Finite Group Databasebeta

← Group #13168598

Character table — Group #13168598

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444466668888888888889999121212121212121212121212121212121212121212121212121212121818181818182424242424242424242424243636363636365454545472727272
order122233344666666666333666666666121212121212121212124444366612121212121212124444224466661212121212121212121212121212121212121212441212121266666612121212121244441212224412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-11-111-1-11111111111-1-111111111-1-1-1-1-1-11-111-1-11-111-1-11-11-1-1-1-1-1-1-11-11-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1-11111111111-1-11111111111-1-1-1-1-1-1-11-1-111-11-1-111-11-11-1-1-1-1-1-1-11-11
χ51111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1-11-11-1-11111-11-11
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-1111-11-1-1-111111-11-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-111-1-1-11-1-1111-1-11-1-111-1-1-111-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-11111-11-1-1111-111-1-1-111-1-1-111-1-11-1-11
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111111-111-1-1-11-1-111-111-1-1-1-1-1111-1-11
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-11-1-1111-111-1-11-1-11-1-1-1-111-111-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ17222222-122-122-12222-12-1-1-1-12-1-122-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-100000000-1-1-1-10000000022-1-1-1-122-1-1-1-122-1-1-1-10000-1-100000000
χ18222222-122-122-12222-12-1-1-1-12-1-122-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211110000000011110000000022-1-1-1-1-2-21111-2-211110000-1-100000000
χ19222222-122-122-12222-12-1-1-1-12-1-122-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-22-2-1-11100000000-1-11100000000-2-211112-2-1-1112-2-1-11100001100000000
χ20222222-122-122-12222-12-1-1-1-12-1-122-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22-2211-1-10000000011-1-100000000-2-21111-2211-1-1-2211-1-100001100000000
χ21222222-1-2-2-122-12222-12-1-1-1-12-1-122-1-111-2-2-2-2-2-2-2-20000-1-1-1-11111111122222-2-22-1-1110000000011-1-100000000-2-2-1-1-1-12-2-1-111-2211-1-100001100000000
χ22222222-1-2-2-122-12222-12-1-1-1-12-1-122-1-111-2-2-2-2-2-2-2-20000-1-1-1-1111111112222-222-211-1-100000000-1-11100000000-2-2-1-1-1-1-2211-1-12-2-1-11100001100000000
χ23222222-1-2-2-122-12222-12-1-1-1-12-1-122-1-111-2-2-2-2-2-2-2-20000-1-1-1-111111111-2-2-2-222-2-2-1-1-1-10000000011110000000022111122-1-1-1-1-2-211110000-1-100000000
χ24222222-1-2-2-122-12222-12-1-1-1-12-1-122-1-111-2-2-2-2-2-2-2-20000-1-1-1-111111111-2-2-2-2-2-222111100000000-1-1-1-100000000221111-2-2111122-1-1-1-10000-1-100000000
χ2522222-122222-122-12-12-12-12-1-12-1-1-12-12222-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-100000202002222-1-122-1-10022-1-1-1-1-1-1-1-10000000-100-1-10-100-1-102020000000-10-1
χ2622222-122222-122-12-12-12-12-1-12-1-1-12-12222-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-100000-20-200-2-222-1-122-1-100-2-2-1-1-1-1-1-1-1-10000000100110100110-20-20000000101
χ2722222-122222-122-12-12-12-12-1-12-1-1-12-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1000002020022-2-211-2-2110022111111110000000-100-1-10-100-1-10-20-20000000101
χ2822222-122222-122-12-12-12-12-1-12-1-1-12-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-100000-20-200-2-2-2-211-2-21100-2-21111111100000001001101001102020000000-10-1
