Finite Group Databasebeta

← Group #13168391

Character table — Group #13168391

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212124444121212123666121212121212121212444412121212121212121212121212121212121212121212441212121212121212121212122244466121212126121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-111111111-1-111111111111111-1-11-1-1-1-1-11111-1-1-11-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1111-1-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-111-1-1-1-1-1-1-1-11-1111
χ51111111111111111111111111111111111111-1-11111111111111111111-111111-1-1-1-1-1-111111111111111-1-111-111111-1-1-1-1-111-1-1-1-1-1-1-1-11-11-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-1-11-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1-11-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-11-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-11-1-1-11111-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-11111-1-1-1-1111-1-1-1-1-11111-1-11-11-1-11111-1-1-1-11-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-11111-1-1-1-111-11-1111-1-111-1-1-11-1-11-1-111-1-111-11-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-111-1-1-1-11111-1-11-1-1-1-1-11111-1-111-11-111-1-1111-1-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111-1-1-11-1111-1-111-1-1-1-1111-1-1-1-111-111-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11-11-1-1-111-1-111-1-1111-1-1-1-111-1111-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-111111-1-1-1-11111-11-111-1-1111-1-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-111-1-111-1-111-1-111-1-1-1-11111111-11-1-1-111-1-111-11-1-11-1-111-1-111-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-1-1-111-1-1-1-1111111-111111-1-1-1-1111-11-1-11111-1-1-1-111-1
χ17222222-122-1-1222-122-1-1222-1-1-1-1-1-12-1-122-1-1-1-100222222-1-1-1-12-1-122-1-1-1-10222-1-100000022-1-122-1-1-1-1-1-1-1-100-1-102-1-1-1-1000002200000000-10-100
χ18222222-122-1-1222-122-1-1222-1-1-1-1-1-12-1-122-1-1-1-100222222-1-1-1-12-1-122-1-1-1-10-22-2-1-1000000-2-2-1-122-1-1-1-1-1-1-1-100110-2111100000-2-20000000010100
χ19222222-122-1-1222-122-1-1222-1-1-1-1-1-12-1-122-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-102-22110000002211-2-21111111100-1-102-1-1-1-100000-2-20000000010100
χ20222222-122-1-1222-122-1-1222-1-1-1-1-1-12-1-122-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-10-2-2-211000000-2-211-2-21111111100110-21111000002200000000-10-100
χ21222222-122-1-1222-122-1-1-222-1-1-1-1-1-1211-2-2111100222222-1-1-1-1-211-2-2111102-2-21100000022-1-1-2-2-1-1-1-1111100-110-211-1-100000-220000000010-100
χ22222222-122-1-1222-122-1-1-222-1-1-1-1-1-1211-2-2111100222222-1-1-1-1-211-2-211110-2-2211000000-2-2-1-1-2-2-1-1-1-11111001-102-1-111000002-200000000-10100
χ23222222-122-1-1222-122-1-1-222-1-1-1-1-1-1211-2-2111100-2-2-2-2-2-2-1-1-1-1-211-2-21111022-2-1-10000002211221111-1-1-1-100-110-211-1-1000002-200000000-10100
χ24222222-122-1-1222-122-1-1-222-1-1-1-1-1-1211-2-2111100-2-2-2-2-2-2-1-1-1-1-211-2-211110-222-1-1000000-2-211221111-1-1-1-1001-102-1-11100000-220000000010-100
χ2522222-12-12222-1-122-12-12-1-1-1222-1-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-12202002222-1-1-1-10000000000000022-1-1-1-1-1-1-1-1-1-120002-1-100000-1000
χ2622222-12-12222-1-122-12-12-1-1-1222-1-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-12-20-2002222-1-11100000000000000-2-2-111111-1-1-1-1-2000-211000001000
χ2722222-12-12222-1-122-12-12-1-1-1222-1-1-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-220200-2-2-2-211-1-100000000000000221-1-1-1-1-11111-2000-211000001000
