Finite Group Databasebeta

← Group #11721775

Character table — Group #11721775

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124
size1111111111112222226666666666666666666666666666666618181818181818181818181811111111111122222266666666666666666666666666666666181818181818181818181818
order12334466121212128824242424333366661212121212121212242424242424242424242424242424242466881212242424242266446612121212882424242466666666121212121212121224242424242424242424242424242424246688121224242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ4111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111-1-111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-111i−i-1-1ii−i−i1111-1-111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-111i−i-1-1ii−i−i
χ61111-1-111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-1−ii11−i−iii1111-1-111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-1−ii11−i−iii
χ71111-1-111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-111−ii-1-1−i−iii1111-1-111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-111−ii-1-1−i−iii
χ81111-1-111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-1i−i11ii−i−i1111-1-111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-1i−i11ii−i−i
χ92222222222222222222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000002222222222222222222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ10222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000
χ11222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000
χ12222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000
χ13222222222222-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111000000000000222222222222-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111000000000000
χ14222222222222-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-111-2-2111111-2-21111000000000000222222222222-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-111-2-2111111-2-21111000000000000
χ15222222222222-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-11111-2-2111111-2-211000000000000222222222222-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-11111-2-2111111-2-211000000000000
χ16222222222222-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122111111-2-2111111-2-2000000000000222222222222-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122111111-2-2111111-2-2000000000000
χ172222-2-222-2-2-2-22i−2i2i2i−2i−2i2-1-1-12-1-1-1-2-21111112i2i−i−i−i−i−i−i−2i−2iiiiiii0000000000002222-2-222-2-2-2-22i−2i2i2i−2i−2i2-1-1-12-1-1-1-2-21111112i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000
χ182222-2-222-2-2-2-22i−2i2i2i−2i−2i-12-1-1-12-1-111-2-21111−i−i2i2i−i−i−i−iii−2i−2iiiii0000000000002222-2-222-2-2-2-22i−2i2i2i−2i−2i-12-1-1-12-1-111-2-21111−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000
χ192222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-12-1-1-12-11111-2-211−i−i−i−i2i2i−i−iiiii−2i−2iii0000000000002222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-12-1-1-12-11111-2-211−i−i−i−i2i2i−i−iiiii−2i−2iii000000000000
χ202222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-1-12-1-1-12111111-2-2−i−i−i−i−i−i2i2iiiiiii−2i−2i0000000000002222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-1-12-1-1-12111111-2-2−i−i−i−i−i−i2i2iiiiiii−2i−2i000000000000
χ212222-2-222-2-2-2-2−2i2i−2i−2i2i2i2-1-1-12-1-1-1-2-2111111−2i−2iiiiiii2i2i−i−i−i−i−i−i0000000000002222-2-222-2-2-2-2−2i2i−2i−2i2i2i2-1-1-12-1-1-1-2-2111111−2i−2iiiiiii2i2i−i−i−i−i−i−i000000000000
χ222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-12-1-1-12-1-111-2-21111ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000000002222-2-222-2-2-2-2−2i2i−2i−2i2i2i-12-1-1-12-1-111-2-21111ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000
χ232222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-12-1-1-12-11111-2-211iiii−2i−2iii−i−i−i−i2i2i−i−i0000000000002222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-12-1-1-12-11111-2-211iiii−2i−2iii−i−i−i−i2i2i−i−i000000000000
χ242222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-1-12-1-1-12111111-2-2iiiiii−2i−2i−i−i−i−i−i−i2i2i0000000000002222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-1-12-1-1-12111111-2-2iiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000
χ252-2222i−2i-2-22i2i−2i−2i0000002222-2-2-2-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000002-2222i−2i-2-22i2i−2i−2i0000002222-2-2-2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ262-2222i−2i-2-22i2i−2i−2i0000002-1-1-1-21112i−2i−ii−ii−ii00−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000002-2222i−2i-2-22i2i−2i−2i0000002-1-1-1-21112i−2i−ii−ii−ii00−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000
