Finite Group Databasebeta

← Group #10691816

Character table — Group #10691816

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order12223444444666121212122444888812121212242424242424242422446666688888812121212121212242424242424242424242424888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111-1-1-1-1111-1-1-1-1-11-11ii−i−i11-1-1iiii−i−i−i−i11-1-1-11111i−iii−i−i1-11-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111111-1-1-1-1111-1-1-1-1-11-11ii−i−i11-1-1iiii−i−i−i−i11-1-1-11111i−iii−i−i1-11-1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-11−ii
χ111111111-1-1-1-1111-1-1-1-1-11-11ii−i−i11-1-1iiii−i−i−i−i-1-111-1-1-1-1-1i−i−i−iii1-111111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111111-1-1-1-1111-1-1-1-1-11-11ii−i−i11-1-1iiii−i−i−i−i-1-111-1-1-1-1-1i−i−i−iii1-111111ii−i−i−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111111-1-1-1-1111-1-1-1-1-11-11−i−iii11-1-1−i−i−i−iiiii11-1-1-11111−ii−i−iii1-11-1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111111-1-1-1-1111-1-1-1-1-11-11−i−iii11-1-1−i−i−i−iiiii11-1-1-11111−ii−i−iii1-11-1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111111-1-1-1-1111-1-1-1-1-11-11−i−iii11-1-1−i−i−i−iiiii-1-111-1-1-1-1-1−iiii−i−i1-111111−i−iiiiiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111111-1-1-1-1111-1-1-1-1-11-11−i−iii11-1-1−i−i−i−iiiii-1-111-1-1-1-1-1−iiii−i−i1-111111−i−iiiiiii−i−i−i−i-1-111ii−i−i1-1−ii
χ17222222222222222222-2-2-2-222222222222222220000-20000-2-20000-2-2-20000-2-2-2-200000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000-20000220000-2-2-20000222200000000000000000000
χ192222222-2-2-2-2222-2-2-2-22-22-22i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i000020000−2i2i0000-22-20000−2i−2i2i2i00000000000000000000
χ202222222-2-2-2-2222-2-2-2-22-22-2−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i0000200002i−2i0000-22-200002i2i−2i−2i00000000000000000000
χ2122222-2-222-2-222222222-2-220000-2-2-2-2000000002-22-2222-2-2000000-2-2222-2-2000000000000000000000000
χ2222222-2-222-2-222222222-2-220000-2-2-2-200000000-22-222-2-222000000-2-22-2-222000000000000000000000000
χ2322222-2-222-2-22222222-222-20000-2-2-2-2000000000000-20000002-22-222-20000000022-2-222-2-2000000000000
χ2422222-2-222-2-22222222-222-20000-2-2-2-2000000000000-2000000-22-2222-200000000-2-222-2-222000000000000
χ2522222-2-2-2-222222-2-2-2-222-2-20000-2-22200000000000020000002i−2i−2i2i2-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2622222-2-2-2-222222-2-2-2-222-2-20000-2-2220000000000002000000−2i2i2i−2i2-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2722222-2-2-2-222222-2-2-2-2-2-2220000-2-222000000002-2-22-222-2-2000000-222-2-222000000000000000000000000
χ2822222-2-2-2-222222-2-2-2-2-2-2220000-2-22200000000-222-2-2-2-222000000-22222-2-2000000000000000000000000
χ292222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1111122-2-2-2-2-1-1-11111-1-1-1-111111111000000000000
χ312222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1111111112222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1111111111111000000000000
χ322222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-2-2-11111-2-22222-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ332222-1222222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-100001−i3i3−i3i3-2-20000111−i3i3−i3i31111−i3i3−i3i3−i3i3−i3i3000000000000
