Finite Group Databasebeta

← Group #13173406

Character table — Group #13173406

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size111122222222224444444444444444444444444444444444444444444444449999181818181818181818185454545454545454111122222222224444444444444444444444444444444444444444444444449999181818181818181818185454545454545454
order1222344666121212123333336666666666666666661212121212121212121212121212121212121212121212122222446666121212124444444422226446661212121266666666666666666666666612121212121212121212121212121212121212121212121222224466661212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ511111-1-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-111111-1-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-1
χ611111-1-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111111-1-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111
χ711111-1-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii11111-1-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii
χ811111-1-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i11111-1-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i
χ911-1-11i−i1-1-1ii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i1-11-1i−i11-1-1ii−i−i1-1i−i1-1i−i11-1-11i−i1-1-1ii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i1-11-1i−i11-1-1ii−i−i1-1i−i1-1i−i
χ1011-1-11i−i1-1-1ii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i1-11-1i−i11-1-1ii−i−i-11−ii-11−ii11-1-11i−i1-1-1ii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i1-11-1i−i11-1-1ii−i−i-11−ii-11−ii
χ1111-1-11i−i1-1-1ii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-11-11−ii-1-111−i−iiii−i-11−ii1-111-1-11i−i1-1-1ii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-11-11−ii-1-111−i−iiii−i-11−ii1-1
χ1211-1-11i−i1-1-1ii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-11-11−ii-1-111−i−iii−ii1-1i−i-1111-1-11i−i1-1-1ii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-11-11−ii-1-111−i−iii−ii1-1i−i-11
χ1311-1-11−ii1-1-1−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii1-11-1−ii11-1-1−i−iii1-1−ii1-1−ii11-1-11−ii1-1-1−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii1-11-1−ii11-1-1−i−iii1-1−ii1-1−ii
χ1411-1-11−ii1-1-1−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii1-11-1−ii11-1-1−i−iii-11i−i-11i−i11-1-11−ii1-1-1−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii1-11-1−ii11-1-1−i−iii-11i−i-11i−i
χ1511-1-11−ii1-1-1−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-11-11i−i-1-111ii−i−ii−i1-1−ii-1111-1-11−ii1-1-1−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-11-11i−i-1-111ii−i−ii−i1-1−ii-11
χ1611-1-11−ii1-1-1−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-11-11i−i-1-111ii−i−i−ii-11i−i1-111-1-11−ii1-1-1−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-11-11i−i-1-111ii−i−i−ii-11i−i1-1
χ172222-122-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1000000002222-122-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000
χ182222-122-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111000000002222-122-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000
χ192222-1-2-2-1-1-1111122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-2-2-1-1-1-11111000000002222-1-2-2-1-1-1111122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-2-2-1-1-1-1111100000000
χ202222-1-2-2-1-1-1111122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2221111-1-1-1-1000000002222-1-2-2-1-1-1111122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2221111-1-1-1-100000000
χ2122-2-2-12i−2i-111−i−iii22-1-1-1-122-1-1-1-1-2-21111-2-211112i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii2-22-22i−2i-1-111−i−iii0000000022-2-2-12i−2i-111−i−iii22-1-1-1-122-1-1-1-1-2-21111-2-211112i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii2-22-22i−2i-1-111−i−iii00000000
χ2222-2-2-12i−2i-111−i−iii22-1-1-1-122-1-1-1-1-2-21111-2-211112i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii-22-22−2i2i11-1-1ii−i−i0000000022-2-2-12i−2i-111−i−iii22-1-1-1-122-1-1-1-1-2-21111-2-211112i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii-22-22−2i2i11-1-1ii−i−i00000000
χ2322-2-2-1−2i2i-111ii−i−i22-1-1-1-122-1-1-1-1-2-21111-2-21111−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i2-22-2−2i2i-1-111ii−i−i0000000022-2-2-1−2i2i-111ii−i−i22-1-1-1-122-1-1-1-1-2-21111-2-21111−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i2-22-2−2i2i-1-111ii−i−i00000000