χ272-2222i−2i-2-22i2i−2i−2i0000002-1-1-1-21112i−2i−ii−ii−ii00ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000002-2222i−2i-2-22i2i−2i−2i0000002-1-1-1-21112i−2i−ii−ii−ii00ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000
χ282-2222i−2i-2-22i2i−2i−2i000000-12-1-11-211−ii2i−2i−ii−ii−ζ7+ζ23ζ7−ζ2300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000002-2222i−2i-2-22i2i−2i−2i000000-12-1-11-211−ii2i−2i−ii−ii−ζ7+ζ23ζ7−ζ2300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000
χ292-2222i−2i-2-22i2i−2i−2i000000-12-1-11-211−ii2i−2i−ii−iiζ7−ζ23−ζ7+ζ2300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000002-2222i−2i-2-22i2i−2i−2i000000-12-1-11-211−ii2i−2i−ii−iiζ7−ζ23−ζ7+ζ2300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000
χ302-2222i−2i-2-22i2i−2i−2i000000-1-12-111-21−ii−ii2i−2i−ii−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300ζ5−ζ13−ζ5+ζ130000000000002-2222i−2i-2-22i2i−2i−2i000000-1-12-111-21−ii−ii2i−2i−ii−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300ζ5−ζ13−ζ5+ζ13000000000000
χ312-2222i−2i-2-22i2i−2i−2i000000-1-12-111-21−ii−ii2i−2i−iiζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300−ζ5+ζ13ζ5−ζ130000000000002-2222i−2i-2-22i2i−2i−2i000000-1-12-111-21−ii−ii2i−2i−iiζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300−ζ5+ζ13ζ5−ζ13000000000000
χ322-2222i−2i-2-22i2i−2i−2i000000-1-1-12111-2−ii−ii−ii2i−2i−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000002-2222i−2i-2-22i2i−2i−2i000000-1-1-12111-2−ii−ii−ii2i−2i−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000000000
χ332-2222i−2i-2-22i2i−2i−2i000000-1-1-12111-2−ii−ii−ii2i−2iζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000002-2222i−2i-2-22i2i−2i−2i000000-1-1-12111-2−ii−ii−ii2i−2iζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000000000
χ342-222−2i2i-2-2−2i−2i2i2i0000002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002-222−2i2i-2-2−2i−2i2i2i0000002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ352-222−2i2i-2-2−2i−2i2i2i0000002-1-1-1-2111−2i2ii−ii−ii−i00ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000002-222−2i2i-2-2−2i−2i2i2i0000002-1-1-1-2111−2i2ii−ii−ii−i00ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000
χ362-222−2i2i-2-2−2i−2i2i2i0000002-1-1-1-2111−2i2ii−ii−ii−i00−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000002-222−2i2i-2-2−2i−2i2i2i0000002-1-1-1-2111−2i2ii−ii−ii−i00−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000
χ372-222−2i2i-2-2−2i−2i2i2i000000-12-1-11-211i−i−2i2ii−ii−iζ5−ζ13−ζ5+ζ1300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000002-222−2i2i-2-2−2i−2i2i2i000000-12-1-11-211i−i−2i2ii−ii−iζ5−ζ13−ζ5+ζ1300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000
χ382-222−2i2i-2-2−2i−2i2i2i000000-12-1-11-211i−i−2i2ii−ii−i−ζ5+ζ13ζ5−ζ1300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000002-222−2i2i-2-2−2i−2i2i2i000000-12-1-11-211i−i−2i2ii−ii−i−ζ5+ζ13ζ5−ζ1300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000
χ392-222−2i2i-2-2−2i−2i2i2i000000-1-12-111-21i−ii−i−2i2ii−iζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300−ζ7+ζ23ζ7−ζ230000000000002-222−2i2i-2-2−2i−2i2i2i000000-1-12-111-21i−ii−i−2i2ii−iζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300−ζ7+ζ23ζ7−ζ23000000000000
χ402-222−2i2i-2-2−2i−2i2i2i000000-1-12-111-21i−ii−i−2i2ii−i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300ζ7−ζ23−ζ7+ζ230000000000002-222−2i2i-2-2−2i−2i2i2i000000-1-12-111-21i−ii−i−2i2ii−i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300ζ7−ζ23−ζ7+ζ23000000000000
χ412-222−2i2i-2-2−2i−2i2i2i000000-1-1-12111-2i−ii−ii−i−2i2iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000002-222−2i2i-2-2−2i−2i2i2i000000-1-1-12111-2i−ii−ii−i−2i2iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000000000
χ422-222−2i2i-2-2−2i−2i2i2i000000-1-1-12111-2i−ii−ii−i−2i2i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000002-222−2i2i-2-2−2i−2i2i2i000000-1-1-12111-2i−ii−ii−i−2i2i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000000000
χ4333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000011−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000011−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000-1-11+i321−i32-1-11+i321−i321+i321−i321+i321−i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000-1-11+i321−i32-1-11+i321−i321+i321−i321+i321−i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.