Finite Group Databasebeta

← Group #13168388

Character table — Group #13168388

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order12223336666666663334666666666121212121212121244441212121236661212121212121212124444121212121212121212121212121212121212121212124412121212121212121212121224444661212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-11-1111111111-1-1111111111111111-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111111111111111111-11111-1-1-1-1-1-111111111111111-1-1-11111111-1-1-1-1-11-11-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-1-1-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-111-1-1-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-11-11-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11111111-1-1-1-1-1-1-1-11-1-11111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-11-1111-1-111-1-1-1-111-1-1-111-1-111-11-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1111111-1-11111-1-1-1-111-1-11-1-1-11111-1-111-1-1-11111-1-1-1-11-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1111-1-1-1-1111-1-11111-1-111-11-1-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11-11-1-1-111-1-111-111-11-1-1-1-1111-111-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-1-111-1-1-1-11111-1-1-11-1111-1-111-1-1-111-11-1-1-1-1111-11-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-11-1-1-11111-1-11-1-11111-1-111-11-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1111-1-111-1-1-1-1-1-111-1-1-1-111111111-1111-1-1-1-11111-1-1-11111-1-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-111-1-1-1-11111111-11-1-1-111-1-111-1-111-1-1-111-1-111-1-11
χ17222222-1-1222-1-12222-1-12-1-1-1222-1-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-12220002222-1-1-1-100000000000000-1-122-1-1-1-1-1-1-1-120200-1-10000-10000
χ18222222-1-1222-1-12222-1-12-1-1-1222-1-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1-22-20002222-1-11100000000000000-11-2-21111-1-1-1-1-20-20011000010000
χ19222222-1-1222-1-12222-1-12-1-1-1222-1-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-12-22000-2-2-2-211-1-1000000000000001-122-1-1-1-11111-20-20011000010000
χ20222222-1-1222-1-12222-1-12-1-1-1222-1-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2000-2-2-2-211110000000000000011-2-21111111120200-1-10000-10000
χ21222222-1-1222-1-12222-1-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200220000-1-1-1-11111111112-2-200022-2-2-1-111000000000000001-1-22-1-111-1-111-20200110000-10000
χ22222222-1-1222-1-12222-1-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-2-2200022-2-2-1-1-1-100000000000000112-211-1-1-1-11120-200-1-1000010000
χ23222222-1-1222-1-12222-1-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-111111111122-2000-2-222111100000000000000-1-1-22-1-11111-1-120-200-1-1000010000
χ24222222-1-1222-1-12222-1-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111-222000-2-22211-1-100000000000000-112-211-1-111-1-1-20200110000-10000
χ2522222-1222-1222-1-12-12-1222-1-1-1-1-1-1222-1-1-1-1-1-122002222-1-1-1-12-1-122-1-1-1-12022-1-100000022-1-122-1-1-1-1-1-1-1-10002-1-1-1-1-1-10000020200000000-1-100
χ2622222-1222-1222-1-12-12-1222-1-1-1-1-1-1222-1-1-1-1-1-122002222-1-1-1-12-1-122-1-1-1-1-20-22-1-1000000-2-2-1-122-1-1-1-1-1-1-1-1000-211111100000-20-2000000001100
χ2722222-1222-1222-1-12-12-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-1202-2110000002211-2-2111111110002-1-1-1-1-1-100000-20-2000000001100
