Finite Group Databasebeta

← Group #13135165

Character table — Group #13135165

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order12224444223446661212121266121233666666666612121212121212121212121236666666661212121212121212121244444444121212121212121212121212121212124444888812121212121212122424242424242424
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
χ51111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-11111111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i
χ61111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-11111111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii
χ71111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-11111111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii
χ81111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-11111111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i
χ911-1-111-1-1-1111-11-1-111-1-11-11-111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-111-1-111-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i
χ1011-1-111-1-1-1111-11-1-111-1-11-11-111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-111-1-111-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii
χ1111-1-111-1-1-1111-11-1-111-1-11-11-111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-111-1-111-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii
χ1211-1-111-1-1-1111-11-1-111-1-11-11-111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-111-1-111-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i
χ1311-1-1-1-1111-111-11-1-1-1-111-111-111-1-1-1-11111-1-111-1-1-1-1-1-111111-11-1-1-1-11111-111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1ii−i−i−i−iii-1-11111-1-1
χ1411-1-1-1-1111-111-11-1-1-1-111-111-111-1-1-1-11111-1-111-1-1-1-1-1-111111-11-1-1-1-11111-111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11−i−iiiii−i−i11-1-1-1-111
χ1511-1-1-1-1111-111-11-1-1-1-111-111-111-1-1-1-11111-1-111-1-1-1-1-1-111111-11-1-1-1-11111-111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11ii−i−i−i−iii11-1-1-1-111
χ1611-1-1-1-1111-111-11-1-1-1-111-111-111-1-1-1-11111-1-111-1-1-1-1-1-111111-11-1-1-1-11111-111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1−i−iiiii−i−i-1-11111-1-1
χ172222222222222222222222222-122-1-1222-122222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ182222222222222222222222222-122-1-1222-122222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-20000000011111111
χ19222222222222222222222222-12-1-122-1-1-12-1-1-1-1-1-1-1-122-1-122-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ20222222222222222222222222-12-1-122-1-1-12-1-1-1-1-1-1-1-122-1-122-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ2122222222-2-22-2-22222222-2-2-2-2222222-2-222-2-2-2-2-2-2222222222-2-222-2-2-2-22-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2222222222-2-22-2-22222222-2-2-2-22-122-1-1-2-22-1-2-2-2-2-2-222-1-122-1-1-111-1-11111-1111111-1-1-1-10000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i3
χ2322222222-2-22-2-22222222-2-2-2-22-122-1-1-2-22-1-2-2-2-2-2-222-1-122-1-1-111-1-11111-1111111-1-1-1-10000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i3
χ2422222222-2-22-2-22222222-2-2-2-2-12-1-12211-12111111-1-122-1-122-1-2-2-1-11111-1-2-21111-1-1-1-10000000033−3−333−3−333−3−333−3−3000000000000000000000000
χ2522222222-2-22-2-22222222-2-2-2-2-12-1-12211-12111111-1-122-1-122-1-2-2-1-11111-1-2-21111-1-1-1-100000000−3−333−3−333−3−333−3−333000000000000000000000000
χ262222-2-2-2-2222-2-2222-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ272222-2-2-2-2222-2-2222-2-2-2-222-2-22-122-1-1222-122-2-2-2-2-2-211-2-211-1-1-1-1-1-1-1-1-1-1111111111100000000000000000000000000000000000000003−33−3−33−33
χ282222-2-2-2-2222-2-2222-2-2-2-222-2-22-122-1-1222-122-2-2-2-2-2-211-2-211-1-1-1-1-1-1-1-1-1-111111111110000000000000000000000000000000000000000−33−333−33−3
χ292222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-122-1-1-12-1-1111111-2-211-2-2-122-1-1-1-1-1-1-1-2-21111111100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ302222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-122-1-1-12-1-1111111-2-211-2-2-122-1-1-1-1-1-1-1-2-21111111100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ312222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-1-1-2-22-1-2-22222-2-211-2-211-111-1-11111-1-1-1-1-1-1-1111100000000000000000000000000002i2i−2i−2i00000000−i−i−i−iiiii
χ322222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-1-1-2-22-1-2-22222-2-211-2-211-111-1-11111-1-1-1-1-1-1-111110000000000000000000000000000−2i−2i2i2i00000000iiii−i−i−i−i
χ332222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-12211-1211-1-1-1-111-2-211-2-2-1-2-2-1-11111-122-1-1-1-111112i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii000000000000000000000000
χ342222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-12211-1211-1-1-1-111-2-211-2-2-1-2-2-1-11111-122-1-1-1-11111−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i000000000000000000000000