χ2822222-12-12222-1-122-12-12-1-1-1222-1-1-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-200-2-2-2-2111100000000000000-2-2111111111120002-1-100000-1000
χ2922222-12-12222-1-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-220-20022-2-2-1-1-1-1000000000000002-21111-1-1-1-1112000-2-1-1000001000
χ3022222-12-12222-1-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-2-2020022-2-2-1-11100000000000000-221-1-1-111-1-111-200021100000-1000
χ3122222-12-12222-1-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-1111111111220-200-2-22211-1-1000000000000002-2-1111-1-111-1-1-200021100000-1000
χ3222222-12-12222-1-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111112-20200-2-222111100000000000000-22-1-1-1-11111-1-12000-2-1-1000001000
χ332222-1222-122-1222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1202022-1-1-1-1220022-1-1-1-1-1-1-1-1-1-12200200000-1-1-1-10002000-1-1-1-100000
χ342222-1222-122-1222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-122-2-21111-1-1-1-1222-1-1-1-1-1-120-20-2-2-1-1-1-12200-2-21111111111-2-200200000-1-1-1-1000-2000111100000
χ352222-1222-122-1222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-1-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2020221111-2-20022-1-1-1-1-1-1-1-1-1-1-2-200-2000001111000-2000111100000
χ362222-1222-122-1222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1-20-20-2-21111-2-200-2-211111111112200-20000011110002000-1-1-1-100000
χ372222-1222-122-1222-1-1-12-2-1-12-1-1-122-1-2-21111112222-1-1-1-1-1-1-1-1-2-2-2111111-20-20-2-2-1-11122002211-1-1-1-111112200-200000-1-111000-2000-1-11100000
χ382222-1222-122-1222-1-1-12-2-1-12-1-1-122-1-2-211111122-2-21111-1-1-1-1-2-2-2111111-202022-1-1112200-2-2-1-11111-1-1-1-1-2-200-200000-1-111000200011-1-100000
χ392222-1222-122-1222-1-1-12-2-1-12-1-1-122-1-2-2111111-2-222-1-1-1-1-1-1-1-1-2-2-211111120-20-2-211-1-1-2-2002211-1-1-1-11111-2-20020000011-1-1000200011-1-100000
χ402222-1222-122-1222-1-1-12-2-1-12-1-1-122-1-2-2111111-2-2-2-21111-1-1-1-1-2-2-211111120202211-1-1-2-200-2-2-1-11111-1-1-1-1220020000011-1-1000-2000-1-11100000
χ4122-2-2222-2-22-222-2-2-22220-2-2-22-2-2-222000000002-22i−2i2i2i−2i−2i2-2-220000000000000002-2002-2002i−2i002i2i−2i−2i00002i−2i000000002-20000000002i−2i0000000
χ4222-2-2222-2-22-222-2-2-22220-2-2-22-2-2-222000000002-2−2i2i−2i−2i2i2i2-2-220000000000000002-2002-200−2i2i00−2i−2i2i2i0000−2i2i000000002-2000000000−2i2i0000000
χ4322-2-2222-2-22-222-2-2-22220-2-2-22-2-2-22200000000-222i−2i2i2i−2i−2i2-2-22000000000000000-2200-22002i−2i002i2i−2i−2i0000−2i2i00000000-22000000000−2i2i0000000
χ4422-2-2222-2-22-222-2-2-22220-2-2-22-2-2-22200000000-22−2i2i−2i−2i2i2i2-2-22000000000000000-2200-2200−2i2i00−2i−2i2i2i00002i−2i00000000-220000000002i−2i0000000
χ4522-2-2-122-212-2-12-2-21-1-12011-2-111-22-100−i3i3−i3−i3i3i32-22i−2i−i−iii-111-1000−i3i3−i3−i3i3i3000000-11−i3i32-2002i−2i3−3−i−iii33−3−32i−2i00000000-11−i3i30000000−ii3−300000
χ4622-2-2-122-212-2-12-2-21-1-12011-2-111-22-100−i3i3−i3−i3i3i32-2−2i2iii−i−i-111-1000−i3i3−i3−i3i3i3000000-11−i3i32-200−2i2i−33ii−i−i−3−333−2i2i00000000-11−i3i30000000i−i−3300000
χ4722-2-2-122-212-2-12-2-21-1-12011-2-111-22-100−i3i3−i3−i3i3i3-222i−2i−i−iii-111-1000−i3i3−i3−i3i3i30000001-1i3−i3-22002i−2i3−3−i−iii33−3−3−2i2i000000001-1i3−i30000000i−i−3300000
χ4822-2-2-122-212-2-12-2-21-1-12011-2-111-22-100−i3i3−i3−i3i3i3-22−2i2iii−i−i-111-1000−i3i3−i3−i3i3i30000001-1i3−i3-2200−2i2i−33ii−i−i−3−3332i−2i000000001-1i3−i30000000−ii3−300000
