Finite Group Databasebeta

← Group #10691087

Character table — Group #10691087

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order122222344444466612121212444444466888812121212121212121212121212122424242424242424246688888812121212242424242424242424242424888888882288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-111-1-1-11-1111-1-1-1-11111-1-1-1-1-1ii−i−i1111-1-11111-1-1-1-1iiii−i−i−i−i1-111i−iii−i−i1-1-1-1ii−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-111-1-1-11-1111-1-1-1-11111-1-1-1-1-1ii−i−i1111-1-11111-1-1-1-1iiii−i−i−i−i1-111i−iii−i−i1-1-1-1ii−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-111-1-1-11-1111-1-1-1-11111-1-1-1-1-1−i−iii1111-1-11111-1-1-1-1−i−i−i−iiiii1-111−ii−i−iii1-1-1-1−i−iii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-111-1-1-11-1111-1-1-1-11111-1-1-1-1-1−i−iii1111-1-11111-1-1-1-1−i−i−i−iiiii1-111−ii−i−iii1-1-1-1−i−iii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-111-1-1-11-1111-1-1-1-111-1-111-1-1-1ii−i−i1111-1-1-1-1-1-11111iiii−i−i−i−i-11-1-1i−i−i−iii1-111ii−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-111-1-1-11-1111-1-1-1-111-1-111-1-1-1ii−i−i1111-1-1-1-1-1-11111iiii−i−i−i−i-11-1-1i−i−i−iii1-111ii−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-111-1-1-11-1111-1-1-1-111-1-111-1-1-1−i−iii1111-1-1-1-1-1-11111−i−i−i−iiiii-11-1-1−iiii−i−i1-111−i−iiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-111-1-1-11-1111-1-1-1-111-1-111-1-1-1−i−iii1111-1-1-1-1-1-11111−i−i−i−iiiii-11-1-1−iiii−i−i1-111−i−iiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222-2222-22222222-2-22222-222000022-2-2-2-22222222200000000-2-2-2-2000000-2-2-2-2000000000000000000000000
χ1822222222-2222-22222222-2-2-2-2-2-2-222000022-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000-2-222000000000000000000000000
χ192222222-22-2-2-22222-2-2-2-22-20000-2220000-2-2-2-22200000000000000000000002i−2i2i−2i2-20000002i2i−2i−2i2i2i−2i−2i000000000000
χ202222222-22-2-2-22222-2-2-2-22-20000-2220000-2-2-2-2220000000000000000000000−2i2i−2i2i2-2000000−2i−2i2i2i−2i−2i2i2i000000000000
χ212222222-2-2-2-2-2-2222-2-2-2-2-2200002222i2i−2i−2i-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i0000−2i2i0000-2200−2i−2i2i2i00000000000000000000
χ222222222-2-2-2-2-2-2222-2-2-2-2-220000222−2i−2i2i2i-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i00002i−2i0000-22002i2i−2i−2i00000000000000000000
χ23222222-1222222-1-1-1-1-1-1-12222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-12222222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111122-1-1-2-2-2-2-2-2-1-1-1-1111111111111000000000000
χ25222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-12222-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-21122-2-2-2-2-1-111-1-1-1-111111111000000000000
χ26222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-2-2-2-2-1-1-1-1-1-11111111111111111-2-211-2-22222-1-1111111-1-1-1-1-1-1-1-1000000000000
χ27222222-12-2222-2-1-1-1-1-1-1-1-2-22222-2-1-10000-1-11111-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i3-2-2110000001111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-12-2222-2-1-1-1-1-1-1-1-2-22222-2-1-10000-1-11111-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i3-2-2110000001111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-12-2222-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-10000-1-1111111111111−i3−i3i3i3−i3−i3i3i322-1-100000011-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000