χ3522-2-222-2-22-22-222-2-222-2-2-22-2222-2-2-2-22222-2-2-2-2222222-2-2-2-22-22-2-2-2-2222-22-2-22222-2-2000000000000000000000000000000000000000000000000
χ3622-2-222-2-22-22-222-2-222-2-2-22-222-1-2-211222-1-2-2-2-22222-1-1-2-211-11-11111-1-1-11-111-1-1-1-11100000000000000000000000000000000000000003−3−333−3−33
χ3722-2-222-2-22-22-222-2-222-2-2-22-222-1-2-211222-1-2-2-2-22222-1-1-2-211-11-11111-1-1-11-111-1-1-1-1110000000000000000000000000000000000000000−333−3−333−3
χ3822-2-222-2-22-22-222-2-222-2-2-22-22-1211-2-2-1-1-121111-1-1-1-12211-2-2-1-221111-1-1-1-2211-1-1-1-1110000000033−3−3−3−33333−3−3−3−333000000000000000000000000
χ3922-2-222-2-22-22-222-2-222-2-2-22-22-1211-2-2-1-1-121111-1-1-1-12211-2-2-1-221111-1-1-1-2211-1-1-1-11100000000−3−33333−3−3−3−33333−3−3000000000000000000000000
χ4022-2-222-2-2-2222-22-2-222-2-22-22-22-1-2-211-2-22-12222-2-222-1-1-2-211-1-1111-1-111-1-11-1-111-1-11100000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii
χ4122-2-222-2-2-2222-22-2-222-2-22-22-22-1-2-211-2-22-12222-2-222-1-1-2-211-1-1111-1-111-1-11-1-111-1-1110000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i
χ4222-2-222-2-2-2222-22-2-222-2-22-22-2-1211-2-211-12-1-1-1-111-1-12211-2-2-12-211-1-111-12-2-1-111-1-11122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ4322-2-222-2-2-2222-22-2-222-2-22-22-2-1211-2-211-12-1-1-1-111-1-12211-2-2-12-211-1-111-12-2-1-111-1-111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ4422-2-2-2-2222-222-22-2-2-2-222-222-22-1-2-211222-1-2-222-2-2-2-21122-1-1-11-11111-1-1-1-11-1-11111-1-100000000000000000000000000002-2-2200000000-1-11111-1-1
χ4522-2-2-2-2222-222-22-2-2-2-222-222-22-1-2-211222-1-2-222-2-2-2-21122-1-1-11-11111-1-1-1-11-1-11111-1-10000000000000000000000000000-222-20000000011-1-1-1-111
χ4622-2-2-2-2222-222-22-2-2-2-222-222-2-1211-2-2-1-1-1211-1-11111-2-2-1-122-1-221111-1-1-12-2-1-11111-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ4722-2-2-2-2222-222-22-2-2-2-222-222-2-1211-2-2-1-1-1211-1-11111-2-2-1-122-1-221111-1-1-12-2-1-11111-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
χ4822-2-2-2-222-222-222-2-2-2-2222-2-2222-2-2-2-2-2-22222-2-222-2-2-2-2222222-2-2-222-2-22-22-2-222-2-222000000000000000000000000000000000000000000000000
χ4922-2-2-2-222-222-222-2-2-2-2222-2-222-1-2-211-2-22-122-2-222-2-21122-1-1-1-1111-1-111-11-111-1-111-1-10000000000000000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ5022-2-2-2-222-222-222-2-2-2-2222-2-222-1-2-211-2-22-122-2-222-2-21122-1-1-1-1111-1-111-11-111-1-111-1-10000000000000000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
χ5122-2-2-2-222-222-222-2-2-2-2222-2-22-1211-2-211-12-1-111-1-111-2-2-1-122-12-211-1-111-1-2211-1-111-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ5222-2-2-2-222-222-222-2-2-2-2222-2-22-1211-2-211-12-1-111-1-111-2-2-1-122-12-211-1-111-1-2211-1-111-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ532-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000222-22-200-2-20000002i−2i2i−2i2i−2i2i−2i2002-20000-20000002i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i000000000000000000000000
χ542-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000222-22-200-2-20000002i−2i2i−2i2i−2i2i−2i2002-20000-20000002i−2i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i000000000000000000000000
χ552-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-112-2−i3i31-2−i3i33−33−3−ii2i−2i−ii2i−2i-100-11−i3i3−i3i31003−33−3−ii−ii1+i−1−i1+i−1−i1−i−1+i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000000000000000
χ562-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-112-2−i3i31-2−i3i33−33−3−ii2i−2i−ii2i−2i-100-11−i3i3−i3i31003−33−3−ii−ii−1−i1+i−1−i1+i−1+i1−i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000000000000000
χ572-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-112-2i3−i31-2i3−i3−33−33−ii2i−2i−ii2i−2i-100-11i3−i3i3−i3100−33−33−ii−ii1+i−1−i1+i−1−i1−i−1+i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000000000000000
χ582-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-112-2i3−i31-2i3−i3−33−33−ii2i−2i−ii2i−2i-100-11i3−i3i3−i3100−33−33−ii−ii−1−i1+i−1−i1+i−1+i1−i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000000000000000
χ592-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000222-22-200-2-2000000−2i2i−2i2i−2i2i−2i2i2002-20000-2000000−2i2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000000000000000000000
χ602-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000222-22-200-2-2000000−2i2i−2i2i−2i2i−2i2i2002-20000-2000000−2i2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000000000000000000000
χ612-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-112-2−i3i31-2−i3i3−33−33i−i−2i2ii−i−2i2i-100-11−i3i3−i3i3100−33−33i−ii−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000000000000000
χ622-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-112-2−i3i31-2−i3i3−33−33i−i−2i2ii−i−2i2i-100-11−i3i3−i3i3100−33−33i−ii−i−1+i1−i−1+i1−i−1−i1+i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.