Finite Group Databasebeta

← Group #11791191

Character table — Group #11791191

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11111111222222222222222222224444444444444444666666666666666688888888888888888888881212121212121212121212121212121218181818181818182424242424242424242424247272
order122244442233446666661212121212121212366666661212121212121212888888888888888824666666666612121212121212121212242424242424242424242424242424244444444424668812122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1
χ91111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11iiii−i−i−i−i1111-1-1-1-11-11111-1-11111-1-1-1-111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−ii−i
χ101111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11iiii−i−i−i−i1111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii−ii
χ111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11iiii−i−i−i−i-1-1-1-111111-11111-1-11111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1-1i−i11ii−i−i−ii
χ121111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11iiii−i−i−i−i-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-111−ii-1-1−i−iiii−i
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11−i−i−i−iiiii1111-1-1-1-11-11111-1-11111-1-1-1-111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii−ii
χ141111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11−i−i−i−iiiii1111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−ii−i
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11−i−i−i−iiiii-1-1-1-111111-11111-1-11111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-1-1−ii11−i−iiii−i
χ161111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11−i−i−i−iiiii-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-111i−i-1-1ii−i−i−ii
χ1722222222222-12222-1-12-1-1-1-1-12222-122-1-1-1-1-122-1-1-1-1-1-100000000222222222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000000022-1-100-1-1000000
χ1822222222222-12222-1-12-1-1-1-1-12222-122-1-1-1-1-122-1-1-1-1-1-10000000022222222-2-2-2-211-1-11111-2-211-1-1111100000000-1-1-1-1-1-1-1-100000000-2-2110011000000
χ1922222222222-12222-1-12-1-1-1-1-12222-122-1-1-1-1-122-1-1-1-1-1-100000000-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000001111111100000000-2-2110011000000
χ2022222222222-12222-1-12-1-1-1-1-12222-122-1-1-1-1-122-1-1-1-1-1-100000000-2-2-2-2-2-2-2-2-2-2-2-211-1-11111-2-211-1-1111100000000111111110000000022-1-100-1-1000000
χ212222222222-1222-1-122-122222-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-12222222220000000022-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000002200-1-1-1-100
χ222222222222-1222-1-122-122222-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-122222222200000000-2-211-2-2-1-1111111-2-2-1-11111-1-1-1-1-1-1-1-100000000000000000000-2-200111100
χ232222222222-1222-1-122-122222-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-12-2-2-2-2-2-2-2-20000000022-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-11111111100000000000000000000-2-200111100
χ242222222222-1222-1-122-122222-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-12-2-2-2-2-2-2-2-200000000-2-211-2-2-1-1111111-2-2-1-1111111111111000000000000000000002200-1-1-1-100
χ2522222222-2-222-2-2222222222222222-2-2-2-2222-2-2-22222-222-2-222-2-200000000000000-2-200000000-2-2000022-2-222-2-2000000000000000000000000000000
χ2622222222-2-222-2-2222222222222222-2-2-2-2222-2-2-22222-2-2-222-2-22200000000000000-2-200000000-2-20000-2-222-2-222000000000000000000000000000000
χ2722222222-2-2-12-2-2-1-122-122222-1-1-1-1-111-2-2-1-1-111-2-1-1-1-1-222-2-222-2-20000000000−i3i30011−i3−i3i3i3−i3i30011−i3−i3i3i3-1-111-1-111000000000000000000000000−i3i3−i3i300
χ2822222222-2-2-12-2-2-1-122-122222-1-1-1-1-111-2-2-1-1-111-2-1-1-1-1-222-2-222-2-20000000000i3−i30011i3i3−i3−i3i3−i30011i3i3−i3−i3-1-111-1-111000000000000000000000000i3−i3i3−i300
χ2922222222-2-2-12-2-2-1-122-122222-1-1-1-1-111-2-2-1-1-111-2-1-1-1-1-2-2-222-2-2220000000000−i3i30011−i3−i3i3i3−i3i30011−i3−i3i3i311-1-111-1-1000000000000000000000000i3−i3i3−i300
χ3022222222-2-2-12-2-2-1-122-122222-1-1-1-1-111-2-2-1-1-111-2-1-1-1-1-2-2-222-2-2220000000000i3−i30011i3i3−i3−i3i3−i30011i3i3−i3−i311-1-111-1-1000000000000000000000000−i3i3−i3i300
χ312222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22i2i−2i−2i−2i−2i2i2i000000000000002200000000-2-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ322222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2−2i−2i2i2i2i2i−2i−2i000000000000002200000000-2-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ332222-2-2-2-222-12-2-2-1-122-12-2-2-2-21111-1-1-122-1-1-111-21111-22i2i−2i−2i−2i−2i2i2i0000000000−i3i300-1-1−i3−i3i3i3i3−i30011i3i3−i3−i3−i−iiiii−i−i0000000000000000000000003−3−3300
χ342222-2-2-2-222-12-2-2-1-122-12-2-2-2-21111-1-1-122-1-1-111-21111-22i2i−2i−2i−2i−2i2i2i0000000000i3−i300-1-1i3i3−i3−i3−i3i30011−i3−i3i3i3−i−iiiii−i−i000000000000000000000000−333−300
χ352222-2-2-2-222-12-2-2-1-122-12-2-2-2-21111-1-1-122-1-1-111-21111-2−2i−2i2i2i2i2i−2i−2i0000000000−i3i300-1-1−i3−i3i3i3i3−i30011i3i3−i3−i3ii−i−i−i−iii000000000000000000000000−333−300