χ2822222-1222-1222-1-12-12-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-1-20-2-211000000-2-211-2-211111111000-21111110000020200000000-1-100
χ2922222-1222-1222-1-12-12-1-222-1-1-1-1-1-12-2-211111122002222-1-1-1-1-211-2-2111120-2-211000000-2-2-1-1-2-2-1-1-1-1111100021-1-1-11100000-20200000000-1100
χ3022222-1222-1222-1-12-12-1-222-1-1-1-1-1-12-2-211111122002222-1-1-1-1-211-2-21111-202-21100000022-1-1-2-2-1-1-1-11111000-2-1111-1-10000020-2000000001-100
χ3122222-1222-1222-1-12-12-1-222-1-1-1-1-1-12-2-2111111-2-200-2-2-2-2-1-1-1-1-211-2-2111120-22-1-1000000-2-211221111-1-1-1-100021-1-1-1110000020-2000000001-100
χ3222222-1222-1222-1-12-12-1-222-1-1-1-1-1-12-2-2111111-2-200-2-2-2-2-1-1-1-1-211-2-21111-2022-1-10000002211221111-1-1-1-1000-2-1111-1-100000-20200000000-1100
χ332222-1222-12-12222-1-1-122-1-12-1-1-122-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1020222-1-1-1-1220022-1-1-1-1-1-1-1-1-1-12220000000-1-1-1-10000200-1-1-1-100000
χ342222-1222-12-12222-1-1-122-1-12-1-1-122-1-1-122-1-1-1-122-2-2-1-1-1-1-1-1-1-1222-1-1-1-1-1-10-202221111-2-20022-1-1-1-1-1-1-1-1-1-1-2-2-2000000011110000-200111100000
χ352222-1222-12-12222-1-1-122-1-12-1-1-122-1-1-122-1-1-1-1-2-2221111-1-1-1-1222-1-1-1-1-1-1020-2-2-2-1-1-1-12200-2-21111111111-2-220000000-1-1-1-10000-200111100000
χ362222-1222-12-12222-1-1-122-1-12-1-1-122-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-10-20-2-2-21111-2-200-2-2111111111122-2000000011110000200-1-1-1-100000
χ372222-1222-12-12222-1-1-12-2-1-12-1-1-122-111-2-211112222-1-1-1-1-1-1-1-1-2-2-21111110-20-2-2-2-1-11122002211-1-1-1-1111122-20000000-1-1110000-200-1-11100000
χ382222-1222-12-12222-1-1-12-2-1-12-1-1-122-111-2-2111122-2-2-1-1-1-1-1-1-1-1-2-2-2111111020-2-2-211-1-1-2-2002211-1-1-1-11111-2-22000000011-1-1000020011-1-100000
χ392222-1222-12-12222-1-1-12-2-1-12-1-1-122-111-2-21111-2-2221111-1-1-1-1-2-2-21111110-20222-1-1112200-2-2-1-11111-1-1-1-1-2-2-20000000-1-111000020011-1-100000
χ402222-1222-12-12222-1-1-12-2-1-12-1-1-122-111-2-21111-2-2-2-21111-1-1-1-1-2-2-211111102022211-1-1-2-200-2-2-1-11111-1-1-1-1222000000011-1-10000-200-1-11100000
χ412-22-2222-2-2-222-22-2-22220-2-2-22-2-2-222000000002i−2i2-22i2i−2i−2i2-2-220000000000000002-2002-2002i−2i002i2i−2i−2i00002i−2i000000002-20000000002i−2i0000000
χ422-22-2222-2-2-222-22-2-22220-2-2-22-2-2-222000000002i−2i-222i2i−2i−2i2-2-22000000000000000-2200-22002i−2i002i2i−2i−2i0000−2i2i00000000-22000000000−2i2i0000000
χ432-22-2222-2-2-222-22-2-22220-2-2-22-2-2-22200000000−2i2i2-2−2i−2i2i2i2-2-220000000000000002-2002-200−2i2i00−2i−2i2i2i0000−2i2i000000002-2000000000−2i2i0000000
χ442-22-2222-2-2-222-22-2-22220-2-2-22-2-2-22200000000−2i2i-22−2i−2i2i2i2-2-22000000000000000-2200-2200−2i2i00−2i−2i2i2i00002i−2i00000000-220000000002i−2i0000000
χ452-22-2-122-21-2-12-22-21-1-12011-2-111-22-1−i3i300−i3−i3i3i32i−2i2-2−i−iii-111-1000−i3i3−i3−i3i3i3000000-11−i3i32-2002i−2i3−3−i−iii33−3−32i−2i00000000-11−i3i30000000−ii3−300000
χ462-22-2-122-21-2-12-22-21-1-12011-2-111-22-1−i3i300−i3−i3i3i32i−2i-22−i−iii-111-1000−i3i3−i3−i3i3i30000001-1i3−i3-22002i−2i3−3−i−iii33−3−3−2i2i000000001-1i3−i30000000i−i−3300000
χ472-22-2-122-21-2-12-22-21-1-12011-2-111-22-1−i3i300−i3−i3i3i3−2i2i2-2ii−i−i-111-1000−i3i3−i3−i3i3i3000000-11−i3i32-200−2i2i−33ii−i−i−3−333−2i2i00000000-11−i3i30000000i−i−3300000
χ482-22-2-122-21-2-12-22-21-1-12011-2-111-22-1−i3i300−i3−i3i3i3−2i2i-22ii−i−i-111-1000−i3i3−i3−i3i3i30000001-1i3−i3-2200−2i2i−33ii−i−i−3−3332i−2i000000001-1i3−i30000000−ii3−300000
