Finite Group Databasebeta

← Group #10713873

Character table — Group #10713873

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881616161616161616161616162424242424242424242424244848
order12222234466644444444466121212121212121244121212121212121212128888242424242424242444448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111iiii−i−i−i−i-1-1
χ6111111111111111-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1−i−i−i−iiiii11
χ7111111111111111-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111−i−i−i−iiiii-1-1
χ8111111111111111-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i11
χ91111111-1-1111-1111-1-111111-1-1-1-11111-1-111-1-111-1-1-1-11-11-111-1-111-1-111-1-111-1-111-1-11-1
χ101111111-1-1111-1111-1-111111-1-1-1-11111-1-111-1-111-1-1-1-11-11-111-1-111-1-1-1-111-1-111-1-111-11
χ111111111-1-1111-1111-1-111111-1-1-1-11111-1-111-1-111-1-1-1-1-11-11-1-111-1-11111-1-1-1-111-1-1111-1
χ121111111-1-1111-1111-1-111111-1-1-1-11111-1-111-1-111-1-1-1-1-11-11-1-111-1-111-1-11111-1-111-1-1-11
χ131111111-1-1111-111-111-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-11111i−i−iiii−i−i−i−iii11-1-1ii−i−i−i−iii-11
χ141111111-1-1111-111-111-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-11111i−i−iiii−i−i−i−iii-1-111−i−iiiii−i−i1-1
χ151111111-1-1111-111-111-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-11111−iii−i−i−iiiii−i−i11-1-1−i−iiiii−i−i-11
χ161111111-1-1111-111-111-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-11111−iii−i−i−iiiii−i−i-1-111ii−i−i−i−iii1-1
χ172222222222222-2-22-2-22-2-22222222222-22-2-2-2-2-2-222-2-200000000000000000000000000
χ182222222222222-2-2-222-222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000
χ192222222-2-2222-2-2-22222-2-222-2-2-2-222222-2-2-222-2-2-2-22200000000000000000000000000
χ202222222-2-2222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2222222-2-200000000000000000000000000
χ21222222-122-1-1-1222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ22222222-122-1-1-1222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ23222222-122-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-111112-2-1-1-1-11111112i2i−2i−2i−i−i−i−iiiii00000000000000
χ24222222-122-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-111112-2-1-1-1-1111111−2i−2i2i2iiiii−i−i−i−i00000000000000
χ25222222-122-1-1-12-2-22-2-22-2-2-1-1-1-1-1-1-1-1-1-1-22111111-1-1110000−i3i3−i3i3−i3i3−i3i300000000000000
χ26222222-122-1-1-12-2-22-2-22-2-2-1-1-1-1-1-1-1-1-1-1-22111111-1-1110000i3−i3i3−i3i3−i3i3−i300000000000000
χ27222222-122-1-1-12-2-2-222-222-1-1-1-1-1-11111-2-21111-1-111-1-100003−33−3−33−3300000000000000
χ28222222-122-1-1-12-2-2-222-222-1-1-1-1-1-11111-2-21111-1-111-1-10000−33−333−33−300000000000000
χ29222222-1-2-2-1-1-1-2222-2-2222-1-11111-1-1-1-1-2-2-1-111-1-111112-22-2-1-111-1-11100000000000000
χ30222222-1-2-2-1-1-1-2222-2-2222-1-11111-1-1-1-1-2-2-1-111-1-11111-22-2211-1-111-1-100000000000000
χ31222222-1-2-2-1-1-1-222-222-2-2-2-1-111111111-22-1-11111-1-1-1-12i−2i−2i2i−i−iiiii−i−i00000000000000
χ32222222-1-2-2-1-1-1-222-222-2-2-2-1-111111111-22-1-11111-1-1-1-1−2i2i2i−2iii−i−i−i−iii00000000000000
χ33222222-1-2-2-1-1-1-2-2-22222-2-2-1-11111-1-1-1-12-211-1-11111-1-10000−i3i3i3−i3−i3i3i3−i300000000000000