χ4922-2-2-122-212-2-12-2-21-1-12011-2-111-22-100i3−i3i3i3−i3−i32-22i−2i−i−iii-111-1000i3−i3i3i3−i3−i3000000-11i3−i32-2002i−2i−33−i−iii−3−3332i−2i00000000-11i3−i30000000−ii−3300000
χ5022-2-2-122-212-2-12-2-21-1-12011-2-111-22-100i3−i3i3i3−i3−i32-2−2i2iii−i−i-111-1000i3−i3i3i3−i3−i3000000-11i3−i32-200−2i2i3−3ii−i−i33−3−3−2i2i00000000-11i3−i30000000i−i3−300000
χ5122-2-2-122-212-2-12-2-21-1-12011-2-111-22-100i3−i3i3i3−i3−i3-222i−2i−i−iii-111-1000i3−i3i3i3−i3−i30000001-1−i3i3-22002i−2i−33−i−iii−3−333−2i2i000000001-1−i3i30000000i−i3−300000
χ5222-2-2-122-212-2-12-2-21-1-12011-2-111-22-100i3−i3i3i3−i3−i3-22−2i2iii−i−i-111-1000i3−i3i3i3−i3−i30000001-1−i3i3-2200−2i2i3−3ii−i−i33−3−32i−2i000000001-1−i3i30000000−ii−3300000
χ5344444-2-2-24-2-24-2-2-24-2-214-2-21-2-2-211-2-2-244-2-2-2-2000000001111-211-2-21111040400000000-2-200000000000000-2-20-2111100000000000000000000
χ5444444-2-2-24-2-24-2-2-24-2-214-2-21-2-2-211-2-2-244-2-2-2-2000000001111-211-2-211110-40-40000000022000000000000002202-1-1-1-100000000000000000000
χ5544444-2-2-24-2-24-2-2-24-2-21-4-2-21-2-2-211-222-4-422220000000011112-1-122-1-1-1-1040-400000000-2-200000000000000-2202-1-11100000000000000000000
χ5644444-2-2-24-2-24-2-2-24-2-21-4-2-21-2-2-211-222-4-422220000000011112-1-122-1-1-1-10-4040000000022000000000000002-20-211-1-100000000000000000000
χ574444-24-24-2-2-2-244-2-2-21-24-2-2-2111-2-2-2-2-2-2-211110044-2-2-2-211114-2-2-2-211110040-2-200000000-2-2-2-211111111000000000000000000000000000000
χ584444-24-24-2-2-2-244-2-2-21-24-2-2-2111-2-2-2-2-2-2-2111100-4-4222211114-2-2-2-2111100-4022000000002222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ594444-24-24-2-2-2-244-2-2-21-2-4-2-2-2111-2-2-22222-1-1-1-10044-2-2-2-21111-42222-1-1-1-100-402200000000-2-2221111-1-1-1-1000000000000000000000000000000
χ604444-24-24-2-2-2-244-2-2-21-2-4-2-2-2111-2-2-22222-1-1-1-100-4-422221111-42222-1-1-1-10040-2-20000000022-2-2-1-1-1-11111000000000000000000000000000000
χ614444-2-24-2-244-2-2-24-21-2-2411-2-2-2-2-2-2144-2-2-2-2-2-2440000001111-2-2-2111111400000-2-2-2-2-2-2000000000000000000-20000011110000000000000000
χ624444-2-24-2-244-2-2-24-21-2-2411-2-2-2-2-2-2144-2-2-2-2-2-2-4-40000001111-2-2-2111111-400000222222000000000000000000200000-1-1-1-10000000000000000
χ634444-2-24-2-244-2-2-24-21-2-2-411-2-2-2-2-2-21-4-4222222440000001111222-1-1-1-1-1-1-400000-2-222-2-200000000000000000020000011-1-10000000000000000
χ644444-2-24-2-244-2-2-24-21-2-2-411-2-2-2-2-2-21-4-4222222-4-40000001111222-1-1-1-1-1-140000022-2-222000000000000000000-200000-1-1110000000000000000
χ6544-4-444-2-4-4-2244-42-44-2-20-4-42-2222-2400000000004i−4i4i4i−4i−4i-222-200000000000000000000000−2i2i00−2i−2i2i2i0000000000000000000000000000000000
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χ6744-4-44-242-44-44-22-4-4-24-202224-4-42-2-2000000004-4000000-222-20000000000000004-400-22000000000000000000000000-22000000000000000000
χ6844-4-44-242-44-44-22-4-4-24-202224-4-42-2-200000000-44000000-222-2000000000000000-44002-20000000000000000000000002-2000000000000000000
χ6944-4-4-24-2-42-22-24-422-21-202221-1-12-2-200−2i32i3i3i3−i3−i3004i−4i−2i−2i2i2i1-1-11000−2i32i3i3i3−i3−i300000000000000−2i2i23−23ii−i−i−3−333000000000000000000000000000000
χ7044-4-4-24-2-42-22-24-422-21-202221-1-12-2-200−2i32i3i3i3−i3−i300−4i4i2i2i−2i−2i1-1-11000−2i32i3i3i3−i3−i3000000000000002i−2i−2323−i−iii33−3−3000000000000000000000000000000
χ7144-4-4-24-2-42-22-24-422-21-202221-1-12-2-2002i3−2i3−i3−i3i3i3004i−4i−2i−2i2i2i1-1-110002i3−2i3−i3−i3i3i300000000000000−2i2i−2323ii−i−i33−3−3000000000000000000000000000000