χ492-22-2-122-21-2-12-22-21-1-12011-2-111-22-1i3−i300i3i3−i3−i32i−2i2-2−i−iii-111-1000i3−i3i3i3−i3−i3000000-11i3−i32-2002i−2i−33−i−iii−3−3332i−2i00000000-11i3−i30000000−ii−3300000
χ502-22-2-122-21-2-12-22-21-1-12011-2-111-22-1i3−i300i3i3−i3−i32i−2i-22−i−iii-111-1000i3−i3i3i3−i3−i30000001-1−i3i3-22002i−2i−33−i−iii−3−333−2i2i000000001-1−i3i30000000i−i3−300000
χ512-22-2-122-21-2-12-22-21-1-12011-2-111-22-1i3−i300i3i3−i3−i3−2i2i2-2ii−i−i-111-1000i3−i3i3i3−i3−i3000000-11i3−i32-200−2i2i3−3ii−i−i33−3−3−2i2i00000000-11i3−i30000000i−i3−300000
χ522-22-2-122-21-2-12-22-21-1-12011-2-111-22-1i3−i300i3i3−i3−i3−2i2i-22ii−i−i-111-1000i3−i3i3i3−i3−i30000001-1−i3i3-2200−2i2i3−3ii−i−i33−3−32i−2i000000001-1−i3i30000000−ii−3300000
χ5344444-2-2-24-24-2-2-2-24-2-214-2-21-2-2-211-244-2-2-2-2-2-2000000001111-211-2-21111404000000000-2-2000000000000000-2-2-2111100000000000000000000
χ5444444-2-2-24-24-2-2-2-24-2-214-2-21-2-2-211-244-2-2-2-2-2-2000000001111-211-2-21111-40-400000000022000000000000000222-1-1-1-100000000000000000000
χ5544444-2-2-24-24-2-2-2-24-2-21-4-2-21-2-2-211-2-4-42222220000000011112-1-122-1-1-1-140-400000000022000000000000000-22-211-1-100000000000000000000
χ5644444-2-2-24-24-2-2-2-24-2-21-4-2-21-2-2-211-2-4-42222220000000011112-1-122-1-1-1-1-404000000000-2-20000000000000002-22-1-11100000000000000000000
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χ584444-24-2-2-24-2-2-244-2-21-2411-2-2-2-2-2-21-2-244-2-2-2-200-4-400001111-2-2-21111110-40000222222000000000000000020000000-1-1-1-10000000000000000
χ594444-24-2-2-24-2-2-244-2-21-2-411-2-2-2-2-2-2122-4-42222004400001111222-1-1-1-1-1-10-40000-2-222-2-200000000000000002000000011-1-10000000000000000
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χ7644-4-4-2-24-4-222-442-221-2-20-222-11-1-2220023−23−33−330000−2i32i3−2i32i311-1-1023−2300−33−33000000000000000000i3−i3i3−i33i−3i3i−3i000000000000000000000000000000
χ7744-4-4-2-24-4-222-442-221-2-20-222-11-1-2220023−23−33−3300002i3−2i32i3−2i311-1-1023−2300−33−33000000000000000000−i3i3−i3i3−3i3i−3i3i000000000000000000000000000000
χ7844-4-4-2-24-4-222-442-221-2-20-222-11-1-22200−23233−33−30000−2i32i3−2i32i311-1-10−2323003−33−3000000000000000000i3−i3i3−i3−3i3i−3i3i000000000000000000000000000000
χ7944-4-4-2-24-4-222-442-221-2-20-222-11-1-22200−23233−33−300002i3−2i32i3−2i311-1-10−2323003−33−3000000000000000000−i3i3−i3i33i−3i3i−3i000000000000000000000000000000
χ804-44-444-22-4-44-224-4-44-2-202224-4-42-2-200000000004-40000-222-20000000000000004-400-22000000000000000000000000-22000000000000000000
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χ834-44-44-24-4-4244-4-22-4-24-20-4-42-2222-2400000000−4i4i00−4i−4i4i4i-222-2000000000000000000000002i−2i002i2i−2i−2i0000000000000000000000000000000000
χ844-44-4-24-222-4-2-224-42-21-20-1-12-2222-21−2i32i300−2i3−2i32i32i3004-400001-1-11000i3−i3i3i3−i3−i3000000-22−2i32i3-220000000000000000000000001-1i3−i30000000000000000
χ854-44-4-24-222-4-2-224-42-21-20-1-12-2222-21−2i32i300−2i3−2i32i32i300-4400001-1-11000i3−i3i3i3−i3−i30000002-22i3−2i32-2000000000000000000000000-11−i3i30000000000000000
χ864-44-4-24-222-4-2-224-42-21-20-1-12-2222-212i3−2i3002i32i3−2i3−2i3004-400001-1-11000−i3i3−i3−i3i3i3000000-222i3−2i3-220000000000000000000000001-1−i3i30000000000000000
χ874-44-4-24-222-4-2-224-42-21-20-1-12-2222-212i3−2i3002i32i3−2i3−2i300-4400001-1-11000−i3i3−i3−i3i3i30000002-2−2i32i32-2000000000000000000000000-11i3−i30000000000000000