χ30222222-12-2222-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-10000-1-1111111111111i3i3−i3−i3i3i3−i3−i322-1-100000011-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000
χ31222222-1-22-2-2-22-1-1-111112-20000-2-1-100001111-1-1−i3−i3i3i3−i3−i3i3i333−3−3−3−33300−i3i3002i−2i2i−2i-11−i3i3−333−3−i−iii−i−iii000000000000
χ32222222-1-22-2-2-22-1-1-111112-20000-2-1-100001111-1-1−i3−i3i3i3−i3−i3i3i3−3−33333−3−300−i3i300−2i2i−2i2i-11−i3i33−3−33ii−i−iii−i−i000000000000
χ33222222-1-22-2-2-22-1-1-111112-20000-2-1-100001111-1-1i3i3−i3−i3i3i3−i3−i333−3−3−3−33300i3−i300−2i2i−2i2i-11i3−i3−333−3ii−i−iii−i−i000000000000
χ34222222-1-22-2-2-22-1-1-111112-20000-2-1-100001111-1-1i3i3−i3−i3i3i3−i3−i3−3−33333−3−300i3−i3002i−2i2i−2i-11i3−i33−3−33−i−iii−i−iii000000000000
χ35222222-1-2-2-2-2-2-2-1-1-11111-2200002-1-12i2i−2i−2i11-1-111−i3−i3i3i3−i3−i3i3i3−i−i−i−iiiii00i3−i3−2i2i00001-1i3−i3ii−i−i3−3−333−3−33000000000000
χ36222222-1-2-2-2-2-2-2-1-1-11111-2200002-1-12i2i−2i−2i11-1-111i3i3−i3−i3i3i3−i3−i3−i−i−i−iiiii00−i3i3−2i2i00001-1−i3i3ii−i−i−333−3−333−3000000000000
χ37222222-1-2-2-2-2-2-2-1-1-11111-2200002-1-1−2i−2i2i2i11-1-111−i3−i3i3i3−i3−i3i3i3iiii−i−i−i−i00i3−i32i−2i00001-1i3−i3−i−iii−333−3−333−3000000000000
χ38222222-1-2-2-2-2-2-2-1-1-11111-2200002-1-1−2i−2i2i2i11-1-111i3i3−i3−i3i3i3−i3−i3iiii−i−i−i−i00−i3i32i−2i00001-1−i3i3−i−iii3−3−333−3−33000000000000
χ392222-2-2222-2-222222-2-2-2-2-2-222-2-22-2-2000022-2-2222222-2-2-2-200000000-22-2-2000000-2222000000000000000000000000
χ402222-2-2222-2-222222-2-2-2-2-2-2-2-2222-2-2000022-2-222-2-2-2-22222000000002-222000000-22-2-2000000000000000000000000
χ412222-2-22-2222-222222222-220000-2-2-22222-2-2222200000000222222220000-2-20000-2-200-2-2-2-200000000000000000000
χ422222-2-22-2222-222222222-220000-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2-2-2-2-20000220000-2-200222200000000000000000000
χ432222-2-22-2-222-2-222222222-200002-2-20000-2-2-2-2-2-200000000000000000000002-2-222200000022-2-2-2-222000000000000
χ442222-2-22-2-222-2-222222222-200002-2-20000-2-2-2-2-2-20000000000000000000000-222-222000000-2-22222-2-2000000000000
χ452222-2-2-122-2-222-1-1-11111-2-222-2-22110000-1-111-1-1-1-1-1-1111133−3−3−3−333-22110000001-1-1-13−3−333−33−3−33−33000000000000
χ462222-2-2-122-2-222-1-1-11111-2-222-2-22110000-1-111-1-1-1-1-1-11111−3−33333−3−3-22110000001-1-1-1−333−3−33−333−33−3000000000000
χ472222-2-2-122-2-222-1-1-11111-2-2-2-2222110000-1-111-1-11111-1-1-1-133−3−3−3−3332-2-1-10000001-1113−3−33−33−333−33−3000000000000
χ482222-2-2-122-2-222-1-1-11111-2-2-2-2222110000-1-111-1-11111-1-1-1-1−3−33333−3−32-2-1-10000001-111−333−33−33−3−33−33000000000000
χ492222-2-2-12-2-2-22-2-1-1-111112222-2-2-2112i2i−2i−2i-1-1-1-111-1-1-1-11111−i−i−i−iiiii2-2-1-12i−2i2i2i−2i−2i-1111−i−iii−i−i−i−iiiii000000000000
χ502222-2-2-12-2-2-22-2-1-1-111112222-2-2-211−2i−2i2i2i-1-1-1-111-1-1-1-11111iiii−i−i−i−i2-2-1-1−2i2i−2i−2i2i2i-1111ii−i−iiiii−i−i−i−i000000000000
χ512222-2-2-12-2-2-22-2-1-1-1111122-2-222-2112i2i−2i−2i-1-1-1-1111111-1-1-1-1−i−i−i−iiiii-22112i−2i−2i−2i2i2i-11-1-1−i−iiiiiii−i−i−i−i000000000000