χ7244-4-4-24-2-42-22-24-422-21-202221-1-12-2-2002i3−2i3−i3−i3i3i300−4i4i2i2i−2i−2i1-1-110002i3−2i3−i3−i3i3i3000000000000002i−2i23−23−i−iii−3−333000000000000000000000000000000
χ7344-4-4-2-24224-4-2-22-421-2-20-1-12-2222-2100−2i32i3−2i3−2i32i32i34-40000001-1-11000i3−i3i3i3−i3−i3000000-22−2i32i3-220000000000000000000000001-1i3−i30000000000000000
χ7444-4-4-2-24224-4-2-22-421-2-20-1-12-2222-2100−2i32i3−2i3−2i32i32i3-440000001-1-11000i3−i3i3i3−i3−i30000002-22i3−2i32-2000000000000000000000000-11−i3i30000000000000000
χ7544-4-4-2-24224-4-2-22-421-2-20-1-12-2222-21002i3−2i32i32i3−2i3−2i34-40000001-1-11000−i3i3−i3−i3i3i3000000-222i3−2i3-220000000000000000000000001-1−i3i30000000000000000
χ7644-4-4-2-24224-4-2-22-421-2-20-1-12-2222-21002i3−2i32i32i3−2i3−2i3-440000001-1-11000−i3i3−i3−i3i3i30000002-2−2i32i32-2000000000000000000000000-11i3−i30000000000000000
χ774-44-444444-4-4-4-4-44-444404-44-44-4-4-4-4000000000000000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ784-44-444-24422-4-4-4-2-44-2-204-4-22-2222-40000000000000000-2-222000000000000023−23000000000000000023−2323−23000000000000000000000000000000
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χ804-44-44-24-24-4-4-4224-4-24-20-22-2-44-42220000000000000000-2-222000000000000000000000000000000000000000000000000000000−2i32i3000000000
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χ844-44-4-24-24-2222-4-4-22-21-20-22-2-11-122200003i−3i3i−3i0000−2i32i3−2i32i311-1-1000003i−3i3i−3i000023−23000000000000i3−i3i3−i3−33−33000000000000000000000000000000
χ854-44-4-24-24-2222-4-4-22-21-20-22-2-11-122200003i−3i3i−3i00002i3−2i32i3−2i311-1-1000003i−3i3i−3i0000−2323000000000000−i3i3−i3i33−33−3000000000000000000000000000000
χ864-44-4-24-24-2222-4-4-22-21-20-22-2-11-12220000−3i3i−3i3i0000−2i32i3−2i32i311-1-100000−3i3i−3i3i0000−2323000000000000i3−i3i3−i33−33−3000000000000000000000000000000
χ874-44-4-24-24-2222-4-4-22-21-20-22-2-11-12220000−3i3i−3i3i00002i3−2i32i3−2i311-1-100000−3i3i−3i3i000023−23000000000000−i3i3−i3i3−33−33000000000000000000000000000000
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χ1004-4-44-24-2-422-22-442-2-21-202-22-1-11-22223−2300−333−30000−232323−231-11-1023−2300−333−30000000000000000003−3−333-3-33000000000000000000000000000000
χ1014-4-44-24-2-422-22-442-2-21-202-22-1-11-222−2323003−3−33000023−23−23231-11-10−2323003−3−33000000000000000000−333−33-3-33000000000000000000000000000000
χ1024-4-44-24-2-422-22-442-2-21-202-22-1-11-222−2323003−3−330000−232323−231-11-10−2323003−3−330000000000000000003−3−33-333-3000000000000000000000000000000
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χ10688-8-8-4-4-444-44-4-44442220-2-2-22-2-2-22200−4i34i32i32i3−2i3−2i300000000-111-10002i3−2i3−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-444-44-4-44442220-2-2-22-2-2-222004i3−4i3−2i3−2i32i32i300000000-111-1000−2i32i3i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-4844-844-4-8-4-420-4424-44-2-24000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-48-4-4-8-8444842-4-402-2-44-4444-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
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χ1118-88-8-4-4-4-4-444444-4422202-22-22-2-2-2-20000−6i6i−6i6i00000000-1-111000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-4844-8844-4-8-42-4-40-22444-4-44-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
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χ1148-8-88-4-4-4444-444-44-42220-22-2-2-222-2-2−43430023−23−232300000000-11-11023−2300−333−300000000000000000000000000000000000000000000000000000000

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