χ2922222-12-2-222-122-12-12-12-12-1-12-1-1-12-1-2-2-2-211111122-2-2-1-1-1-1-2-21111110000020-2002222-1-1-2-21100-2-2-1-1-1-111110000000-100-1-1010011020-2000000010-1
χ3022222-12-2-222-122-12-12-12-12-1-12-1-1-12-1-2-2-2-211111122-2-2-1-1-1-1-2-211111100000-20200-2-222-1-1-2-2110022-1-1-1-111110000000100110-100-1-10-2020000000-101
χ3122222-12-2-222-122-12-12-12-12-1-12-1-1-12-1-2-2-2-2111111-2-222-1-1-1-1-2-21111110000020-20022-2-21122-1-100-2-21111-1-1-1-10000000-100-1-10100110-2020000000-101
χ3222222-12-2-222-122-12-12-12-12-1-12-1-1-12-1-2-2-2-2111111-2-222-1-1-1-1-2-211111100000-20200-2-2-2-21122-1-100221111-1-1-1-10000000100110-100-1-1020-2000000010-1
χ332222-122222-122-12-122-1-12-12-1-12-1-1-1222-1-122-1-1-1-12222-1-1-1-1-1-122-1-1-1-1000020202200-1-122-1-1222200-1-1-1-1-1-1-1-1000000-10-1-100-10-1-1002020000000-10-10
χ342222-122222-122-12-122-1-12-12-1-12-1-1-1222-1-122-1-1-1-12222-1-1-1-1-1-122-1-1-1-10000-20-20-2-200-1-122-1-122-2-200-1-1-1-1-1-1-1-1000000101100101100-20-200000001010
χ352222-122222-122-12-122-1-12-12-1-12-1-1-1222-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-100002020220011-2-211-2-2220011111111000000-10-1-100-10-1-100-20-200000001010
χ362222-122222-122-12-122-1-12-12-1-12-1-1-1222-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-10000-20-20-2-20011-2-211-2-2-2-200111111110000001011001011002020000000-10-10
χ372222-122-2-22-122-12-122-1-12-12-1-12-1-1-12-2-211-2-2111122-2-2-1-1-1-111-2-21111000020-202200-1-12211-2-2-2-200-1-1-1-11111000000-10-1-10010110020-2000000010-10
χ382222-122-2-22-122-12-122-1-12-12-1-12-1-1-12-2-211-2-2111122-2-2-1-1-1-111-2-211110000-2020-2-200-1-12211-2-22200-1-1-1-11111000000101100-10-1-100-2020000000-1010
χ392222-122-2-22-122-12-122-1-12-12-1-12-1-1-12-2-211-2-21111-2-222-1-1-1-111-2-21111000020-20220011-2-2-1-122-2-2001111-1-1-1-1000000-10-1-100101100-2020000000-1010
χ402222-122-2-22-122-12-122-1-12-12-1-12-1-1-12-2-211-2-21111-2-222-1-1-1-111-2-211110000-2020-2-20011-2-2-1-12222001111-1-1-1-1000000101100-10-1-10020-2000000010-10
χ4122-2-222200-222-2-2-2-2-22222-2-2-2-2-22-2220000000000002i−2i22-2-20000000022-2-20000000000002i−2i2i−2i000000002i2i−2i−2i0022-2-2000000000000000000002i−2i0000
χ4222-2-222200-222-2-2-2-2-22222-2-2-2-2-22-2220000000000002i−2i22-2-200000000-2-2220000000000002i−2i2i−2i000000002i2i−2i−2i00-2-22200000000000000000000−2i2i0000
χ4322-2-222200-222-2-2-2-2-22222-2-2-2-2-22-222000000000000−2i2i22-2-20000000022-2-2000000000000−2i2i−2i2i00000000−2i−2i2i2i0022-2-200000000000000000000−2i2i0000
χ4422-2-222200-222-2-2-2-2-22222-2-2-2-2-22-222000000000000−2i2i22-2-200000000-2-222000000000000−2i2i−2i2i00000000−2i−2i2i2i00-2-222000000000000000000002i−2i0000
χ452-22-22222i−2i-2-2-22-2-222-222222-2-2-2-22-2-22i−2i2i−2i2i−2i2i2i−2i−2i00002-22-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i00000000000000000000000000002-22i−2i2i−2i00000000000000002-200000000
χ462-22-22222i−2i-2-2-22-2-222-222222-2-2-2-22-2-22i−2i2i−2i2i−2i2i2i−2i−2i00002-22-22i−2i2i−2i2i2i−2i−2i−2i2i−2i2i0000000000000000000000000000-22−2i2i−2i2i0000000000000000-2200000000
χ472-22-2222−2i2i-2-2-22-2-222-222222-2-2-2-22-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00002-22-2−2i2i−2i2i−2i−2i2i2i2i−2i2i−2i0000000000000000000000000000-222i−2i2i−2i0000000000000000-2200000000
