Finite Group Databasebeta

← Group #370503

Character table — Group #370503

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444422224444444444888888884444444444448888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ51111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-11111-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−i11-111-1-1-111-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−i11-1-1-111-1-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiii-11-11−ii−ii
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii11-111-1-1-111-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii1-11-1−ii−ii
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii11-1-1-111-1-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−i-11-11i−ii−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i-1-1111-1-1111-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11-11−ii−ii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i-1-11-1-1111-1-111−i−i−i−iiiiiii−i−i−i−i−i−iiiii1-11-1i−ii−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiii-1-1111-1-1111-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiii-11-11i−ii−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiii-1-11-1-1111-1-111iiii−i−i−i−i−i−iiiiiii−i−i−i−i1-11-1−ii−ii
χ17111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1111111111-111111-1-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ18111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1111111111-11-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ19111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-1-111-1-1111111-1-111-1-111-1-11111-1-1
χ20111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-111-1-111111111-1-111-1-111-1-1-1-111
χ21111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111111111-11-111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-1
χ22111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111111111-11-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111
χ23111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-111111-1-1-1-111-1-111-1-11111-1-111-1-11111-1-1-1-111
χ24111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111-1-111-1-1111111-1-111-1-1-1-11111-1-1
χ25111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111iiii−i−i−i−i1-1-111-1-11-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iii-111-1−iii−i
χ26111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111iiii−i−i−i−i1-1-1-1-111111-1-1ii−i−i−i−iii−i−iii−i−iiiii−i−i1-1-11i−i−ii
χ27111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111−i−i−i−iiiii1-1-111-1-11-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i-111-1i−i−ii
χ28111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111−i−i−i−iiiii1-1-1-1-111111-1-1−i−iiiii−i−iii−i−iii−i−i−i−iii1-1-11−iii−i
χ29111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i-11111-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-11i−i−ii
χ30111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i-111-1-111-111-1-1−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-1−iii−i
χ31111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiii-11111-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-11−iii−i
χ32111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiii-111-1-111-111-1-1ii−i−i−i−iiiii−i−iii−i−i−i−iii-111-1i−i−ii
χ3322222222-2-2-2-2222222-22-2-2-2222-2-222-2-222-2-2-2-200000000-2-220000200000000000000000000000000000000
χ3422222222-2-2-2-2222222-22-2-2-2222-2-2-2-2-2-2-2-222220000000022-20000-200000000000000000000000000000000
χ3522222222-2-2-2-22222-2-22-2222-2-2-22222-2-222222200000000-2-2-20000-200000000000000000000000000000000
χ3622222222-2-2-2-22222-2-22-2222-2-2-222-2-2-2-2-2-2-2-2-2-2000000002220000200000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222-22-2-2-22-2-2222222-2-2-2-22200000000-2220000-200000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-22-2-2-22-2-222-2-2222222-2-2000000002-2-20000200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22-2222-222-2-22222-2-222-2-200000000-22-20000200000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22-2222-222-2-2-2-22222-2-222000000002-220000-200000000000000000000000000000000
χ41222-22-2-2-222-2-222-2-2222-2-2-22-22-22-2002-200000022-2-222-2-2000000000000000000002-22-20000000000000000
χ42222-22-2-2-222-2-222-2-2222-2-2-22-22-22-2002-2000000-2-222-2-22200000000000000000000-22-220000000000000000
χ43222-22-2-2-222-2-222-2-2-2-2-2222-22-22-22002-20000002i2i−2i−2i−2i−2i2i2i000000000000000000002i−2i−2i2i0000000000000000
