Finite Group Databasebeta

← Group #72215126

Character table — Group #72215126

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size1111111122223333333366666666666666666666888888881212121212121212242424242424242432323232323232323232323232323232323232323232323232323232323232324848484848484848484848484848484848484848484848484848484848484848
order12224444224422224444224444444444444444448888888844444444888888883666666612121212121212122424242424242424242424242424242488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i
χ61111-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii
χ71111-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ81111-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ91-1-1111-1-11-11-1-1-11111-1-11-11-11111-1-1-1-111-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-1-111-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i
χ101-1-1111-1-11-11-1-1-11111-1-11-11-11111-1-1-1-111-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-1-111-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-11-11−ii−ii-1-111-1-111−i−iii−i−iii
χ111-1-1111-1-11-11-1-1-11111-1-11-11-11111-1-1-1-111-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-1-111-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-11-1−ii−ii11-1-111-1-1−i−iii−i−iii
χ121-1-1111-1-11-11-1-1-11111-1-11-11-11111-1-1-1-111-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-1-111-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-11-11i−ii−i-1-111-1-111ii−i−iii−i−i
χ131-1-11-1-111-111-1-1-111-1-111-111-11111-1-1-1-1-1-111-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii1-1-1-1-111111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1i−i−ii-111-1ii−i−i−i−iii-1-11111-1-1
χ141-1-11-1-111-111-1-1-111-1-111-111-11111-1-1-1-1-1-111-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii1-1-1-1-111111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11−iii−i1-1-11−i−iiiii−i−i11-1-1-1-111
χ151-1-11-1-111-111-1-1-111-1-111-111-11111-1-1-1-1-1-111-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i1-1-1-1-111111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-111
χ161-1-11-1-111-111-1-1-111-1-111-111-11111-1-1-1-1-1-111-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i1-1-1-1-111111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1−iii−i-111-1−i−iiiii−i−i-1-11111-1-1
χ172222222222222222222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ182222222222222222222222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000000000
χ1922222222-2-2-2-222222222-2-2-2-2222222222222222200000000-2-2-2-2-2-2-2-200000000222-2-2-2-22-2-22222-2-2000000000000000000000000000000000000000000000000
χ2022222222-2-2-2-222222222-2-2-2-2222222222222222200000000-2-2-2-2-2-2-2-200000000-1-1-11111-111-1-1-1-11133−3−333−3−333−3−333−3−300000000000000000000000000000000
χ2122222222-2-2-2-222222222-2-2-2-2222222222222222200000000-2-2-2-2-2-2-2-200000000-1-1-11111-111-1-1-1-111−3−333−3−333−3−333−3−33300000000000000000000000000000000
χ222222-2-2-2-222-2-22222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000022222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ232222-2-2-2-222-2-22222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000-1-1-1-1-1-1-1-11111111133−3−333−3−3−3−333−3−33300000000000000000000000000000000
χ242222-2-2-2-222-2-22222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000-1-1-1-1-1-1-1-111111111−3−333−3−33333−3−333−3−300000000000000000000000000000000
χ252222-2-2-2-2-2-2222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000000000000000000000
χ262222-2-2-2-2-2-2222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-1-1-11111-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000000000000000
χ2722-2-22i−2i2i−2i00002-22-22i−2i2i−2i000022-2-222-2-22i−2i2i−2i2i−2i2i−2i2−22−2−i2i2−i2i2000000002−22−2−i2i2−i2i222-20000-2002i−2i2i−2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000
χ2822-2-22i−2i2i−2i00002-22-22i−2i2i−2i000022-2-222-2-22i−2i2i−2i2i−2i2i−2i2−22−2−i2i2−i2i2000000002−22−2−i2i2−i2i2-1-11−i3i3−i3i313−3−ii−ii3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000000000000000000
χ2922-2-22i−2i2i−2i00002-22-22i−2i2i−2i000022-2-222-2-22i−2i2i−2i2i−2i2i−2i2−22−2−i2i2−i2i2000000002−22−2−i2i2−i2i2-1-11i3−i3i3−i31−33−ii−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000000000000000000
χ3022-2-22i−2i2i−2i00002-22-22i−2i2i−2i000022-2-222-2-22i−2i2i−2i2i−2i2i−2i−22−22i2−i2i2−i200000000−22−22i2−i2i2−i222-20000-2002i−2i2i−2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000