χ482-22-2222−2i2i-2-2-22-2-222-222222-2-2-2-22-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00002-22-2−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i00000000000000000000000000002-2−2i2i−2i2i00000000000000002-200000000
χ492-22-222-12i−2i1-2-2-1-2-22212-1-1-1-1-211-2211−ii2i−2i2i−2i2i2i−2i−2i0000-11-11−ii−ii−i−iii2i−2i2i−2i0000−i3i3−i3i3000000003−33−3000000002-2−ii−ii00−i3i3−i3i3003−33−30000-1100000000
χ502-22-222-12i−2i1-2-2-1-2-22212-1-1-1-1-211-2211−ii2i−2i2i−2i2i2i−2i−2i0000-11-11−ii−ii−i−iii2i−2i2i−2i0000i3−i3i3−i300000000−33−33000000002-2−ii−ii00i3−i3i3−i300−33−330000-1100000000
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χ522-22-222-12i−2i1-2-2-1-2-22212-1-1-1-1-211-2211−ii2i−2i2i−2i2i2i−2i−2i0000-11-11−ii−ii−i−iii−2i2i−2i2i0000i3−i3−i3i300000000−333−300000000-22i−ii−i00i3−i3−i3i300−333−300001-100000000
χ532-22-222-1−2i2i1-2-2-1-2-22212-1-1-1-1-211-2211i−i−2i2i−2i2i−2i−2i2i2i0000-11-11i−ii−iii−i−i2i−2i2i−2i0000−i3i3i3−i300000000−333−300000000-22−ii−ii00−i3i3i3−i300−333−300001-100000000
χ542-22-222-1−2i2i1-2-2-1-2-22212-1-1-1-1-211-2211i−i−2i2i−2i2i−2i−2i2i2i0000-11-11i−ii−iii−i−i2i−2i2i−2i0000i3−i3−i3i3000000003−3−3300000000-22−ii−ii00i3−i3−i3i3003−3−3300001-100000000
χ552-22-222-1−2i2i1-2-2-1-2-22212-1-1-1-1-211-2211i−i−2i2i−2i2i−2i−2i2i2i0000-11-11i−ii−iii−i−i−2i2i−2i2i0000−i3i3−i3i300000000−33−33000000002-2i−ii−i00−i3i3−i3i300−33−330000-1100000000
χ562-22-222-1−2i2i1-2-2-1-2-22212-1-1-1-1-211-2211i−i−2i2i−2i2i−2i−2i2i2i0000-11-11i−ii−iii−i−i−2i2i−2i2i0000i3−i3i3−i3000000003−33−3000000002-2i−ii−i00i3−i3i3−i3003−33−30000-1100000000
χ572-2-22222002-2-2-222-2-2-2222-2-2222-2-2-2-200000000002i−2i002-2-22000000002i−2i−2i2i000000002i−2i2i−2i000000002i2i−2i−2i0000002i−2i−2i2i0000000000000000002-2000000
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χ6244444-2-244-24-2-24-24-2-2-2-21-21-2-21-2-2-21-2-244-2-2-2-2-2-200001111-2-211111100000-40-40022000000000022000000000000000200-1-10200-1-100000000000000
χ6344444-2-2-4-4-24-2-24-24-2-2-2-21-21-2-21-2-2-2122-4-42222220000111122-1-1-1-1-1-10000040-400-2-2000000000022000000000000000-200110200-1-100000000000000
χ6444444-2-2-4-4-24-2-24-24-2-2-2-21-21-2-21-2-2-2122-4-42222220000111122-1-1-1-1-1-100000-40400220000000000-2-2000000000000000200-1-10-2001100000000000000
χ654444-24-244-2-24-2-24-24-2-21-21-2-21-2-2-21-2-2-2-2-244-2-2-2-20000111111-2-2111100004040-2-20000000000-2-20000000000000000-201100-20110000000000000000
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χ684444-24-2-4-4-2-24-2-24-24-2-21-21-2-21-2-2-21-22222-4-4222200001111-1-122-1-1-1-10000-4040220000000000-2-2000000000000000020-1-100-20110000000000000000
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χ704444-2-24444-2-24-2-2-2-241-2-2-2-21-2-211-2-244-2-2-2-21111-4-4-4-41111-2-2-2-21111000000000000222222220000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ714444-2-24-4-44-2-24-2-2-2-241-2-2-2-21-2-211-2-2-4-42222-1-1-1-144-4-411112222-1-1-1-1000000000000-2-2-2-2222200001111-1-1-1-100000000000000000000000000000000
χ724444-2-24-4-44-2-24-2-2-2-241-2-2-2-21-2-211-2-2-4-42222-1-1-1-1-4-44411112222-1-1-1-10000000000002222-2-2-2-20000-1-1-1-1111100000000000000000000000000000000
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χ854-44-44-2-24i−4i2-42-2-424-22-2-21-2122-12-22-1−2i2i4i−4i−2i2i−2i−2i2i2i00001-11-1−2i2ii−iii−i−i0000000000−2i32i3000000000023−23000000000000000000i3−i30000−3300000000000000
