2-222-20000-22-22-2-2-222000000-2200000000−2−222−2−22222−2−222−2−2000000000000
χ332222-2-2-2-222-20000-2-22-2222-2-2000000-220000000022−2−2−2−22222−2−2−2−222000000000000
χ342222-2-2-2-222-20000-2-22-2222-2-2000000-2200000000−2−22222−2−2−2−22222−2−2000000000000
χ352222-2-2-2-222-20000-2-22-22-2-2220000002-20000000022−2−2−2−222−2−22222−2−2000000000000
χ362222-2-2-2-222-20000-2-22-22-2-2220000002-200000000−2−22222−2−222−2−2−2−222000000000000
χ3722-2-222-2-22-2-22-22-2200002i−2i2i−2i00002-20000002i−2i0000002i−2i2i−2i00002-22-2000000000000
χ3822-2-222-2-22-2-22-22-2200002i−2i2i−2i00002-20000002i−2i000000−2i2i−2i2i0000-22-22000000000000
χ3922-2-222-2-22-2-22-22-220000−2i2i−2i2i00002-2000000−2i2i0000002i−2i2i−2i0000-22-22000000000000
χ4022-2-222-2-22-2-22-22-220000−2i2i−2i2i00002-2000000−2i2i000000−2i2i−2i2i00002-22-2000000000000
χ4122-2-222-2-22-2-2-22-22200002i−2i2i−2i0000-22000000−2i2i002i−2i2i−2i00002-22-20000000000000000
χ4222-2-222-2-22-2-2-22-22200002i−2i2i−2i0000-22000000−2i2i00−2i2i−2i2i0000-22-220000000000000000
χ4322-2-222-2-22-2-2-22-2220000−2i2i−2i2i0000-220000002i−2i002i−2i2i−2i0000-22-220000000000000000
χ4422-2-222-2-22-2-2-22-2220000−2i2i−2i2i0000-220000002i−2i00−2i2i−2i2i00002-22-20000000000000000
χ4522-2-2-2-2222-220000-200002i−2i−2i2i2-22-200000000002i−2ii2−i2−i2i2i2−i2−i2i22−2−222−2−22000000000000
χ4622-2-2-2-2222-220000-200002i−2i−2i2i2-22-200000000002i−2i−i2i2i2−i2−i2i2i2−i2−222−2−222−2000000000000
χ4722-2-2-2-2222-220000-200002i−2i−2i2i-22-220000000000−2i2ii2−i2−i2i2−i2i2i2−i22−2−22−222−2000000000000
χ4822-2-2-2-2222-220000-200002i−2i−2i2i-22-220000000000−2i2i−i2i2i2−i2i2−i2−i2i2−222−22−2−22000000000000
χ4922-2-2-2-2222-220000-20000−2i2i2i−2i2-22-20000000000−2i2ii2−i2−i2i2i2−i2−i2i2−222−2−222−2000000000000
χ5022-2-2-2-2222-220000-20000−2i2i2i−2i2-22-20000000000−2i2i−i2i2i2−i2−i2i2i2−i22−2−222−2−22000000000000
χ5122-2-2-2-2222-220000-20000−2i2i2i−2i-22-2200000000002i−2ii2−i2−i2i2−i2i2i2−i2−222−22−2−22000000000000
χ5222-2-2-2-2222-220000-20000−2i2i2i−2i-22-2200000000002i−2i−i2i2i2−i2i2−i2−i2i22−2−22−222−2000000000000
χ534444-4-4-4-4-4-44000044-4-44000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4400004-444-4000000000000000000000000000000000000000000000000
χ5544-4-444-4-4-4444-44-4-4000000000000-4400000000000000000000000000000000000000
χ5644-4-444-4-4-444-44-44-40000000000004-400000000000000000000000000000000000000
χ5744-4-4-4-444-44-400004000000004-4-440000000000000000000000000000000000000000
χ5844-4-4-4-444-44-40000400000000-444-40000000000000000000000000000000000000000
χ594-44-4-44-4400044-4-400000000000000000000000000000000000000000000000002i2−2i200
χ604-44-4-44-4400044-4-40000000000000000000000000000000000000000000000000−2i22i200
χ614-44-4-44-44000-4-4440000000000000000000000000000000000000000000000022−220000
χ624-44-4-44-44000-4-44400000000000000000000000000000000000000000000000−22220000
χ634-4-44-444-40004-4-44000000000000000004i−4i0000000000000000000000000000000000
χ644-4-44-444-40004-4-4400000000000000000−4i4i0000000000000000000000000000000000
χ654-4-44-444-4000-444-400000000000000000004i−4i00000000000000000000000000000000
χ664-4-44-444-4000-444-40000000000000000000−4i4i00000000000000000000000000000000
χ678-88-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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