Finite Group Databasebeta

← Group #13138742

Character table — Group #13138742

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order12224444366688881212121224242424336666661212121212121212242424242424242436661212121224242424242424242424242444448888121212121212121224242424242424244444888812121212121212122424242424242424
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
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ5111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ7111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11111ii−i−i-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-11111ii−i−i-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-11111ii−i−i-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1-11i−i−ii11-1-1-1-111ii−i−i−i−iii
χ121111-1-1-1-11111ii−i−i-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-111-1−iii−i-1-11111-1-1−i−iiiii−i−i
χ131111-1-1-1-11111−i−iii-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii11-1-111-1-1−i−iii−i−iii
χ141111-1-1-1-11111−i−iii-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i-1-111-1-111ii−i−iii−i−i
χ151111-1-1-1-11111−i−iii-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1-11−iii−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-11111−i−iii-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-111-1i−i−ii-1-11111-1-1ii−i−i−i−iii
χ172222222222222222222222222-12-122-1-122-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000002200220000-1-1-1-10000-1-1-1-1
χ182222222222222222222222222-12-122-1-122-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-200-2-20000111100001111
χ19222222222222222222222222-12-12-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ20222222222222222222222222-12-12-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ21222222222222-2-2-2-22222-2-2-2-22-12-122-1-122-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111000000000000000000000000002200-2-20000-1-1-1-100001111
χ22222222222222-2-2-2-22222-2-2-2-22-12-122-1-122-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111100000000000000000000000000-2-20022000011110000-1-1-1-1
χ23222222222222-2-2-2-22222-2-2-2-2-12-12-1-122-1-122-1-12211111111-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ24222222222222-2-2-2-22222-2-2-2-2-12-12-1-122-1-122-1-12211111111-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ252222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i2-12-122-1-1-2-211-2-2112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−iii−i−i−i−iiiii000000000000000000000000002-2002i−2i0000-1-1110000−i−iii
χ262222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i2-12-122-1-1-2-211-2-2112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−iii−i−i−i−iiiii00000000000000000000000000-2200−2i2i000011-1-10000ii−i−i
χ272222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i-12-12-1-12211-2-211-2-2−i−i−i−iiiii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000000000000000
χ282222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i-12-12-1-12211-2-211-2-2−i−i−i−iiiii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ292222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i2-12-122-1-1-2-211-2-211−2i−2i−2i−2i2i2i2i2i-1-1-1-11111ii−i−iiiii−i−i−i−i000000000000000000000000002-200−2i2i0000-1-1110000ii−i−i
χ302222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i2-12-122-1-1-2-211-2-211−2i−2i−2i−2i2i2i2i2i-1-1-1-11111ii−i−iiiii−i−i−i−i00000000000000000000000000-22002i−2i000011-1-10000−i−iii
χ312222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i-12-12-1-12211-2-211-2-2iiii−i−i−i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000000000000000
χ322222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i-12-12-1-12211-2-211-2-2iiii−i−i−i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ3322-2-222-2-222-2-22-22-222-2-22-22-22222-2-2-2-22222-2-2-2-222-2-222-2-22-2-22-2-2222-22-222-2-222-2-2000000000000000000000000000000000000000000000000
χ3422-2-222-2-222-2-22-22-222-2-22-22-22-12-1-2-21122-1-1-2-21122-2-222-2-2-111-111-1-1-11-11-1-111-1-1110000000000000000000000000000000000003−33−300003−33−3
χ3522-2-222-2-222-2-22-22-222-2-22-22-22-12-1-2-21122-1-1-2-21122-2-222-2-2-111-111-1-1-11-11-1-111-1-111000000000000000000000000000000000000−33−330000−33−33
χ3622-2-222-2-222-2-22-22-222-2-22-22-2-12-1211-2-2-1-12211-2-2-1-111-1-111-111-111-1-12-22-2-1-111-1-1110000000033−3−333−3−333−3−333−3−3000000000000000000000000