χ34222222-1-2-2-1-1-1-2-2-22222-2-2-1-11111-1-1-1-12-211-1-11111-1-10000i3−i3−i3i3i3−i3−i3i300000000000000
χ35222222-1-2-2-1-1-1-2-2-2-2-2-2-222-1-1111111112211-1-1-1-1-1-11100003−3−33−333−300000000000000
χ36222222-1-2-2-1-1-1-2-2-2-2-2-2-222-1-1111111112211-1-1-1-1-1-1110000−333−33−3−3300000000000000
χ372-22-22-2200-22-202-2200-22-22-2000022-2-2002-2002-200000000000000000000002-2002-200
χ382-22-22-2200-22-202-2200-22-22-2000022-2-2002-2002-20000000000000000000000-2200-2200
χ392-22-22-2200-22-202-2-2002-222-20000-2-222002-200-2200000000000000000000002i−2i00−2i2i00
χ402-22-22-2200-22-202-2-2002-222-20000-2-222002-200-220000000000000000000000−2i2i002i−2i00
χ412-22-22-2200-22-20-22200-2-222-2000022-2-200-2200-22000000000000000000002-2002-20000
χ422-22-22-2200-22-20-22200-2-222-2000022-2-200-2200-2200000000000000000000-2200-220000
χ432-22-22-2200-22-20-22-20022-22-20000-2-22200-22002-2000000000000000000002i−2i00−2i2i0000
χ442-22-22-2200-22-20-22-20022-22-20000-2-22200-22002-200000000000000000000−2i2i002i−2i0000
χ454444-4-4444444-400000000-4-444-4-4000000000000000000000000000000000000000000
χ464444-4-44-4-4444400000000-4-4-4-444000000000000000000000000000000000000000000
χ474444-4-4-244-2-2-2-40000000022-2-222−2i32i3−2i32i300000000−2i32i30000000000000000000000000000
χ484444-4-4-244-2-2-2-40000000022-2-2222i3−2i32i3−2i3000000002i3−2i30000000000000000000000000000
χ494444-4-4-2-4-4-2-2-24000000002222-2-2−2i32i3−2i32i3000000002i3−2i30000000000000000000000000000
χ504444-4-4-2-4-4-2-2-24000000002222-2-22i3−2i32i3−2i300000000−2i32i30000000000000000000000000000
χ5144-4-40044-44-4-4000000000004-40000000000000000000000000000002-22-20000000000
χ5244-4-40044-44-4-4000000000004-4000000000000000000000000000000-22-220000000000
χ5344-4-4004-444-4-400000000000-440000000000000000000000000000002-2-220000000000
χ5444-4-4004-444-4-400000000000-44000000000000000000000000000000-222-20000000000
χ554-44-44-4-2002-2204-4400-44-4-220000-2-22200-2200-22000000000000000000000000000000
χ564-44-44-4-2002-2204-4-4004-44-22000022-2-200-22002-2000000000000000000000000000000
χ574-44-44-4-2002-220-44400-4-44-220000-2-222002-2002-2000000000000000000000000000000
χ584-44-44-4-2002-220-44-40044-4-22000022-2-2002-200-22000000000000000000000000000000
χ594-44-4-44400-44-400004i−4i000-440000000000000000004i−4i00000000000000000000000000
χ604-44-4-44400-44-40000−4i4i000-44000000000000000000−4i4i00000000000000000000000000
χ614-44-4-44-2002-2200004i−4i0002-20000−2i32i32i3−2i3000023−230000−2i2i00000000000000000000000000
χ624-44-4-44-2002-2200004i−4i0002-200002i3−2i3−2i32i30000−23230000−2i2i00000000000000000000000000
χ634-44-4-44-2002-220000−4i4i0002-20000−2i32i32i3−2i30000−232300002i−2i00000000000000000000000000
χ644-44-4-44-2002-220000−4i4i0002-200002i3−2i3−2i32i3000023−2300002i−2i00000000000000000000000000
χ6588-8-800-48-8-44400000000000-4400000000000000000000000000000000000000000000
χ6688-8-800-4-88-444000000000004-400000000000000000000000000000000000000000000
χ678-8-8800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800-40044-4000000000000043−43000000000000000000000000000000000000000000
χ698-8-8800-40044-40000000000000−4343000000000000000000000000000000000000000000

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