Finite Group Databasebeta

← Group #10691988

Character table — Group #10691988

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122222344444466644466121212121212121288881212242424242424242424446612121212121244448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ91111-1-111-1-1-11-111111-1-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-11-1ii−i−iii−i−i1-1
χ101111-1-111-1-1-11-111111-1-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−i-11-11−i−iii−i−iii-11
χ111111-1-111-1-1-11-111111-1-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i-11−ii-1-111−i−iii1-11-1ii−i−i−i−iii-11
χ121111-1-111-1-1-11-111111-1-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i-11−ii-1-111−i−iii-11-11−i−iiiii−i−i1-1
χ131111-1-111-1-1-11-111111-1-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii1-1−ii11-1-1−i−iii1-11-1−i−iii−i−iii1-1
χ141111-1-111-1-1-11-111111-1-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii1-1−ii11-1-1−i−iii-11-11ii−i−iii−i−i-11
χ151111-1-111-1-1-11-111111-1-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii-11i−i-1-111ii−i−i1-11-1−i−iiiii−i−i-11
χ161111-1-111-1-1-11-111111-1-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii-11i−i-1-111ii−i−i-11-11ii−i−i−i−iii1-1
χ17222222222-2-222222-2-2-222-2-22222-2-20000-2-20000000000000000000022-2-20000000000
χ18222222222-2-222222-2-2-222-2-22222-2-20000-2-200000000000000000000-2-2220000000000
χ192222222-2-222-2-22222-2-222-2-2-2-2-2-2222-22-22-222-2-222-2-200000000000000000000000000
χ202222222-2-222-2-22222-2-222-2-2-2-2-2-222-22-222-2-2-222-2-22200000000000000000000000000
χ212222222-2-2-2-2-2-2222-2222222-2-2-2-2-2-20000-220000000000000000000000002i−2i2i−2i000000
χ222222222-2-2-2-2-2-2222-2222222-2-2-2-2-2-20000-22000000000000000000000000−2i2i−2i2i000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ26222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ27222222-1-2-222-2-2-1-1-12-2-2-1-1111111-1-12-22-2-11-1-111-1-1110000−i3i3−i3i3−i3i3−i3i300000000000000
χ28222222-1-2-222-2-2-1-1-12-2-2-1-1111111-1-12-22-2-11-1-111-1-1110000i3−i3i3−i3i3−i3i3−i300000000000000
χ29222222-1-2-222-2-2-1-1-12-2-2-1-1111111-1-1-22-22-1111-1-111-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ30222222-1-2-222-2-2-1-1-12-2-2-1-1111111-1-1-22-22-1111-1-111-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ312222-2-222-2222-2222-2-22-2-22222-2-2220000-2-2000000000000000000002-2-220000000000
χ322222-2-222-2222-2222-2-22-2-22222-2-2220000-2-200000000000000000000-222-20000000000
χ332222-2-22-2222-22222-22-2-2-2-2-2-2-222220000-220000000000000000000000002-2-22000000
χ342222-2-22-2222-22222-22-2-2-2-2-2-2-222220000-22000000000000000000000000-222-2000000
χ352222-2-22-22-2-2-222222-22-2-222-2-222-2-22i−2i−2i2i2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-22-2-2-222222-22-2-222-2-222-2-2−2i2i2i−2i2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-12-2-2-22-2-1-1-122-21111-1-111112i2i−2i−2i-1-1−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ382222-2-2-12-2-2-22-2-1-1-122-21111-1-111112i2i−2i−2i-1-1−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ392222-2-2-12-2-2-22-2-1-1-122-21111-1-11111−2i−2i2i2i-1-1iiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ402222-2-2-12-2-2-22-2-1-1-122-21111-1-11111−2i−2i2i2i-1-1iiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ412222-2-2-1-22-2-2-22-1-1-12-2211-1-111-1-1112i−2i−2i2i-11−i−iiiii−i−i0000−i3i3i3−i33−3−3300000000000000
χ422222-2-2-1-22-2-2-22-1-1-12-2211-1-111-1-1112i−2i−2i2i-11−i−iiiii−i−i0000i3−i3−i3i3−333−300000000000000
χ432222-2-2-1-22-2-2-22-1-1-12-2211-1-111-1-111−2i2i2i−2i-11ii−i−i−i−iii0000−i3i3i3−i3−333−300000000000000
χ442222-2-2-1-22-2-2-22-1-1-12-2211-1-111-1-111−2i2i2i−2i-11ii−i−i−i−iii0000i3−i3−i3i33−3−3300000000000000
χ45444444-244-4-444-2-2-2-4-4-4-2-222-2-2-2-2220000220000000000000000000000000000000000
χ46444444-2-4-4-4-4-4-4-2-2-2-444-2-2-2-222222200002-20000000000000000000000000000000000
χ474444-4-4-24-4444-4-2-2-2-4-4422-2-2-2-222-2-20000220000000000000000000000000000000000
χ484444-4-4-2-4444-44-2-2-2-44-4222222-2-2-2-200002-20000000000000000000000000000000000
χ494-44-4004004i−4i004-4-4000000000004i−4i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ504-44-4004004i−4i004-4-4000000000004i−4i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ514-44-400400−4i4i004-4-400000000000−4i4i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ524-44-400400−4i4i004-4-400000000000−4i4i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ534-4-444-444400-4-4-4-440004-4004-44-4000000000000000000000000000000000000000000
χ544-4-444-44-4-40044-4-440004-400-44-44000000000000000000000000000000000000000000
χ554-4-444-4-24400-4-422-2000-2200-22-22000000006−66−66−66−600000000000000000000000000
χ564-4-444-4-24400-4-422-2000-2200-22-2200000000−66−66−66−6600000000000000000000000000
χ574-4-444-4-2-4-4004422-2000-22002-22-2000000006−6−666−6−6600000000000000000000000000
χ584-4-444-4-2-4-4004422-2000-22002-22-200000000−666−6−666−600000000000000000000000000
χ594-4-44-4444-400-44-4-44000-44004-4-44000000000000000000000000000000000000000000
χ604-4-44-444-44004-4-4-44000-4400-444-4000000000000000000000000000000000000000000
χ614-4-44-44-24-400-4422-20002-200-222-200000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ624-4-44-44-24-400-4422-20002-200-222-200000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ634-4-44-44-2-44004-422-20002-2002-2-2200000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ644-4-44-44-2-44004-422-20002-2002-2-2200000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6588-8-8008000000-88-800000000000000000000000000000000000000000000000000000
χ6688-8-800-40000004-440000043−430000000000000000000000000000000000000000000000
χ6788-8-800-40000004-4400000−43430000000000000000000000000000000000000000000000
χ688-88-800-4008i−8i00-44400000000000−4i4i0000000000000000000000000000000000000000
χ698-88-800-400−8i8i00-444000000000004i−4i0000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.