Finite Group Databasebeta

← Group #10691990

Character table — Group #10691990

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244488121212122424242444448888888824
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ91111-1-111-11-1-1-111111-1-1-1111-1-1-1-11ii−i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-11-11-1ii−i−iii−i−i1-1
χ101111-1-111-11-1-1-111111-1-1-1111-1-1-1-11ii−i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-1-11-11−i−iii−i−iii-11
χ111111-1-111-11-1-1-111111-1-1-1111-1-1-1-11ii−i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-1111-11-1ii−i−i−i−iii-11
χ121111-1-111-11-1-1-111111-1-1-1111-1-1-1-11ii−i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-111-11-11−i−iiiii−i−i1-1
χ131111-1-111-11-1-1-111111-1-1-1111-1-1-1-11−i−iii1-1−i−i−i−iiiiii−i-11ii−i−i-1-1111-11-1−i−iiiii−i−i-11
χ141111-1-111-11-1-1-111111-1-1-1111-1-1-1-11−i−iii1-1−i−i−i−iiiiii−i-11ii−i−i-1-111-11-11ii−i−i−i−iii1-1
χ151111-1-111-11-1-1-111111-1-1-1111-1-1-1-11−i−iii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-11-11-1−i−iii−i−iii1-1
χ161111-1-111-11-1-1-111111-1-1-1111-1-1-1-11−i−iii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-1-11-11ii−i−iii−i−i-11
χ172222222222-2-22222-2-2-2222-2-222-2-220000-2-20000000000000000000022-2-20000000000
χ182222222222-2-22222-2-2-2222-2-222-2-220000-2-200000000000000000000-2-2220000000000
χ192222222-2-2-222-22222-2-222-2-2-2-2-222-200002-20000000000000000000000002-22-2000000
χ202222222-2-2-222-22222-2-222-2-2-2-2-222-200002-2000000000000000000000000-22-22000000
χ212222222-2-2-2-2-2-2222-22222-222-2-2-2-2-22i−2i2i−2i-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ222222222-2-2-2-2-2-2222-22222-222-2-2-2-2-2−2i2i−2i2i-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
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
χ27222222-1-2-2-2-2-2-2-1-1-1-222-1-11-1-1111112i−2i2i−2i1-1−i−iii−i−iii0000−i3i3−i3i33−33−300000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-222-1-11-1-1111112i−2i2i−2i1-1−i−iii−i−iii0000i3−i3i3−i3−33−3300000000000000
χ29222222-1-2-2-2-2-2-2-1-1-1-222-1-11-1-111111−2i2i−2i2i1-1ii−i−iii−i−i0000−i3i3−i3i3−33−3300000000000000
χ30222222-1-2-2-2-2-2-2-1-1-1-222-1-11-1-111111−2i2i−2i2i1-1ii−i−iii−i−i0000i3−i3i3−i33−33−300000000000000
χ312222-2-222-2222-2222-2-22-2-22-2-2-2-22220000-22000000000000000000002-2-220000000000
χ322222-2-222-2222-2222-2-22-2-22-2-2-2-22220000-2200000000000000000000-222-20000000000
χ332222-2-22-22-2222222-22-2-2-2-2222222-22-2-22-2-222-2-2-2-22200000000000000000000000000
χ342222-2-22-22-2222222-22-2-2-2-2222222-2-222-2-2-2-2-22222-2-200000000000000000000000000
χ352222-2-22-22-2-2-222222-22-2-2-2-2-222-2-2-20000220000000000000000000000002i−2i−2i2i000000
χ362222-2-22-22-2-2-222222-22-2-2-2-2-222-2-2-2000022000000000000000000000000−2i2i2i−2i000000
χ372222-2-2-12-22-2-2-2-1-1-122-211-1-1-11111-12i2i−2i−2i-11−i−i−i−iiiii2i−2i2-2−i−iii-1-11100000000000000
χ382222-2-2-12-22-2-2-2-1-1-122-211-1-1-11111-12i2i−2i−2i-11−i−i−i−iiiii−2i2i-22ii−i−i11-1-100000000000000
χ392222-2-2-12-22-2-2-2-1-1-122-211-1-1-11111-1−2i−2i2i2i-11iiii−i−i−i−i2i−2i-22−i−iii11-1-100000000000000
χ402222-2-2-12-22-2-2-2-1-1-122-211-1-1-11111-1−2i−2i2i2i-11iiii−i−i−i−i−2i2i2-2ii−i−i-1-11100000000000000
χ412222-2-2-1-22-2222-1-1-1-22-2111-1-1-1-1-1-112-2-2211-1-11111-1-100003−3−33−333−300000000000000
χ422222-2-2-1-22-2222-1-1-1-22-2111-1-1-1-1-1-112-2-2211-1-11111-1-10000−333−33−3−3300000000000000
χ432222-2-2-1-22-2222-1-1-1-22-2111-1-1-1-1-1-11-222-21111-1-1-1-11100003−3−333−3−3300000000000000
χ442222-2-2-1-22-2222-1-1-1-22-2111-1-1-1-1-1-11-222-21111-1-1-1-1110000−333−3−333−300000000000000
χ45444444-2444-4-44-2-2-2-4-4-4-2-2-222-2-222-20000220000000000000000000000000000000000
χ46444444-2-4-4-444-4-2-2-24-4-4-2-222222-2-220000-220000000000000000000000000000000000
χ474444-4-4-24-4444-4-2-2-2-4-4422-22222-2-2-200002-20000000000000000000000000000000000
χ484444-4-4-2-44-4-4-44-2-2-24-4422222-2-22220000-2-20000000000000000000000000000000000
χ494-44-40040004i−4i04-4-400000000004i−4i000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ504-44-40040004i−4i04-4-400000000004i−4i00000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ514-44-4004000−4i4i04-4-40000000000−4i4i00000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ524-44-4004000−4i4i04-4-40000000000−4i4i000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ534-4-444-4444-400-4-44-40004-44004-400-40000000000000000000000000000000000000000
χ544-4-444-44-4-44004-44-40004-4-400-440040000000000000000000000000000000000000000
χ554-4-444-4-244-400-42-22000-22-200-22002000000i6−i6i6−i6i6−i6i6−i600000000000000000000000000
χ564-4-444-4-244-400-42-22000-22-200-22002000000−i6i6−i6i6−i6i6−i6i600000000000000000000000000
χ574-4-444-4-2-4-440042-22000-222002-200-20000006−6−666−6−6600000000000000000000000000
χ584-4-444-4-2-4-440042-22000-222002-200-2000000−666−6−666−600000000000000000000000000
χ594-4-44-4444-4-4004-44-4000-44400-4400-40000000000000000000000000000000000000000
χ604-4-44-444-44400-4-44-4000-44-4004-40040000000000000000000000000000000000000000
χ614-4-44-44-24-4-40042-220002-2-2002-20020000006−66−6−66−6600000000000000000000000000
χ624-4-44-44-24-4-40042-220002-2-2002-2002000000−66−666−66−600000000000000000000000000
χ634-4-44-44-2-44400-42-220002-2200-2200-2000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ644-4-44-44-2-44400-42-220002-2200-2200-2000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6588-8-8008000000-8-8800000000000000000000000000000000000000000000000000000
χ6688-8-800-400000044-400000043−43000000000000000000000000000000000000000000000
χ6788-8-800-400000044-4000000−4343000000000000000000000000000000000000000000000
χ688-88-800-40008i−8i0-4440000000000−4i4i00000000000000000000000000000000000000000
χ698-88-800-4000−8i8i0-44400000000004i−4i00000000000000000000000000000000000000000

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