Finite Group Databasebeta

← Group #13172717

Character table — Group #13172717

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order122233366666666623336666666666622444436666666666666662222444666612121212121212121212121244446666661212121212121212121212121212222661212121222664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1-1-1-111-111111111-1-1-1-111-1-111-1-1-1-1-1-111111-1111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-11-111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1111-1-1-1-11111-11-1-1-1-1-111-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-1111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111111111-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-11-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-11-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-1-1-111-1-1111-11
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111-1111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1111111-1-111-1-111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1111111-1-1-1
χ101111111111111111-1111-1-11111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-11-1-111-1-1-1-111-1111111-1-1-1-1-111
χ111111111111111111-1111-1-111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-111-1-111-1-1-1-111-1-11-1-1-1-1-11111-1-11-1111-1-111-1-11-11
χ121111111111111111-1111-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-11111-1111111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-11111-1
χ131111111111111111-1111-1-1111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1111
χ141111111111111111-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-111111-1-1-1-1111-1111-1-111111-1-1
χ151111111111111111-1111-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-111-1-11111-1-1-1111111-1-111-11-1
χ161111111111111111-1111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1111111-1-111-1-111-1-1-1-1-11111-1-1-1-11
χ17222222-122-122-1-1222-1-12-1-1-1-122-1-1-1-12002222-122-1-1-1-122-1-1-1-1-1-1-122220220000-1-1-1-1-1-1-1-122220000-1-1-1-100002200-1-1-1-1-1-1-1-1002-1-1000000000
χ18222222-122-122-1-1222-1-12-1-1-1-122-1-1-1-120022-2-2-122-1-1-1-122-1-1-1-1-1-1-1-2-2-2-202-20000-1-1-1-1111122-2-20000111100002-200-1-1-1-1111100-211000000000
χ19222222-122-122-1-1222-1-12-1-1-1-122-1-1-1-1200-2-222-122-1-1-1-122-1-1-1-1-1-1-1-2-2-2-20-2200001111-1-1-1-1-2-222000011110000-22001111-1-1-1-100-211000000000
χ20222222-122-122-1-1222-1-12-1-1-1-122-1-1-1-1200-2-2-2-2-122-1-1-1-122-1-1-1-1-1-1-122220-2-2000011111111-2-2-2-20000-1-1-1-10000-2-20011111111002-1-1000000000
χ21222222-122-122-1-122-2-1-1211-1-122-1-1-1-12002222-1-2-21111-2-2-1-1-1111122220-2-20000-1-111-1-11122220000-1-1-1-10000-2-200-1-111-1-11100-211000000000
χ22222222-122-122-1-122-2-1-1211-1-122-1-1-1-120022-2-2-1-2-21111-2-2-1-1-11111-2-2-2-20-220000-1-11111-1-122-2-2000011110000-2200-1-11111-1-1002-1-1000000000
χ23222222-122-122-1-122-2-1-1211-1-122-1-1-1-1200-2-222-1-2-21111-2-2-1-1-11111-2-2-2-202-2000011-1-1-1-111-2-2220000111100002-20011-1-1-1-111002-1-1000000000
χ24222222-122-122-1-122-2-1-1211-1-122-1-1-1-1200-2-2-2-2-1-2-21111-2-2-1-1-111112222022000011-1-111-1-1-2-2-2-20000-1-1-1-10000220011-1-111-1-100-211000000000
