Finite Group Databasebeta

← Group #10692900

Character table — Group #10692900

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order12222234466644444661212121212121212444488881212121212121212121244448824242424242424244488882288
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
χ91111111-1-1111-111-1-1111111-1-1-1-111-1-1ii−i−i-1-11111-1-1-1-111-1-1i−iii−i−iii−i−i1-1ii−i−i1-1i−i
χ101111111-1-1111-111-1-1111111-1-1-1-111-1-1ii−i−i-1-11111-1-1-1-1-1-111i−iii−i−iii−i−i-11−i−iii-11−ii
χ111111111-1-1111-111-1-1111111-1-1-1-111-1-1−i−iii-1-11111-1-1-1-111-1-1−ii−i−iii−i−iii1-1−i−iii1-1−ii
χ121111111-1-1111-111-1-1111111-1-1-1-111-1-1−i−iii-1-11111-1-1-1-1-1-111−ii−i−iii−i−iii-11ii−i−i-11i−i
χ131111111-1-1111-111-1-1111111-1-1-1-1-1-111ii−i−i-1-1-1-1-1-1111111-1-1−iiii−i−i−i−iii1-1ii−i−i-11−ii
χ141111111-1-1111-111-1-1111111-1-1-1-1-1-111ii−i−i-1-1-1-1-1-11111-1-111−iiii−i−i−i−iii-11−i−iii1-1i−i
χ151111111-1-1111-111-1-1111111-1-1-1-1-1-111−i−iii-1-1-1-1-1-1111111-1-1i−i−i−iiiii−i−i1-1−i−iii-11i−i
χ161111111-1-1111-111-1-1111111-1-1-1-1-1-111−i−iii-1-1-1-1-1-11111-1-111i−i−i−iiiii−i−i-11ii−i−i1-1−ii
χ172222222222222-2-2-2-222-2-2-2-222-2-2000000002-20000000022220000000000-2-200000000
χ182222222222222-2-2-2-222-2-2-2-222-2-2000000002-200000000-2-2-2-200000000002200000000
χ192222222-2-2222-2-2-22222-2-2-2-2-2-22200000000-220000000022-2-20000000000-2200000000
χ202222222-2-2222-2-2-22222-2-2-2-2-2-22200000000-2200000000-2-22200000000002-200000000
χ21222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-10000000000
χ22222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-2111111110000000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1111111110000-2-2-1-1-1-111110000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-10000000000
χ25222222-1-2-2-1-1-1-222-2-2-1-1-1-1-1-1111122-2-22i2i−2i−2i11-1-1-1-1111100002i−2i−i−iii−i−iii0000000000
χ26222222-1-2-2-1-1-1-222-2-2-1-1-1-1-1-1111122-2-2−2i−2i2i2i11-1-1-1-111110000−2i2iii−i−iii−i−i0000000000
χ27222222-1-2-2-1-1-1-222-2-2-1-1-1-1-1-11111-2-2222i2i−2i−2i111111-1-1-1-10000−2i2i−i−iiiii−i−i0000000000
χ28222222-1-2-2-1-1-1-222-2-2-1-1-1-1-1-11111-2-222−2i−2i2i2i111111-1-1-1-100002i−2iii−i−i−i−iii0000000000
χ292222-2-2222222-22-22-2-2-222-2-2222200000000-2-20000000000000000000000002-22-20000
χ302222-2-2222222-22-22-2-2-222-2-2222200000000-2-2000000000000000000000000-22-220000
χ312222-2-2222222-2-22-22-2-2-2-22222-2-200002-22-2-22000000000000002-22-200000000000000
χ322222-2-2222222-2-22-22-2-2-2-22222-2-20000-22-22-2200000000000000-22-2200000000000000
χ332222-2-22-2-222222-2-22-2-222-2-2-2-2-2-200000000220000000000000000000000002i−2i−2i2i0000
χ342222-2-22-2-222222-2-22-2-222-2-2-2-2-2-20000000022000000000000000000000000−2i2i2i−2i0000
χ352222-2-22-2-22222-222-2-2-2-2-222-2-22200002i−2i−2i2i2-2000000000000002i−2i−2i2i00000000000000
χ362222-2-22-2-22222-222-2-2-2-2-222-2-2220000−2i2i2i−2i2-200000000000000−2i2i2i−2i00000000000000
χ372222-2-2-122-1-1-1-2-22-221111-1-1-1-11100002-22-21-133−3−333−3−3000000-11-113−33−30000000000
χ382222-2-2-122-1-1-1-2-22-221111-1-1-1-11100002-22-21-1−3−333−3−333000000-11-11−33−330000000000
χ392222-2-2-122-1-1-1-2-22-221111-1-1-1-1110000-22-221-133−3−333−3−30000001-11-1−33−330000000000
χ402222-2-2-122-1-1-1-2-22-221111-1-1-1-1110000-22-221-1−3−333−3−3330000001-11-13−33−30000000000
χ412222-2-2-1-2-2-1-1-12-222-21111-1-111-1-100002i−2i−2i2i-1133−3−3−3−333000000−iii−ii3−i3−i3i30000000000
χ422222-2-2-1-2-2-1-1-12-222-21111-1-111-1-100002i−2i−2i2i-11−3−33333−3−3000000−iii−i−i3i3i3−i30000000000
χ432222-2-2-1-2-2-1-1-12-222-21111-1-111-1-10000−2i2i2i−2i-1133−3−3−3−333000000i−i−ii−i3i3i3−i30000000000
χ442222-2-2-1-2-2-1-1-12-222-21111-1-111-1-10000−2i2i2i−2i-11−3−33333−3−3000000i−i−iii3−i3−i3i30000000000
χ45444444-244-2-2-24-4-4-4-4-2-22222-2-22200000000-2200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-4-444-2-2222222-2-2000000002-200000000000000000000000000000000
χ474444-4-4-244-2-2-2-44-44-422-2-222-2-2-2-2000000002200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-244-4-4422-2-222222200000000-2-200000000000000000000000000000000
χ4944-4-40044-44-4-4000000000004-4002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5044-4-40044-44-4-4000000000004-400−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5144-4-4004-444-4-400000000000-44002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5244-4-4004-444-4-400000000000-4400−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5344-4-400-24-4-222000000023−2300-2223−232i−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
χ5444-4-400-24-4-222000000023−2300-2223−23−2i2i−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
χ5544-4-400-24-4-2220000000−232300-22−23232i−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
χ5644-4-400-24-4-2220000000−232300-22−2323−2i2i−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
χ5744-4-400-2-44-222000000023−23002-2−23232i−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
χ5844-4-400-2-44-222000000023−23002-2−2323−2i2i2i−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
χ5944-4-400-2-44-2220000000−2323002-223−232i−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
χ6044-4-400-2-44-2220000000−2323002-223−23−2i2i2i−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
χ614-44-44-4400-44-4000004-400000000000000000000000000004i−4i00000000000000000000
χ624-44-44-4400-44-4000004-40000000000000000000000000000−4i4i00000000000000000000
χ634-44-4-44400-44-400000-44000000000000000000000000004-40000000000000000000000
χ644-44-4-44400-44-400000-4400000000000000000000000000-440000000000000000000000
χ658-88-88-8-4004-4400000-4400000000000000000000000000000000000000000000000000
χ668-88-8-88-4004-44000004-400000000000000000000000000000000000000000000000000
χ678-8-8800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800-40044-400000000043−430000000000000000000000000000000000000000000000
χ698-8-8800-40044-4000000000−43430000000000000000000000000000000000000000000000

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