Finite Group Databasebeta

← Group #10692072

Character table — Group #10692072

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order1222223444444666444661212121212121212888812122424242424242424226666882424242424444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111
χ91111-1-111-1-1-11-111111-1-1-111-1-1-1-1-1-1i−ii−i11iiii−i−i−i−i1-111-1-1i−iii−i−i11-1-1ii−i−iii−i−i1-1
χ101111-1-111-1-1-11-111111-1-1-111-1-1-1-1-1-1i−ii−i11iiii−i−i−i−i1-111-1-1i−iii−i−i-1-111−i−iii−i−iii-11
χ111111-1-111-1-1-11-111111-1-1-111-1-1-1-1-1-1i−ii−i11iiii−i−i−i−i-11-1-111−ii−i−iii11-1-1−i−iiiii−i−i-11
χ121111-1-111-1-1-11-111111-1-1-111-1-1-1-1-1-1i−ii−i11iiii−i−i−i−i-11-1-111−ii−i−iii-1-111ii−i−i−i−iii1-1
χ131111-1-111-1-1-11-111111-1-1-111-1-1-1-1-1-1−ii−ii11−i−i−i−iiiii1-111-1-1−ii−i−iii11-1-1−i−iii−i−iii1-1
χ141111-1-111-1-1-11-111111-1-1-111-1-1-1-1-1-1−ii−ii11−i−i−i−iiiii1-111-1-1−ii−i−iii-1-111ii−i−iii−i−i-11
χ151111-1-111-1-1-11-111111-1-1-111-1-1-1-1-1-1−ii−ii11−i−i−i−iiiii-11-1-111i−iii−i−i11-1-1ii−i−i−i−iii-11
χ161111-1-111-1-1-11-111111-1-1-111-1-1-1-1-1-1−ii−ii11−i−i−i−iiiii-11-1-111i−iii−i−i-1-111−i−iiiii−i−i1-1
χ17222222222-222-2222-2-2-222222-2-2-2-220000-2-2000000000000000000002-22-20000000000
χ18222222222-222-2222-2-2-222222-2-2-2-220000-2-200000000000000000000-22-220000000000
χ192222222-2-22-2-222222-2-222-2-2-2-2-222-200002-200000000000000000000000000002-22-200
χ202222222-2-22-2-222222-2-222-2-2-2-2-222-200002-20000000000000000000000000000-22-2200
χ212222222-2-2-2-2-2-2222-22222-2-2-222-2-2-22i−2i−2i2i-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ222222222-2-2-2-2-2-2222-22222-2-2-222-2-2-2−2i2i2i−2i-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100000000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111100000000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-1-1-2-2111100000000000000
χ26222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2111122-1-1-1-100000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-11112i−2i−2i2i1-1−i−iii−i−iii00−i3i3−i3i3003−33−300000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-11112i−2i−2i2i1-1−i−iii−i−iii00i3−i3i3−i300−33−3300000000000000
χ29222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-1111−2i2i2i−2i1-1ii−i−iii−i−i00−i3i3−i3i300−33−3300000000000000
χ30222222-1-2-2-2-2-2-2-1-1-1-222-1-1111-1-1111−2i2i2i−2i1-1ii−i−iii−i−i00i3−i3i3−i3003−33−300000000000000
χ312222-2-222-22-222222-2-22-2-222-22222-20000-2-2000000000000000000002-2-220000000000
χ322222-2-222-22-222222-2-22-2-222-22222-20000-2-200000000000000000000-222-20000000000
χ332222-2-22-2222-22222-22-2-2-2-2-22-2-222222-2-2-2222-2-2-2-22200000000000000000000000000
χ342222-2-22-2222-22222-22-2-2-2-2-22-2-2222-2-222-22-2-22222-2-200000000000000000000000000
χ352222-2-22-22-22-2-22222-22-2-2-2-2222-2-2200002-200000000000000000000000000002i−2i−2i2i00
χ362222-2-22-22-22-2-22222-22-2-2-2-2222-2-2200002-20000000000000000000000000000−2i2i2i−2i00