χ44222-22-2-2-222-2-222-2-2-2-2-2222-22-22-22002-2000000−2i−2i2i2i2i2i−2i−2i00000000000000000000−2i2i2i−2i0000000000000000
χ45222-22-2-2-222-2-2-2-222222-2-2-22-2-22-2200-2200000022-2-222-2-200000000000000000000-22-220000000000000000
χ46222-22-2-2-222-2-2-2-222222-2-2-22-2-22-2200-22000000-2-222-2-222000000000000000000002-22-20000000000000000
χ47222-22-2-2-222-2-2-2-222-2-2-2222-222-22-200-220000002i2i−2i−2i−2i−2i2i2i00000000000000000000−2i2i2i−2i0000000000000000
χ48222-22-2-2-222-2-2-2-222-2-2-2222-222-22-200-22000000−2i−2i2i2i2i2i−2i−2i000000000000000000002i−2i−2i2i0000000000000000
χ49222-22-2-2-2-2-22222-2-222-2-222-2-22-2-2200-22000000000000000000000000002-22-22-22-200000000000000000000
χ50222-22-2-2-2-2-22222-2-222-2-222-2-22-2-2200-2200000000000000000000000000-22-22-22-2200000000000000000000
χ51222-22-2-2-2-2-22222-2-2-2-222-2-222-222-200-22000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ52222-22-2-2-2-2-22222-2-2-2-222-2-222-222-200-2200000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ53222-22-2-2-2-2-222-2-22222-2-222-2-2-222-2002-2000000000000000000000000002-2-222-2-2200000000000000000000
χ54222-22-2-2-2-2-222-2-22222-2-222-2-2-222-2002-200000000000000000000000000-222-2-222-200000000000000000000
χ55222-22-2-2-2-2-222-2-222-2-222-2-2222-2-22002-2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ56222-22-2-2-2-2-222-2-222-2-222-2-2222-2-22002-200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ572-2-2222-2-22-22-200002-22-22-2-22000000000000002i−2i2i−2i2i−2i2i−2i0002i−2i2i−2i000000000000000002-2002-20000000000
χ582-2-2222-2-22-22-200002-22-22-2-22000000000000002i−2i2i−2i2i−2i2i−2i000−2i2i−2i2i00000000000000000-2200-220000000000
χ592-2-2222-2-22-22-200002-22-22-2-2200000000000000−2i2i−2i2i−2i2i−2i2i0002i−2i2i−2i00000000000000000-2200-220000000000
χ602-2-2222-2-22-22-200002-22-22-2-2200000000000000−2i2i−2i2i−2i2i−2i2i000−2i2i−2i2i000000000000000002-2002-20000000000
χ612-2-2222-2-22-22-20000-22-22-222-2000000000000002-22-2-22-220002i−2i−2i2i00000000000000000−2i2i002i−2i0000000000
χ622-2-2222-2-22-22-20000-22-22-222-2000000000000002-22-2-22-22000−2i2i2i−2i000000000000000002i−2i00−2i2i0000000000
χ632-2-2222-2-22-22-20000-22-22-222-200000000000000-22-222-22-20002i−2i−2i2i000000000000000002i−2i00−2i2i0000000000
χ642-2-2222-2-22-22-20000-22-22-222-200000000000000-22-222-22-2000−2i2i2i−2i00000000000000000−2i2i002i−2i0000000000
χ652-2-2-22-2222-2-2200002-222-22-2-2000000000000002i−2i−2i2i2i−2i−2i2i000000002-22-2000000000000002i−2i002i−2i00000000
χ662-2-2-22-2222-2-2200002-222-22-2-2000000000000002i−2i−2i2i2i−2i−2i2i00000000-22-2200000000000000−2i2i00−2i2i00000000
χ672-2-2-22-2222-2-2200002-222-22-2-200000000000000−2i2i2i−2i−2i2i2i−2i000000002-22-200000000000000−2i2i00−2i2i00000000
χ682-2-2-22-2222-2-2200002-222-22-2-200000000000000−2i2i2i−2i−2i2i2i−2i00000000-22-22000000000000002i−2i002i−2i00000000
χ692-2-2-22-2222-2-220000-22-2-22-222000000000000002-2-22-222-2000000002-2-22000000000000002-200-2200000000
χ702-2-2-22-2222-2-220000-22-2-22-222000000000000002-2-22-222-200000000-222-200000000000000-22002-200000000
χ712-2-2-22-2222-2-220000-22-2-22-22200000000000000-222-22-2-22000000002-2-2200000000000000-22002-200000000
χ722-2-2-22-2222-2-220000-22-2-22-22200000000000000-222-22-2-2200000000-222-2000000000000002-200-2200000000
χ7344-44-4-4-4400004i−4i4i−4i0000000000000000004i−4i4-4000000000000000000000000000000000000000000000000
χ7444-44-4-4-4400004i−4i4i−4i000000000000000000−4i4i-44000000000000000000000000000000000000000000000000
χ7544-44-4-4-440000−4i4i−4i4i0000000000000000004i−4i-44000000000000000000000000000000000000000000000000
χ7644-44-4-4-440000−4i4i−4i4i000000000000000000−4i4i4-4000000000000000000000000000000000000000000000000
χ7744-4-4-444-400004i−4i−4i4i0000000000004i−4i004-40000000000000000000000000000000000000000000000000000
χ7844-4-4-444-400004i−4i−4i4i000000000000−4i4i00-440000000000000000000000000000000000000000000000000000
χ7944-4-4-444-40000−4i4i4i−4i0000000000004i−4i00-440000000000000000000000000000000000000000000000000000
χ8044-4-4-444-40000−4i4i4i−4i000000000000−4i4i004-40000000000000000000000000000000000000000000000000000
χ814-4-4444-4-4-44-4400004-4-4-4-444400000000000000000000000000000000000000000000000000000000000000
χ824-4-4444-4-4-44-440000-44444-4-4-400000000000000000000000000000000000000000000000000000000000000
χ834-4-4-44-444-444-400004-4-444-44-400000000000000000000000000000000000000000000000000000000000000
χ844-4-4-44-444-444-40000-444-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ858-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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