χ3122-2-22i−2i2i−2i00002-22-22i−2i2i−2i000022-2-222-2-22i−2i2i−2i2i−2i2i−2i−22−22i2−i2i2−i200000000−22−22i2−i2i2−i2-1-11−i3i3−i3i313−3−ii−ii3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000000000000000000
χ3222-2-22i−2i2i−2i00002-22-22i−2i2i−2i000022-2-222-2-22i−2i2i−2i2i−2i2i−2i−22−22i2−i2i2−i200000000−22−22i2−i2i2−i2-1-11i3−i3i3−i31−33−ii−ii−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000000000000000000
χ3322-2-2−2i2i−2i2i00002-22-2−2i2i−2i2i000022-2-222-2-2−2i2i−2i2i−2i2i−2i2i2−22−2i2−i2i2−i2000000002−22−2i2−i2i2−i222-20000-200−2i2i−2i2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000
χ3422-2-2−2i2i−2i2i00002-22-2−2i2i−2i2i000022-2-222-2-2−2i2i−2i2i−2i2i−2i2i2−22−2i2−i2i2−i2000000002−22−2i2−i2i2−i2-1-11−i3i3−i3i31−33i−ii−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000000000000000000
χ3522-2-2−2i2i−2i2i00002-22-2−2i2i−2i2i000022-2-222-2-2−2i2i−2i2i−2i2i−2i2i2−22−2i2−i2i2−i2000000002−22−2i2−i2i2−i2-1-11i3−i3i3−i313−3i−ii−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000000000000000000
χ3622-2-2−2i2i−2i2i00002-22-2−2i2i−2i2i000022-2-222-2-2−2i2i−2i2i−2i2i−2i2i−22−22−i2i2−i2i200000000−22−22−i2i2−i2i222-20000-200−2i2i−2i2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000
χ3722-2-2−2i2i−2i2i00002-22-2−2i2i−2i2i000022-2-222-2-2−2i2i−2i2i−2i2i−2i2i−22−22−i2i2−i2i200000000−22−22−i2i2−i2i2-1-11−i3i3−i3i31−33i−ii−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000000000000000000
χ3822-2-2−2i2i−2i2i00002-22-2−2i2i−2i2i000022-2-222-2-2−2i2i−2i2i−2i2i−2i2i−22−22−i2i2−i2i200000000−22−22−i2i2−i2i2-1-11i3−i3i3−i313−3i−ii−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000000000000000000
χ392-22-22i−2i−2i2i0000-222-22i−2i−2i2i000022-2-2-2-2222i−2i−2i2i2i−2i−2i2i−i2i2i2−i2−222−200000000−i2i2i2−i2−222−22-220000-2002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000000000000000000000000000
χ402-22-22i−2i−2i2i0000-222-22i−2i−2i2i000022-2-2-2-2222i−2i−2i2i2i−2i−2i2i−i2i2i2−i2−222−200000000−i2i2i2−i2−222−2-11-1−i3i3i3−i313−3−iii−i−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000000000000000
χ412-22-22i−2i−2i2i0000-222-22i−2i−2i2i000022-2-2-2-2222i−2i−2i2i2i−2i−2i2i−i2i2i2−i2−222−200000000−i2i2i2−i2−222−2-11-1i3−i3−i3i31−33−iii−i3−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000000000000000
χ422-22-22i−2i−2i2i0000-222-22i−2i−2i2i000022-2-2-2-2222i−2i−2i2i2i−2i−2i2ii2−i2−i2i22−2−2200000000i2−i2−i2i22−2−222-220000-2002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000000000000000000000000000
χ432-22-22i−2i−2i2i0000-222-22i−2i−2i2i000022-2-2-2-2222i−2i−2i2i2i−2i−2i2ii2−i2−i2i22−2−2200000000i2−i2−i2i22−2−22-11-1−i3i3i3−i313−3−iii−i−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000000000000000
χ442-22-22i−2i−2i2i0000-222-22i−2i−2i2i000022-2-2-2-2222i−2i−2i2i2i−2i−2i2ii2−i2−i2i22−2−2200000000i2−i2−i2i22−2−22-11-1i3−i3−i3i31−33−iii−i3−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000000000000000
χ452-22-2−2i2i2i−2i0000-222-2−2i2i2i−2i000022-2-2-2-222−2i2i2i−2i−2i2i2i−2i−i2i2i2−i22−2−2200000000−i2i2i2−i22−2−222-220000-200−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000000000000000000000000000
χ462-22-2−2i2i2i−2i0000-222-2−2i2i2i−2i000022-2-2-2-222−2i2i2i−2i−2i2i2i−2i−i2i2i2−i22−2−2200000000−i2i2i2−i22−2−22-11-1−i3i3i3−i31−33i−i−ii3−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000000000000000
χ472-22-2−2i2i2i−2i0000-222-2−2i2i2i−2i000022-2-2-2-222−2i2i2i−2i−2i2i2i−2i−i2i2i2−i22−2−2200000000−i2i2i2−i22−2−22-11-1i3−i3−i3i313−3i−i−ii−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000000000000000
χ482-22-2−2i2i2i−2i0000-222-2−2i2i2i−2i000022-2-2-2-222−2i2i2i−2i−2i2i2i−2ii2−i2−i2i2−222−200000000i2−i2−i2i2−222−22-220000-200−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000000000000000000000000000
χ492-22-2−2i2i2i−2i0000-222-2−2i2i2i−2i000022-2-2-2-222−2i2i2i−2i−2i2i2i−2ii2−i2−i2i2−222−200000000i2−i2−i2i2−222−2-11-1−i3i3i3−i31−33i−i−ii3−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000000000000000
χ502-22-2−2i2i2i−2i0000-222-2−2i2i2i−2i000022-2-2-2-222−2i2i2i−2i−2i2i2i−2ii2−i2−i2i2−222−200000000i2−i2−i2i2−222−2-11-1i3−i3−i3i313−3i−i−ii−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000000000000000
χ512-2-2222-2-22-22-2-2-22222-2-22-22-22222-2-2-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i22-2-222-2-22i2i−2i−2i2i2i−2i−2i-111-1-111-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.