Finite Group Databasebeta

← Group #13137413

Character table — Group #13137413

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111222222222222222222226666666666666666121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order1222444434444666121212121212121212121212336666661212121212121212366612121212121212121212121212121212121212122244444466661212121212121212121212128888888824242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ7111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-11-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-11-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-11-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-11-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222222222222-1222-1-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222222222-1222-1-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-20000000011111111
χ192222222222222222222222222222-12-1-1-1222-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022220000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222222222-12-1-1-1222-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-200001111111100000000
χ21222222222-2-2-2-22222222-2-2-2-2-2-2-2-22-1222-1-1-122-1-122-1-1-1-1-1-1-2-211-2-211-1-1-1-111111111000000000000000000000000000022-2-200000000-1-1-1-11111
χ22222222222-2-2-2-22222222-2-2-2-2-2-2-2-22-1222-1-1-122-1-122-1-1-1-1-1-1-2-211-2-211-1-1-1-1111111110000000000000000000000000000-2-222000000001111-1-1-1-1
χ23222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-1-1-1222-1-122-1-122-1-1-1-111-2-211-2-2-1-1-1-11111111100000000000000000000000022-2-20000-1-1-1-1111100000000
χ24222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-1-1-1222-1-122-1-122-1-1-1-111-2-211-2-2-1-1-1-111111111000000000000000000000000-2-22200001111-1-1-1-100000000
χ252222-2-2-2-2222-2-2222-2-2-2-22222-2-2-2-22-1222-1-1-1-2-211-2-211-1-1-1-122-1-1-2-2111111-1-1-1-1111100000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii
χ262222-2-2-2-2222-2-2222-2-2-2-22222-2-2-2-22-1222-1-1-1-2-211-2-211-1-1-1-122-1-1-2-2111111-1-1-1-111110000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i
χ272222-2-2-2-2222-2-2222-2-2-2-22222-2-2-2-2-12-1-1-122211-2-211-2-2-1-1-1-1-1-12211-2-21111-1-1-1-111110000000000000000000000002i−2i2i−2i0000−i−iii−i−iii00000000
χ282222-2-2-2-2222-2-2222-2-2-2-22222-2-2-2-2-12-1-1-122211-2-211-2-2-1-1-1-1-1-12211-2-21111-1-1-1-11111000000000000000000000000−2i2i−2i2i0000ii−i−iii−i−i00000000
χ292222-2-2-2-22-2-222222-2-2-2-2-2-2-2-222222-1222-1-1-1-2-211-2-211-1-1-1-1-2-21122-1-111111111-1-1-1-100000000000000000000000000002i−2i−2i2i00000000−i−iiiii−i−i
χ302222-2-2-2-22-2-222222-2-2-2-2-2-2-2-222222-1222-1-1-1-2-211-2-211-1-1-1-1-2-21122-1-111111111-1-1-1-10000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii
χ312222-2-2-2-22-2-222222-2-2-2-2-2-2-2-22222-12-1-1-122211-2-211-2-2-1-1-1-111-2-2-1-12211111111-1-1-1-10000000000000000000000002i−2i−2i2i0000−i−iiiii−i−i00000000
χ322222-2-2-2-22-2-222222-2-2-2-2-2-2-2-22222-12-1-1-122211-2-211-2-2-1-1-1-111-2-2-1-12211111111-1-1-1-1000000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii00000000
χ3322-2-222-2-2200002-2-222-2-200000000222-2-22-2-22222-2-2-2-222-2-20000000022-2-2000000002-22-2000022-2-222-2-200000000000000000000000000000000
χ3422-2-222-2-2200002-2-222-2-200000000222-2-22-2-22222-2-2-2-222-2-20000000022-2-200000000-22-220000-2-222-2-22200000000000000000000000000000000
χ3522-2-2-2-222200002-2-2-2-22200000000222-2-22-2-2-2-2-2-2222222-2-200000000-2-222000000002-2-22000022-2-2-2-22200000000000000000000000000000000
χ3622-2-2-2-222200002-2-2-2-22200000000222-2-22-2-2-2-2-2-2222222-2-200000000-2-22200000000-222-20000-2-22222-2-200000000000000000000000000000000
χ372-22-22i−2i2i−2i20000-22-22i−2i2i−2i0000000022-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i0000000000002-22i−2i0000000022-2-22i2i−2i−2i000000000000000000000000
χ382-22-22i−2i2i−2i20000-22-22i−2i2i−2i0000000022-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i000000000000-22−2i2i00000000-2-222−2i−2i2i2i000000000000000000000000
χ392-22-2−2i2i−2i2i20000-22-2−2i2i−2i2i0000000022-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i0000000000002-2−2i2i0000000022-2-2−2i−2i2i2i000000000000000000000000