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χ914-44-4-24-24i−4i22-4-22-4-242-21-21-22-122-2-12−2i2i−2i2i4i−4i−2i−2i2i2i00001-11-1i−i−2i2iii−i−i00000000−2i32i3000000000023−23000000000000000000i3−i30000−330000000000000000
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χ934-44-4-24-2−4i4i22-4-22-4-242-21-21-22-122-2-122i−2i2i−2i−4i4i2i2i−2i−2i00001-11-1−ii2i−2i−i−iii00000000−2i32i30000000000−2323000000000000000000i3−i300003−30000000000000000
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χ974-44-4-2-24−4i4i-422422-2-2-41-2-2-2-2-122-1122−4i4i2i−2i2i−2i−i−iii00001-11-12i−2i2i−2i−i−iii0000000000000000000000003i−3i−3i3i-33-3300000000000000000000000000000000
χ984-44-4-2-24−4i4i-422422-2-2-41-2-2-2-2-122-1122−4i4i2i−2i2i−2i−i−iii00001-11-12i−2i2i−2i−i−iii000000000000000000000000−3i3i3i−3i3-33-300000000000000000000000000000000
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χ1034-4-44-2440042-4-4-242-4-4-2-242-4-2-24222-400000000004i−4i00-222-200000000000000000000−2i2i4i−4i00000000−2i−2i2i2i000000000000000000000000000000000000
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χ1054-4-44-2-2400422-4-2-222-41-2-2221-2-2-1-1220000003-3-334i−4i001-1-1100003-3-33000000000000−2i2i−2i2i00000000ii−i−i−3i3i3i−3i00000000000000000000000000000000
χ1064-4-44-2-2400422-4-2-222-41-2-2221-2-2-1-1220000003-3-33−4i4i001-1-1100003-3-330000000000002i−2i2i−2i00000000−i−iii3i−3i−3i3i00000000000000000000000000000000
χ1074-4-44-2-2400422-4-2-222-41-2-2221-2-2-1-122000000-333-34i−4i001-1-110000-333-3000000000000−2i2i−2i2i00000000ii−i−i3i−3i−3i3i00000000000000000000000000000000
χ1084-4-44-2-2400422-4-2-222-41-2-2221-2-2-1-122000000-333-3−4i4i001-1-110000-333-30000000000002i−2i2i−2i00000000−i−iii−3i3i3i−3i00000000000000000000000000000000
χ1098888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-422220000-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000000000000000
χ1108888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-2-2-2-20000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000000000000000
χ11188-8-88-4-40048-44-84-84-4-4-424-244-2-44-420000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
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χ11388-8-8-4-4-4004-4-444444-4222-2-2-2-2-22-2220000006i−6i6i−6i0000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000000
χ11488-8-8-4-4-4004-4-444444-4222-2-2-2-2-22-222000000−6i6i−6i6i0000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000000000
χ1158-88-8-4-4-48i−8i444-444-4-4422222-2-2-2-22-2-2−4i4i−4i4i−4i4i2i2i−2i−2i0000-11-112i−2i2i−2i−i−iii0000000000000000000000000000000000000000000000000000000000000000
χ1168-88-8-4-4-4−8i8i444-444-4-4422222-2-2-2-22-2-24i−4i4i−4i4i−4i−2i−2i2i2i0000-11-11−2i2i−2i2iii−i−i0000000000000000000000000000000000000000000000000000000000000000
χ1178-8-888-4-400-4-8448-4-844-4-424-2-4-42444-2000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1188-8-88-48-400-44-84-484-84-42-4-24-42-444-24000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1198-8-88-4-4-400-4444-4-4444222-2-2222-2-2-2-20000006-6-660000-111-10000-333-30000000000000000000000000000000000000000000000000000000000000000
χ1208-8-88-4-4-400-4444-4-4444222-2-2222-2-2-2-2000000-666-60000-111-100003-3-330000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).