χ2422-2-2-1−2i2i-111ii−i−i22-1-1-1-122-1-1-1-1-2-21111-2-21111−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i-22-222i−2i11-1-1−i−iii0000000022-2-2-1−2i2i-111ii−i−i22-1-1-1-122-1-1-1-1-2-21111-2-21111−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i-22-222i−2i11-1-1−i−iii00000000
χ252-22-2200-22-20000222222-2-2-2-2-2-2222222-2-2-2-2-2-200000000000000000000000022-2-2002-22-20000000000002-22-2200-22-20000222222-2-2-2-2-2-2222222-2-2-2-2-2-200000000000000000000000022-2-2002-22-2000000000000
χ262-22-2200-22-20000222222-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000-2-22200-22-220000000000002-22-2200-22-20000222222-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000-2-22200-22-22000000000000
χ272-22-2-1001-113−33−322-1-1-1-1-2-2111122-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−322-2-200-11-113−33−3000000002-22-2-1001-113−33−322-1-1-1-1-2-2111122-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−322-2-200-11-113−33−300000000
χ282-22-2-1001-113−33−322-1-1-1-1-2-2111122-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−3-2-222001-11-1−33−33000000002-22-2-1001-113−33−322-1-1-1-1-2-2111122-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−3-2-222001-11-1−33−3300000000
χ292-22-2-1001-11−33−3322-1-1-1-1-2-2111122-1-1-1-1-2-211110000−3−3−3−333330000−3−3−3−3333322-2-200-11-11−33−33000000002-22-2-1001-11−33−3322-1-1-1-1-2-2111122-1-1-1-1-2-211110000−3−3−3−333330000−3−3−3−3333322-2-200-11-11−33−3300000000
χ302-22-2-1001-11−33−3322-1-1-1-1-2-2111122-1-1-1-1-2-211110000−3−3−3−333330000−3−3−3−33333-2-222001-11-13−33−3000000002-22-2-1001-11−33−3322-1-1-1-1-2-2111122-1-1-1-1-2-211110000−3−3−3−333330000−3−3−3−33333-2-222001-11-13−33−300000000
χ312-2-22200-2-220000222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000002-2-22002-2-220000000000002-2-22200-2-220000222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000002-2-22002-2-22000000000000
χ322-2-22200-2-220000222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000-222-200-222-20000000000002-2-22200-2-220000222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000-222-200-222-2000000000000
χ332-2-22-10011-1−i3i3i3−i322-1-1-1-1-2-21111-2-2111122-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i32-2-2200-111-1−i3i3i3−i3000000002-2-22-10011-1−i3i3i3−i322-1-1-1-1-2-21111-2-2111122-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i32-2-2200-111-1−i3i3i3−i300000000
χ342-2-22-10011-1−i3i3i3−i322-1-1-1-1-2-21111-2-2111122-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-222-2001-1-11i3−i3−i3i3000000002-2-22-10011-1−i3i3i3−i322-1-1-1-1-2-21111-2-2111122-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-222-2001-1-11i3−i3−i3i300000000
χ352-2-22-10011-1i3−i3−i3i322-1-1-1-1-2-21111-2-2111122-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i32-2-2200-111-1i3−i3−i3i3000000002-2-22-10011-1i3−i3−i3i322-1-1-1-1-2-21111-2-2111122-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i32-2-2200-111-1i3−i3−i3i300000000
χ362-2-22-10011-1i3−i3−i3i322-1-1-1-1-2-21111-2-2111122-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-222-2001-1-11−i3i3i3−i3000000002-2-22-10011-1i3−i3−i3i322-1-1-1-1-2-21111-2-2111122-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-222-2001-1-11−i3i3i3−i300000000
χ37444444444444441-211-2-21-211-2-21-211-2-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-20000000000000000000000444444444444441-211-2-21-211-2-21-211-2-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-20000000000000000000000
χ3844444444444444-21-2-211-21-2-211-21-2-211-21-2-211-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000000044444444444444-21-2-211-21-2-211-21-2-211-21-2-211-2-211-2-211-2-211-2-211-2-211-2-2110000000000000000000000
χ3944444-4-4444-4-4-4-41-211-2-21-211-2-21-211-2-21-211-2-2-1-122-1-122-1-122-1-122-1-122-1-122000000000000000000000044444-4-4444-4-4-4-41-211-2-21-211-2-21-211-2-21-211-2-2-1-122-1-122-1-122-1-122-1-122-1-1220000000000000000000000
χ4044444-4-4444-4-4-4-4-21-2-211-21-2-211-21-2-211-21-2-21122-1-122-1-122-1-122-1-122-1-122-1-1000000000000000000000044444-4-4444-4-4-4-4-21-2-211-21-2-211-21-2-211-21-2-21122-1-122-1-122-1-122-1-122-1-122-1-10000000000000000000000
χ414444-244-2-2-2-2-2-2-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321100000000000000000000004444-244-2-2-2-2-2-2-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i32110000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.