χ342222-1222222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-100001i3−i3i3−i3-2-20000111i3−i3i3−i31111i3−i3i3−i3i3−i3i3−i3000000000000
χ352222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111100001−i3i3−i3i3220000111−i3i3−i3i3-1-1-1-1i3−i3i3−i3i3−i3i3−i3000000000000
χ362222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111100001i3−i3i3−i3220000111i3−i3i3−i3-1-1-1-1−i3i3−i3i3−i3i3−i3i3000000000000
χ372222-122-2-2-2-2-1-1-111112-22-22i2i−2i−2i-1-111−i−i−i−iiiii0000-1−i3i3−i3i3−2i2i00001-11i3−i3i3−i3ii−i−i3−33−3−33−33000000000000
χ382222-122-2-2-2-2-1-1-111112-22-22i2i−2i−2i-1-111−i−i−i−iiiii0000-1i3−i3i3−i3−2i2i00001-11−i3i3−i3i3ii−i−i−33−333−33−3000000000000
χ392222-122-2-2-2-2-1-1-111112-22-2−2i−2i2i2i-1-111iiii−i−i−i−i0000-1−i3i3−i3i32i−2i00001-11i3−i3i3−i3−i−iii−33−333−33−3000000000000
χ402222-122-2-2-2-2-1-1-111112-22-2−2i−2i2i2i-1-111iiii−i−i−i−i0000-1i3−i3i3−i32i−2i00001-11−i3i3−i3i3−i−iii3−33−3−33−33000000000000
χ412222-122-2-2-2-2-1-1-11111-22-222i2i−2i−2i-1-111−i−i−i−iiiii22-2-21-1-1-1-12i−2i2i2i−2i−2i-11-11111−i−iii−i−i−i−iiiii000000000000
χ422222-122-2-2-2-2-1-1-11111-22-222i2i−2i−2i-1-111−i−i−i−iiiii-2-222111112i−2i−2i−2i2i2i-11-1-1-1-1-1−i−iiiiiii−i−i−i−i000000000000
χ432222-122-2-2-2-2-1-1-11111-22-22−2i−2i2i2i-1-111iiii−i−i−i−i22-2-21-1-1-1-1−2i2i−2i−2i2i2i-11-11111ii−i−iiiii−i−i−i−i000000000000
χ442222-122-2-2-2-2-1-1-11111-22-22−2i−2i2i2i-1-111iiii−i−i−i−i-2-22211111−2i2i2i2i−2i−2i-11-1-1-1-1-1ii−i−i−i−i−i−iiiii000000000000
χ452222-1-2-222-2-2-1-1-1-1-1-1-12-2-2200001111−i3−i3i3i3−i3−i3i3i32-22-2-1-1-11100000011-1-1-111−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3000000000000
χ462222-1-2-222-2-2-1-1-1-1-1-1-12-2-2200001111−i3−i3i3i3−i3−i3i3i3-22-22-111-1-100000011-111-1-1−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000
χ472222-1-2-222-2-2-1-1-1-1-1-1-12-2-2200001111i3i3−i3−i3i3i3−i3−i32-22-2-1-1-11100000011-1-1-111i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000
χ482222-1-2-222-2-2-1-1-1-1-1-1-12-2-2200001111i3i3−i3−i3i3i3−i3−i3-22-22-111-1-100000011-111-1-1i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000
χ492222-1-2-222-2-2-1-1-1-1-1-1-1-222-200001111−i3−i3i3i3−i3−i3i3i300001−i3i3i3−i3002-22-2-1-11−i3i3i3−i3i3−i3i3−i3-1-111-1-111000000000000
χ502222-1-2-222-2-2-1-1-1-1-1-1-1-222-200001111−i3−i3i3i3−i3−i3i3i300001i3−i3−i3i300-22-22-1-11i3−i3−i3i3i3−i3i3−i311-1-111-1-1000000000000
χ512222-1-2-222-2-2-1-1-1-1-1-1-1-222-200001111i3i3−i3−i3i3i3−i3−i300001−i3i3i3−i300-22-22-1-11−i3i3i3−i3−i3i3−i3i311-1-111-1-1000000000000
χ522222-1-2-222-2-2-1-1-1-1-1-1-1-222-200001111i3i3−i3−i3i3i3−i3−i300001i3−i3−i3i3002-22-2-1-11i3−i3−i3i3−i3i3−i3i3-1-111-1-111000000000000
χ532222-1-2-2-2-222-1-1-1111122-2-2000011-1-133−3−3−3−3330000-1−i3i3i3−i3002i−2i−2i2i-111i3−i3−i3i3−333−3−i−iiiii−i−i000000000000
χ542222-1-2-2-2-222-1-1-1111122-2-2000011-1-133−3−3−3−3330000-1i3−i3−i3i300−2i2i2i−2i-111−i3i3i3−i3−333−3ii−i−i−i−iii000000000000
χ552222-1-2-2-2-222-1-1-1111122-2-2000011-1-1−3−33333−3−30000-1−i3i3i3−i300−2i2i2i−2i-111i3−i3−i3i33−3−33ii−i−i−i−iii000000000000
χ562222-1-2-2-2-222-1-1-1111122-2-2000011-1-1−3−33333−3−30000-1i3−i3−i3i3002i−2i−2i2i-111−i3i3i3−i33−3−33−i−iiiii−i−i000000000000
