Finite Group Databasebeta

← Group #10692940

Character table — Group #10692940

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order12222222366624444666612121212121244444444612121212121212121244448812121212242424244444442488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1
χ9111111-1-11111-111-1-111-1-11111-1-111-1-1ii−i−i-1-11111-1-1-1-111-1-1i−iii−i−iii−i−i1-1ii−i−i1-1i−i
χ10111111-1-11111-111-1-111-1-11111-1-111-1-1ii−i−i-1-11111-1-1-1-1-1-111i−iii−i−iii−i−i-11−i−iii-11−ii
χ11111111-1-11111-111-1-111-1-11111-1-111-1-1−i−iii-1-11111-1-1-1-111-1-1−ii−i−iii−i−iii1-1−i−iii1-1−ii
χ12111111-1-11111-111-1-111-1-11111-1-111-1-1−i−iii-1-11111-1-1-1-1-1-111−ii−i−iii−i−iii-11ii−i−i-11i−i
χ13111111-1-11111-111-1-111-1-11111-1-1-1-111ii−i−i-1-1-1-1-1-1111111-1-1−iiii−i−i−i−iii1-1ii−i−i-11−ii
χ14111111-1-11111-111-1-111-1-11111-1-1-1-111ii−i−i-1-1-1-1-1-11111-1-111−iiii−i−i−i−iii-11−i−iii1-1i−i
χ15111111-1-11111-111-1-111-1-11111-1-1-1-111−i−iii-1-1-1-1-1-1111111-1-1i−i−i−iiiii−i−i1-1−i−iii-11i−i
χ16111111-1-11111-111-1-111-1-11111-1-1-1-111−i−iii-1-1-1-1-1-11111-1-111i−i−i−iiiii−i−i-11ii−i−i1-1−ii
χ172222222222222-2-2-2-22222-2-2-2-2-2-2000000002-20000000022220000000000-2-200000000
χ182222222222222-2-2-2-22222-2-2-2-2-2-2000000002-200000000-2-2-2-200000000002200000000
χ1922222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-10000000000
χ2022222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-2111111110000000000
χ2122222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1111111110000-2-2-1-1-1-111110000000000
χ2222222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-10000000000
χ23222222-2-22222-2-2-22222-2-2-2-2-2-22200000000-220000000022-2-20000000000-2200000000
χ24222222-2-22222-2-2-22222-2-2-2-2-2-22200000000-2200000000-2-22200000000002-200000000
χ25222222-2-2-1-1-1-1-222-2-2-1-111-1-1-1-11122-2-22i2i−2i−2i11-1-1-1-1111100002i−2i−i−iii−i−iii0000000000
χ26222222-2-2-1-1-1-1-222-2-2-1-111-1-1-1-11122-2-2−2i−2i2i2i11-1-1-1-111110000−2i2iii−i−iii−i−i0000000000
χ27222222-2-2-1-1-1-1-222-2-2-1-111-1-1-1-111-2-2222i2i−2i−2i111111-1-1-1-10000−2i2i−i−iiiii−i−i0000000000
χ28222222-2-2-1-1-1-1-222-2-2-1-111-1-1-1-111-2-222−2i−2i2i2i111111-1-1-1-100002i−2iii−i−i−i−iii0000000000
χ292222-2-2222222-22-22-2-2-22222-2-22200000000-2-20000000000000000000000002-22-20000
χ302222-2-2222222-22-22-2-2-22222-2-22200000000-2-2000000000000000000000000-22-220000
χ312222-2-2222222-2-22-22-2-222-2-222-2-200002-22-2-22000000000000002-22-200000000000000
χ322222-2-2222222-2-22-22-2-222-2-222-2-20000-22-22-2200000000000000-22-2200000000000000
χ332222-2-222-1-1-1-1-2-22-2211-1-111-1-11100002-22-21-133−3−333−3−3000000-11-113−33−30000000000
χ342222-2-222-1-1-1-1-2-22-2211-1-111-1-11100002-22-21-1−3−333−3−333000000-11-11−33−330000000000
χ352222-2-222-1-1-1-1-2-22-2211-1-111-1-1110000-22-221-133−3−333−3−30000001-11-1−33−330000000000
χ362222-2-222-1-1-1-1-2-22-2211-1-111-1-1110000-22-221-1−3−333−3−3330000001-11-13−33−30000000000