χ402-22-2−2i2i−2i2i20000-22-2−2i2i−2i2i0000000022-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i000000000000-222i−2i00000000-2-2222i2i−2i−2i000000000000000000000000
χ412-2-222i−2i−2i2i22i−2i2-2-2-222i−2i−2i2i2i2i−2i−2i22-2-222-2-22-2-222i−2i2i−2i−2i2i−2i2i2-2-222i−2i2i−2i2-22-22i−2i−2i2i2i2i−2i−2i22-2-2000000000000000000000000000000000000000000000000
χ422-2-222i−2i−2i2i22i−2i2-2-2-222i−2i−2i2i2i2i−2i−2i22-2-22-1-2-2211-12i−2i−ii−2i2ii−i-111-12i−2i−ii2-2-11−iii−i−i−iii-1-1110000000000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ432-2-222i−2i−2i2i22i−2i2-2-2-222i−2i−2i2i2i2i−2i−2i22-2-22-1-2-2211-12i−2i−ii−2i2ii−i-111-12i−2i−ii2-2-11−iii−i−i−iii-1-1110000000000000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ442-2-222i−2i−2i2i22i−2i2-2-2-222i−2i−2i2i2i2i−2i−2i22-2-2-1211-1-2-22−ii2i−2ii−i−2i2i-111-1−ii2i−2i-112-2−iii−i−i−iii-1-11100000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ452-2-222i−2i−2i2i22i−2i2-2-2-222i−2i−2i2i2i2i−2i−2i22-2-2-1211-1-2-22−ii2i−2ii−i−2i2i-111-1−ii2i−2i-112-2−iii−i−i−iii-1-11100000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ462-2-222i−2i−2i2i2−2i2i-22-2-222i−2i−2i2i−2i−2i2i2i-2-22222-2-22-2-222i−2i2i−2i−2i2i−2i2i2-2-22−2i2i−2i2i-22-222i−2i−2i2i−2i−2i2i2i-2-222000000000000000000000000000000000000000000000000
χ472-2-222i−2i−2i2i2−2i2i-22-2-222i−2i−2i2i−2i−2i2i2i-2-2222-1-2-2211-12i−2i−ii−2i2ii−i-111-1−2i2ii−i-221-1−iii−iii−i−i11-1-10000000000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ482-2-222i−2i−2i2i2−2i2i-22-2-222i−2i−2i2i−2i−2i2i2i-2-2222-1-2-2211-12i−2i−ii−2i2ii−i-111-1−2i2ii−i-221-1−iii−iii−i−i11-1-10000000000000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ492-2-222i−2i−2i2i2−2i2i-22-2-222i−2i−2i2i−2i−2i2i2i-2-222-1211-1-2-22−ii2i−2ii−i−2i2i-111-1i−i−2i2i1-1-22−iii−iii−i−i11-1-100000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ502-2-222i−2i−2i2i2−2i2i-22-2-222i−2i−2i2i−2i−2i2i2i-2-222-1211-1-2-22−ii2i−2ii−i−2i2i-111-1i−i−2i2i1-1-22−iii−iii−i−i11-1-100000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ512-2-22−2i2i2i−2i22i−2i-22-2-22−2i2i2i−2i2i2i−2i−2i-2-22222-2-22-2-22−2i2i−2i2i2i−2i2i−2i2-2-222i−2i2i−2i-22-22−2i2i2i−2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000000000
χ522-2-22−2i2i2i−2i22i−2i-22-2-22−2i2i2i−2i2i2i−2i−2i-2-2222-1-2-2211-1−2i2ii−i2i−2i−ii-111-12i−2i−ii-221-1i−i−ii−i−iii11-1-10000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ532-2-22−2i2i2i−2i22i−2i-22-2-22−2i2i2i−2i2i2i−2i−2i-2-2222-1-2-2211-1−2i2ii−i2i−2i−ii-111-12i−2i−ii-221-1i−i−ii−i−iii11-1-10000000000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ542-2-22−2i2i2i−2i22i−2i-22-2-22−2i2i2i−2i2i2i−2i−2i-2-222-1211-1-2-22i−i−2i2i−ii2i−2i-111-1−ii2i−2i1-1-22i−i−ii−i−iii11-1-100000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ552-2-22−2i2i2i−2i22i−2i-22-2-22−2i2i2i−2i2i2i−2i−2i-2-222-1211-1-2-22i−i−2i2i−ii2i−2i-111-1−ii2i−2i1-1-22i−i−ii−i−iii11-1-100000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ562-2-22−2i2i2i−2i2−2i2i2-2-2-22−2i2i2i−2i−2i−2i2i2i22-2-222-2-22-2-22−2i2i−2i2i2i−2i2i−2i2-2-22−2i2i−2i2i2-22-2−2i2i2i−2i−2i−2i2i2i22-2-2000000000000000000000000000000000000000000000000
χ572-2-22−2i2i2i−2i2−2i2i2-2-2-22−2i2i2i−2i−2i−2i2i2i22-2-22-1-2-2211-1−2i2ii−i2i−2i−ii-111-1−2i2ii−i2-2-11i−i−iiii−i−i-1-1110000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ582-2-22−2i2i2i−2i2−2i2i2-2-2-22−2i2i2i−2i−2i−2i2i2i22-2-22-1-2-2211-1−2i2ii−i2i−2i−ii-111-1−2i2ii−i2-2-11i−i−iiii−i−i-1-1110000000000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ592-2-22−2i2i2i−2i2−2i2i2-2-2-22−2i2i2i−2i−2i−2i2i2i22-2-2-1211-1-2-22i−i−2i2i−ii2i−2i-111-1i−i−2i2i-112-2i−i−iiii−i−i-1-11100000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ602-2-22−2i2i2i−2i2−2i2i2-2-2-22−2i2i2i−2i−2i−2i2i2i22-2-2-1211-1-2-22i−i−2i2i−ii2i−2i-111-1i−i−2i2i-112-2i−i−iiii−i−i-1-11100000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ614444444444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000000000000
χ62444444444-4-4-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111222222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000
χ634444-4-4-4-4444-4-4444-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-2-2222222221111-2-2-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.