χ372222-2-2-12-2-2-22-2-1-1-122-211-1-11111112i−2i2i−2i-1-1−i−i−i−iiiii2-2-1-1112i−2i−i−iii00000000000000
χ382222-2-2-12-2-2-22-2-1-1-122-211-1-11111112i−2i2i−2i-1-1−i−i−i−iiiii-2211-1-1−2i2iii−i−i00000000000000
χ392222-2-2-12-2-2-22-2-1-1-122-211-1-1111111−2i2i−2i2i-1-1iiii−i−i−i−i2-2-1-111−2i2iii−i−i00000000000000
χ402222-2-2-12-2-2-22-2-1-1-122-211-1-1111111−2i2i−2i2i-1-1iiii−i−i−i−i-2211-1-12i−2i−i−iii00000000000000
χ412222-2-2-1-2222-22-1-1-1-22-21111-111-1-1-122-2-21-1-1-11111-1-100−i3i3i3−i300−i3i3i3−i300000000000000
χ422222-2-2-1-2222-22-1-1-1-22-21111-111-1-1-122-2-21-1-1-11111-1-100i3−i3−i3i300i3−i3−i3i300000000000000
χ432222-2-2-1-2222-22-1-1-1-22-21111-111-1-1-1-2-2221-111-1-1-1-11100−i3i3i3−i300i3−i3−i3i300000000000000
χ442222-2-2-1-2222-22-1-1-1-22-21111-111-1-1-1-2-2221-111-1-1-1-11100i3−i3−i3i300−i3i3i3−i300000000000000
χ45444444-244-444-4-2-2-2-4-4-4-2-2-2-2-22222-20000220000000000000000000000000000000000
χ46444444-2-4-44-4-44-2-2-24-4-4-2-222222-2-220000-220000000000000000000000000000000000
χ474444-4-4-24-44-444-2-2-2-4-4422-2-22-2-2-2-220000220000000000000000000000000000000000
χ484444-4-4-2-44-44-4-4-2-2-24-442222-2-2-222-20000-220000000000000000000000000000000000
χ4944-4-400400400-44-4-400000000004-400000000000000000000000000000002i−2i2i−2i000000
χ5044-4-400400400-44-4-400000000004-40000000000000000000000000000000−2i2i−2i2i000000
χ5144-4-400400-40044-4-40000000000-4400000000000000000000000000000002-2-22000000
χ5244-4-400400-40044-4-40000000000-440000000000000000000000000000000-222-2000000
χ534-44-44-44440-4-40-44-40004-44-440000-40000000000000000000000000000000000000000
χ544-44-44-44-4-40440-44-40004-4-44-4000040000000000000000000000000000000000000000
χ554-44-44-4-2440-4-402-22000-22-22-2000020000006−66−66−66−600000000000000000000000000
χ564-44-44-4-2440-4-402-22000-22-22-200002000000−66−66−66−6600000000000000000000000000
χ574-44-44-4-2-4-404402-22000-222-220000-2000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ584-44-44-4-2-4-404402-22000-222-220000-2000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ594-44-4-4444-404-40-44-4000-444-4-4000040000000000000000000000000000000000000000
χ604-44-4-444-440-440-44-4000-44-4440000-40000000000000000000000000000000000000000
χ614-44-4-44-24-404-402-220002-2-2220000-2000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ624-44-4-44-24-404-402-220002-2-2220000-2000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ634-44-4-44-2-440-4402-220002-22-2-2000020000006−6−66−666−600000000000000000000000000
χ644-44-4-44-2-440-4402-220002-22-2-200002000000−666−66−6−6600000000000000000000000000
χ6588-8-800-400800-8-4440000000000-4400000000000000000000000000000000000000000
χ6688-8-800-400-8008-44400000000004-400000000000000000000000000000000000000000
χ678-8-88008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-8800-400000044-400000000−4i34i30000000000000000000000000000000000000000000
χ698-8-8800-400000044-4000000004i3−4i30000000000000000000000000000000000000000000

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