χ884-44-4-2-24-422-24-4-2221-2-202221-1-12-2-2−2i32i300i3i3−i3−i34i−4i00−2i−2i2i2i1-1-11000−2i32i3i3i3−i3−i300000000000000−2i2i23−23ii−i−i−3−333000000000000000000000000000000
χ894-44-4-2-24-422-24-4-2221-2-202221-1-12-2-2−2i32i300i3i3−i3−i3−4i4i002i2i−2i−2i1-1-11000−2i32i3i3i3−i3−i3000000000000002i−2i−2323−i−iii33−3−3000000000000000000000000000000
χ904-44-4-2-24-422-24-4-2221-2-202221-1-12-2-22i3−2i300−i3−i3i3i34i−4i00−2i−2i2i2i1-1-110002i3−2i3−i3−i3i3i300000000000000−2i2i−2323ii−i−i33−3−3000000000000000000000000000000
χ914-44-4-2-24-422-24-4-2221-2-202221-1-12-2-22i3−2i300−i3−i3i3i3−4i4i002i2i−2i−2i1-1-110002i3−2i3−i3−i3i3i3000000000000002i−2i23−23−i−iii−3−333000000000000000000000000000000
χ924-4-444444-44-4-4-4-4-444440-444-4-44-4-4-400000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ934-4-4444-2-2-44-422-4-444-2-202-2-2-4-442220000000000000000-22-22000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ944-4-4444-2-2-44-422-4-444-2-202-2-2-4-442220000000000000000-22-220000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ954-4-444-244-4-2-4-4-4224-24-20-44-222-222-40000000000000000-22-220000000000000−2i32i30000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ964-4-444-244-4-2-4-4-4224-24-20-44-222-222-40000000000000000-22-2200000000000002i3−2i300000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ974-4-44-2444242-4-4-4-4-2-2-2402-2422-2-4-4200000000000023−23−2323-22-2200000000000000000000000000023−23−23230000000000000000000000000000000000
χ984-4-44-2444242-4-4-4-4-2-2-2402-2422-2-4-42000000000000−232323−23-22-22000000000000000000000000000−232323−230000000000000000000000000000000000
χ994-4-44-2-2442-22-4-422-21-2-202-2-2-1-1122200003i−3i−3i3i000023−23−23231-11-1000003i−3i−3i3i00002i3−2i3000000000000−333−3−i3i3i3−i3000000000000000000000000000000
χ1004-4-44-2-2442-22-4-422-21-2-202-2-2-1-1122200003i−3i−3i3i0000−232323−231-11-1000003i−3i−3i3i0000−2i32i30000000000003−3−33i3−i3−i3i3000000000000000000000000000000
χ1014-4-44-2-2442-22-4-422-21-2-202-2-2-1-112220000−3i3i3i−3i000023−23−23231-11-100000−3i3i3i−3i0000−2i32i3000000000000−333−3i3−i3−i3i3000000000000000000000000000000
χ1024-4-44-2-2442-22-4-422-21-2-202-2-2-1-112220000−3i3i3i−3i0000−232323−231-11-100000−3i3i3i−3i00002i3−2i30000000000003−3−33−i3i3i3−i3000000000000000000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-8-48-44-4-844-4-884-42-402-244-44-44-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44-4444-44-4422202-2-2-22-22-2-20043−43−2323−232300000000-1-1110−2323003−33−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-44-4444-44-4422202-2-2-22-22-2-200−434323−2323−2300000000-1-111023−2300−33−3300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-44-848-44-44-8-4-42044-2-444-22-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4444-4-44-4442220-2-2-22-2-2-222−4i34i3002i32i3−2i3−2i300000000-111-10002i3−2i3−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444-4-44-4442220-2-2-22-2-2-2224i3−4i300−2i3−2i32i32i300000000-111-1000−2i32i3i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-4-4-8-4-844448-4-4204-4244-4-2-2400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-4-448444-8-8-4-42-40-22-444-444-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-44-444444-42220-222-2-22-2-2-200006i−6i−6i6i00000000-11-1100000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-44-444444-42220-222-2-22-2-2-20000−6i6i6i−6i00000000-11-11000003i−3i−3i3i00000000000000000000000000000000000000000000000000000000

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