χ362222-2-2-2-222-12-2-2-1-122-12-2-2-2-21111-1-1-122-1-1-111-21111-2−2i−2i2i2i2i2i−2i−2i0000000000i3−i300-1-1i3i3−i3−i3−i3i30011−i3−i3i3i3ii−i−i−i−iii0000000000000000000000003−3−3300
χ372222-2-2-2-2-2-22-12222-1-12-11111-2-2-2-2-1-2-211-1-1-122-11111-1000000002222-2-2-2-22-222-1-111-1-1-1-1-2-211-1-1111100000000-1-1-1-11111000000002-2-1-10011000000
χ382222-2-2-2-2-2-22-12222-1-12-11111-2-2-2-2-1-2-211-1-1-122-11111-1000000002222-2-2-2-2-22-2-21111111122-1-1-1-1-1-1-1-100000000-1-1-1-1111100000000-221100-1-1000000
χ392222-2-2-2-2-2-22-12222-1-12-11111-2-2-2-2-1-2-211-1-1-122-11111-100000000-2-2-2-222222-222-1-111-1-1-1-1-2-211-1-11111000000001111-1-1-1-100000000-221100-1-1000000
χ402222-2-2-2-2-2-22-12222-1-12-11111-2-2-2-2-1-2-211-1-1-122-11111-100000000-2-2-2-22222-22-2-21111111122-1-1-1-1-1-1-1-1000000001111-1-1-1-1000000002-2-1-10011000000
χ412222-2-2-2-2-2-2-1222-1-122-12-2-2-2-21111-111-2-2-1-1-1-1-12111122i2i2i2i−2i−2i−2i−2i000000002-2-1-12211-1-1-1-111-2-2-1-11111−i−i−i−iiiii000000000000000000002i−2i00−i−iii00
χ422222-2-2-2-2-2-2-1222-1-122-12-2-2-2-21111-111-2-2-1-1-1-1-12111122i2i2i2i−2i−2i−2i−2i00000000-2211-2-2111111-1-122-1-1-1-1-1-1−i−i−i−iiiii00000000000000000000−2i2i00ii−i−i00
χ432222-2-2-2-2-2-2-1222-1-122-12-2-2-2-21111-111-2-2-1-1-1-1-1211112−2i−2i−2i−2i2i2i2i2i000000002-2-1-12211-1-1-1-111-2-2-1-11111iiii−i−i−i−i00000000000000000000−2i2i00ii−i−i00
χ442222-2-2-2-2-2-2-1222-1-122-12-2-2-2-21111-111-2-2-1-1-1-1-1211112−2i−2i−2i−2i2i2i2i2i00000000-2211-2-2111111-1-122-1-1-1-1-1-1iiii−i−i−i−i000000000000000000002i−2i00−i−iii00
χ4522-2-22i−2i2i−2i0022002-22-2-2-22i2i−2i−2i2i2i−2i−2i200002-2-20002i2i−2i−2i000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2322−2−2−i2−i2i2i2000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2322−2−2−i2−i2i2i21−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ4622-2-22i−2i2i−2i0022002-22-2-2-22i2i−2i−2i2i2i−2i−2i200002-2-20002i2i−2i−2i000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2−222i2i2−i2−i2000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2−222i2i2−i2−i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ4722-2-22i−2i2i−2i0022002-22-2-2-22i2i−2i−2i2i2i−2i−2i200002-2-20002i2i−2i−2i0002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2322−2−2−i2−i2i2i20000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2322−2−2−i2−i2i2i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ4822-2-22i−2i2i−2i0022002-22-2-2-22i2i−2i−2i2i2i−2i−2i200002-2-20002i2i−2i−2i0002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2−222i2i2−i2−i20000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2−222i2i2−i2−i21−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ4922-2-2−2i2i−2i2i0022002-22-2-2-2−2i−2i2i2i−2i−2i2i2i200002-2-2000−2i−2i2i2i0002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1322−2−2i2i2−i2−i20000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1322−2−2i2i2−i2−i21+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ5022-2-2−2i2i−2i2i0022002-22-2-2-2−2i−2i2i2i−2i−2i2i2i200002-2-2000−2i−2i2i2i0002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2−222−i2−i2i2i20000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2−222−i2−i2i2i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ5122-2-2−2i2i−2i2i0022002-22-2-2-2−2i−2i2i2i−2i−2i2i2i200002-2-2000−2i−2i2i2i000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1322−2−2i2i2−i2−i2000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1322−2−2i2i2−i2−i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ5222-2-2−2i2i−2i2i0022002-22-2-2-2−2i−2i2i2i−2i−2i2i2i200002-2-2000−2i−2i2i2i000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2−222−i2−i2i2i2000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2−222−i2−i2i2i21+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ532-22-22i−2i−2i2i002200-22-22-2-22i−2i2i−2i2i−2i2i−2i20000-22-20002i−2i2i−2i02ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13002−22−2−i2i2−i2i200000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13002−22−2−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ542-22-22i−2i−2i2i002200-22-22-2-22i−2i2i−2i2i−2i2i−2i20000-22-20002i−2i2i−2i02ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−22−22i2−i2i2−i200000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−22−22i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ552-22-22i−2i−2i2i002200-22-22-2-22i−2i2i−2i2i−2i2i−2i20000-22-20002i−2i2i−2i0−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13002−22−2−i2i2−i2i20000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13002−22−2−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ562-22-22i−2i−2i2i002200-22-22-2-22i−2i2i−2i2i−2i2i−2i20000-22-20002i−2i2i−2i0−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−22−22i2−i2i2−i20000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−22−22i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ572-22-2−2i2i2i−2i002200-22-22-2-2−2i2i−2i2i−2i2i−2i2i20000-22-2000−2i2i−2i2i0−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23002−22−2i2−i2i2−i20000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23002−22−2i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.