χ522222-2-2-12-2-2-22-2-1-1-1111122-2-222-211−2i−2i2i2i-1-1-1-1111111-1-1-1-1iiii−i−i−i−i-2211−2i2i2i2i−2i−2i-11-1-1ii−i−i−i−i−i−iiiii000000000000
χ532222-2-2-1-2222-22-1-1-1-1-1-1-1-220000-211222211-1-1-1-1−i3−i3i3i3i3i3−i3−i3-1-1-1-1-1-1-1-100i3−i3-2-2000011−i3i31111−i3i3i3−i3i3−i3−i3i3000000000000
χ542222-2-2-1-2222-22-1-1-1-1-1-1-1-220000-211222211-1-1-1-1i3i3−i3−i3−i3−i3i3i3-1-1-1-1-1-1-1-100−i3i3-2-2000011i3−i31111i3−i3−i3i3−i3i3i3−i3000000000000
χ552222-2-2-1-2222-22-1-1-1-1-1-1-1-220000-211-2-2-2-211-1-1-1-1−i3−i3i3i3i3i3−i3−i31111111100i3−i322000011−i3i3-1-1-1-1i3−i3−i3i3−i3i3i3−i3000000000000
χ562222-2-2-1-2222-22-1-1-1-1-1-1-1-220000-211-2-2-2-211-1-1-1-1i3i3−i3−i3−i3−i3i3i31111111100−i3i322000011i3−i3-1-1-1-1−i3i3i3−i3i3−i3−i3i3000000000000
χ572222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-200002110000111111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300−i3i3002-2-22-1-1i3−i3i3−i3i3−i3-1-11111-1-1000000000000
χ582222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-200002110000111111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300−i3i300-222-2-1-1i3−i3−i3i3−i3i311-1-1-1-111000000000000
χ592222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-200002110000111111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300i3−i300-222-2-1-1−i3i3i3−i3i3−i311-1-1-1-111000000000000
χ602222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-200002110000111111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300i3−i3002-2-22-1-1−i3i3−i3i3−i3i3-1-11111-1-1000000000000
χ6122-2-22-22202-2-202-2-222-2-2002i−2i2i−2i02-200002-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000002−22−2−i2i2−i2i20000
χ6222-2-22-22202-2-202-2-222-2-2002i−2i2i−2i02-200002-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−22−22i2−i2i2−i20000
χ6322-2-22-22202-2-202-2-222-2-200−2i2i−2i2i02-200002-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000002−22−2i2−i2i2−i20000
χ6422-2-22-22202-2-202-2-222-2-200−2i2i−2i2i02-200002-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−22−22−i2i2−i2i20000
χ6522-2-2-22220-22-202-2-2-2-222002i−2i−2i2i0-2200002-200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−i2i2i2−i2−222−20000
χ6622-2-2-22220-22-202-2-2-2-222002i−2i−2i2i0-2200002-200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000i2−i2−i2i22−2−220000
χ6722-2-2-22220-22-202-2-2-2-22200−2i2i2i−2i0-2200002-20000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−i2i2i2−i22−2−220000
χ6822-2-2-22220-22-202-2-2-2-22200−2i2i2i−2i0-2200002-20000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000i2−i2−i2i2−222−20000
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χ864-44-400-204000-42-22−2323−23230000000002i2−2i22i2−2i200−2323-2200000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000
χ874-44-400-20-400042-2223−2323−2300000000022−22−222200−23232-2000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000
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χ904-44-400-20-400042-22−2323−2323000000000−222222−220023−232-200000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000000000000
χ918-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000000000
χ938-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000000000

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