χ572222-1-2-2-2-222-1-1-11111-2-222000011-1-133−3−3−3−3332-2-221-1-1110000001-1-111-1-13−3−333−3−33−333−3000000000000
χ582222-1-2-2-2-222-1-1-11111-2-222000011-1-133−3−3−3−333-222-2111-1-10000001-1-1-1-1113−3−33−333−33−3−33000000000000
χ592222-1-2-2-2-222-1-1-11111-2-222000011-1-1−3−33333−3−32-2-221-1-1110000001-1-111-1-1−333−3−333−33−3−33000000000000
χ602222-1-2-2-2-222-1-1-11111-2-222000011-1-1−3−33333−3−3-222-2111-1-10000001-1-1-1-111−333−33−3−33−333−3000000000000
χ612-22-222-22i−2i2i−2i2-2-22i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000002−2−i2i21+i−1−i1−i−1+i0000
χ622-22-222-22i−2i2i−2i2-2-22i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000000000−22i2−i2−1−i1+i−1+i1−i0000
χ632-22-222-22i−2i2i−2i2-2-22i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000002−2−i2i2−1−i1+i−1+i1−i0000
χ642-22-222-22i−2i2i−2i2-2-22i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000000000−22i2−i21+i−1−i1−i−1+i0000
χ652-22-222-2−2i2i−2i2i2-2-2−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000002−2i2−i21−i−1+i1+i−1−i0000
χ662-22-222-2−2i2i−2i2i2-2-2−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000000000−22−i2i2−1+i1−i−1−i1+i0000
χ672-22-222-2−2i2i−2i2i2-2-2−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000002−2i2−i2−1+i1−i−1−i1+i0000
χ682-22-222-2−2i2i−2i2i2-2-2−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000000000−22−i2i21−i−1+i1+i−1−i0000
χ694-44-44-444i−4i−4i4i4-4-44i4i−4i−4i00000000-44−4i4i000000000000000000000000000000000000000000000000000000
χ704-44-44-44−4i4i4i−4i4-4-4−4i−4i4i4i00000000-444i−4i000000000000000000000000000000000000000000000000000000
χ714-44-4-24-44i−4i4i−4i-222−2i−2i2i2i00004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13-22−2i2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000000000000000000000
χ724-44-4-24-44i−4i4i−4i-222−2i−2i2i2i0000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13-22−2i2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000000000000000000000
χ734-44-4-24-4−4i4i−4i4i-2222i2i−2i−2i0000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23-222i−2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000000000000000000000
χ744-44-4-24-4−4i4i−4i4i-2222i2i−2i−2i00004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23-222i−2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000000000000000000000
χ754-44-4-2-444i−4i−4i4i-222−2i−2i2i2i000000002-22i−2i−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000000000000000000000
χ764-44-4-2-444i−4i−4i4i-222−2i−2i2i2i000000002-22i−2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000000000000000000000
χ774-44-4-2-44−4i4i4i−4i-2222i2i−2i−2i000000002-2−2i2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000000000000000000000
χ784-44-4-2-44−4i4i4i−4i-2222i2i−2i−2i000000002-2−2i2i−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000000000000000000000
χ7988-8-88000000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8-40000004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-8-40000004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8-888000000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-88-400000044-4−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-400000044-44i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000000000000000

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