χ3722-2-222-2-222-2-22-22-222-2-22-22-2-12-1211-2-2-1-12211-2-2-1-111-1-111-111-111-1-12-22-2-1-111-1-11100000000−3−333−3−333−3−333−3−333000000000000000000000000
χ3822-2-222-2-222-2-2-22-2222-2-2-22-222222-2-2-2-22222-2-2-2-2-2-222-2-2222-2-22-2-222-22-22-2-222-2-222000000000000000000000000000000000000000000000000
χ3922-2-222-2-222-2-2-22-2222-2-2-22-222-12-1-2-21122-1-1-2-211-2-222-2-222-111-111-1-11-11-111-1-111-1-10000000000000000000000000000000000003−33−30000−33−33
χ4022-2-222-2-222-2-2-22-2222-2-2-22-222-12-1-2-21122-1-1-2-211-2-222-2-222-111-111-1-11-11-111-1-111-1-1000000000000000000000000000000000000−33−3300003−33−3
χ4122-2-222-2-222-2-2-22-2222-2-2-22-22-12-1211-2-2-1-12211-2-211-1-111-1-1-111-111-1-1-22-2211-1-111-1-10000000033−3−333−3−3−3−333−3−333000000000000000000000000
χ4222-2-222-2-222-2-2-22-2222-2-2-22-22-12-1211-2-2-1-12211-2-211-1-111-1-1-111-111-1-1-22-2211-1-111-1-100000000−3−333−3−33333−3−333−3−3000000000000000000000000
χ4322-2-2-2-22222-2-22i−2i−2i2i-2-2222i−2i−2i2i2222-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i2-2-2222-2-22i−2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4422-2-2-2-22222-2-22i−2i−2i2i-2-2222i−2i−2i2i2-12-1-2-211-2-21122-1-12i2i−2i−2i−2i−2i2i2i-111-1-1-111−iii−i−i−iiiii−i−i0000000000000000000000000000000000003−3−330000i3−i3−i3i3
χ4522-2-2-2-22222-2-22i−2i−2i2i-2-2222i−2i−2i2i2-12-1-2-211-2-21122-1-12i2i−2i−2i−2i−2i2i2i-111-1-1-111−iii−i−i−iiiii−i−i000000000000000000000000000000000000−333−30000−i3i3i3−i3
χ4622-2-2-2-22222-2-22i−2i−2i2i-2-2222i−2i−2i2i-12-1211-2-211-2-2-1-122−i−iiiii−i−i-111-1-1-1112i−2i−2i2i−i−iiiii−i−i0000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ4722-2-2-2-22222-2-22i−2i−2i2i-2-2222i−2i−2i2i-12-1211-2-211-2-2-1-122−i−iiiii−i−i-111-1-1-1112i−2i−2i2i−i−iiiii−i−i00000000−3−33333−3−3−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ4822-2-2-2-22222-2-2−2i2i2i−2i-2-222−2i2i2i−2i2222-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i2-2-2222-2-2−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4922-2-2-2-22222-2-2−2i2i2i−2i-2-222−2i2i2i−2i2-12-1-2-211-2-21122-1-1−2i−2i2i2i2i2i−2i−2i-111-1-1-111i−i−iiii−i−i−i−iii0000000000000000000000000000000000003−3−330000−i3i3i3−i3
χ5022-2-2-2-22222-2-2−2i2i2i−2i-2-222−2i2i2i−2i2-12-1-2-211-2-21122-1-1−2i−2i2i2i2i2i−2i−2i-111-1-1-111i−i−iiii−i−i−i−iii000000000000000000000000000000000000−333−30000i3−i3−i3i3
χ5122-2-2-2-22222-2-2−2i2i2i−2i-2-222−2i2i2i−2i-12-1211-2-211-2-2-1-122ii−i−i−i−iii-111-1-1-111−2i2i2i−2iii−i−i−i−iii0000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ5222-2-2-2-22222-2-2−2i2i2i−2i-2-222−2i2i2i−2i-12-1211-2-211-2-2-1-122ii−i−i−i−iii-111-1-1-111−2i2i2i−2iii−i−i−i−iii00000000−3−33333−3−3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ532-22-22i−2i2i−2i2-22-200002i−2i2i−2i000022-2-22-22-22i−2i2i−2i2i−2i2i−2i0000000022-2-22i−2i2i−2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ542-22-22i−2i2i−2i2-22-200002i−2i2i−2i000022-2-22-22-22i−2i2i−2i2i−2i2i−2i0000000022-2-22i−2i2i−2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ552-22-22i−2i2i−2i2-22-200002i−2i2i−2i0000-121-2-112-2−ii2i−2i−ii2i−2i−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13-1-111−ii−ii0000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−i3i3−i3i33−33−3−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13000000000000000000000000
χ562-22-22i−2i2i−2i2-22-200002i−2i2i−2i0000-121-2-112-2−ii2i−2i−ii2i−2i−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13-1-111−ii−ii0000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13i3−i3i3−i3−33−33ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13000000000000000000000000
χ572-22-22i−2i2i−2i2-22-200002i−2i2i−2i0000-121-2-112-2−ii2i−2i−ii2i−2iζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13-1-111−ii−ii0000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13i3−i3i3−i3−33−33−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13000000000000000000000000
χ582-22-22i−2i2i−2i2-22-200002i−2i2i−2i0000-121-2-112-2−ii2i−2i−ii2i−2iζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13-1-111−ii−ii0000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−i3i3−i3i33−33−3ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13000000000000000000000000
χ592-22-2−2i2i−2i2i2-22-20000−2i2i−2i2i000022-2-22-22-2−2i2i−2i2i−2i2i−2i2i0000000022-2-2−2i2i−2i2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.