χ372222-2-2-2-2222222-2-22-2-2-2-222-2-2-2-200000000220000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2222222-2-22-2-2-2-222-2-2-2-20000000022000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-222222-222-2-2-2-2-2-2-2222200002i−2i−2i2i2-2000000000000002i−2i−2i2i00000000000000
χ402222-2-2-2-222222-222-2-2-2-2-2-2-222220000−2i2i2i−2i2-200000000000000−2i2i2i−2i00000000000000
χ412222-2-2-2-2-1-1-1-12-222-2111111-1-1-1-100002i−2i−2i2i-1133−3−3−3−333000000−iii−ii3−i3−i3i30000000000
χ422222-2-2-2-2-1-1-1-12-222-2111111-1-1-1-100002i−2i−2i2i-11−3−33333−3−3000000−iii−i−i3i3i3−i30000000000
χ432222-2-2-2-2-1-1-1-12-222-2111111-1-1-1-10000−2i2i2i−2i-1133−3−3−3−333000000i−i−ii−i3i3i3−i30000000000
χ442222-2-2-2-2-1-1-1-12-222-2111111-1-1-1-10000−2i2i2i−2i-11−3−33333−3−3000000i−i−iii3−i3−i3i30000000000
χ4544444444-2-2-2-24-4-4-4-4-2-2-2-222222200000000-2200000000000000000000000000000000
χ46444444-4-4-2-2-2-2-4-4-444-2-2222222-2-2000000002-200000000000000000000000000000000
χ474444-4-444-2-2-2-2-44-44-422-2-2-2-222-2-2000000002200000000000000000000000000000000
χ484444-4-4-4-4-2-2-2-244-4-442222-2-2222200000000-2-200000000000000000000000000000000
χ494-44-4004-444-4-400000004-40000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ504-44-4004-444-4-400000004-4000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ514-44-4004-4-2-2220000000-2223−230023−232i−2i2i−2i000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ524-44-4004-4-2-2220000000-2223−230023−23−2i2i−2i2i000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ534-44-4004-4-2-2220000000-22−232300−23232i−2i2i−2i000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ544-44-4004-4-2-2220000000-22−232300−2323−2i2i−2i2i000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ554-44-400-4444-4-40000000-440000002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ564-44-400-4444-4-40000000-44000000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ574-44-400-44-2-22200000002-223−2300−23232i−2i−2i2i000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ584-44-400-44-2-22200000002-223−2300−2323−2i2i2i−2i000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ594-44-400-44-2-22200000002-2−23230023−232i−2i−2i2i000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ604-44-400-44-2-22200000002-2−23230023−23−2i2i2i−2i000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ614-4-444-4004-4-44000004-4000000000000000000000000004-40000000000000000000000
χ624-4-444-4004-4-44000004-400000000000000000000000000-440000000000000000000000
χ634-4-44-44004-4-4400000-4400000000000000000000000000004-400000000000000000000
χ644-4-44-44004-4-4400000-440000000000000000000000000000-4400000000000000000000
χ6588-8-800008-88-8000000000000000000000000000000000000000000000000000000000
χ6688-8-80000-44-440000000000043−4300000000000000000000000000000000000000000000
χ6788-8-80000-44-4400000000000−434300000000000000000000000000000000000000000000
χ688-8-888-800-444-400000-4400000000000000000000000000000000000000000000000000
χ698-8-88-8800-444-4000004-400000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.