χ2522222-122-122-1222-122-1-1222-1-1-122-1-1-1220022-12-122-1-1-1-1-1-1-1-1-1-1-1000020222-1-10000222200-1-100220000-1-12-10-1-1-10000-1-1-1-10200000-1-1000-10
χ2622222-122-122-1222-122-1-1222-1-1-122-1-1-12200-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1000020-222-1-10000-2-2-2-2001100-2-20000-1-12-101-1-1000011110-2000001100010
χ2722222-122-122-1222-122-1-1222-1-1-122-1-1-1-2-20022-12-122-1-1-1-1-1-1-1-1-1-1-10000-202-2-2110000222200-1-100-2-2000011-210-1110000-1-1-1-10-2000001100010
χ2822222-122-122-1222-122-1-1222-1-1-122-1-1-1-2-200-2-2-12-122-1-1-1-1-1-1-1-1-1-1-10000-20-2-2-2110000-2-2-2-200110022000011-210111000011110200000-1-1000-10
χ2922222-122-122-1222-1-22-1-1-2-22-1-1-122-1-1-1220022-1-21-2-21111-1-1-111110000-20-222-1-1000022-2-200-1-100220000-1-1-2101110000-1-1110-200000-1-100010
χ3022222-122-122-1222-1-22-1-1-2-22-1-1-122-1-1-12200-2-2-1-21-2-21111-1-1-111110000-20222-1-10000-2-222001100-2-20000-1-1-210-111000011-1-1020000011000-10
χ3122222-122-122-1222-1-22-1-1-2-22-1-1-122-1-1-1-2-20022-1-21-2-21111-1-1-11111000020-2-2-211000022-2-200-1-100-2-20000112-101-1-10000-1-111020000011000-10
χ3222222-122-122-1222-1-22-1-1-2-22-1-1-122-1-1-1-2-200-2-2-1-21-2-21111-1-1-111110000202-2-2110000-2-222001100220000112-10-1-1-1000011-1-10-200000-1-100010
χ332222-122-122-1222-122-12-122-12-1-1-1-122-1222200-1-12-1-122-1-1-1-1-1-1-1-1-10000220-1-12222220000-1-10022000000-1-1-12-10-1-1-1-1-1-1000020000-1-10000-100
χ342222-122-122-1222-122-12-122-12-1-1-1-122-122-2-200-1-12-1-122-1-1-1-1-1-1-1-1-100002-20-1-122-2-2-2-200001100-2-2000000-1-1-1210-1-111110000-20000110000100
χ352222-122-122-1222-122-12-122-12-1-1-1-122-1-2-22200-1-12-1-122-1-1-1-1-1-1-1-1-10000-22011-2-222220000-1-100-2-2000000111-2-1011-1-1-1-10000-20000110000100
χ362222-122-122-1222-122-12-122-12-1-1-1-122-1-2-2-2-200-1-12-1-122-1-1-1-1-1-1-1-1-10000-2-2011-2-2-2-2-2-20000110022000000111-210111111000020000-1-10000-100
χ372222-122-122-1222-12-2-12-1-2-2-12-1-1-1-122-1222200-11-211-2-211-1-1-111110000-2-20-1-12222-2-20000-1-10022000000-1-11-21011-1-1110000-20000-1-10000100
χ382222-122-122-1222-12-2-12-1-2-2-12-1-1-1-122-122-2-200-11-211-2-211-1-1-111110000-220-1-122-2-22200001100-2-2000000-1-11-2-101111-1-1000020000110000-100
χ392222-122-122-1222-12-2-12-1-2-2-12-1-1-1-122-1-2-22200-11-211-2-211-1-1-1111100002-2011-2-222-2-20000-1-100-2-200000011-1210-1-1-1-111000020000110000-100
χ402222-122-122-1222-12-2-12-1-2-2-12-1-1-1-122-1-2-2-2-200-11-211-2-211-1-1-11111000022011-2-2-2-222000011002200000011-12-10-1-111-1-10000-20000-1-10000100
χ4122-2-2222222-2-2-2-2-2-2022200222-2-2-2-2-2-2002i−2i2i−2i2000000002-2-2000022-2-200000002i−2i002i−2i002i−2i2i−2i000022-2-2000000002i−2i002i−2i0000000000000000
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χ4322-2-2222222-2-2-2-2-2-2022200222-2-2-2-2-2-200−2i2i2i−2i2000000002-2-20000-2-2220000000−2i2i002i−2i00−2i2i2i−2i0000-2-22200000000−2i2i002i−2i0000000000000000
χ4422-2-2222222-2-2-2-2-2-2022200222-2-2-2-2-2-200−2i2i−2i2i2000000002-2-2000022-2-20000000−2i2i00−2i2i00−2i2i−2i2i000022-2-200000000−2i2i00−2i2i0000000000000000
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χ4622-2-222-122-1-2-211-2-20-1-12−i3i3-1-12-21111-2002i−2i−2i2i-100−i3i3−i3i300-111−i3−i3i3i3-2-2220000000−ii3−3i−i−332i−2i−2i2i000011-1-100000000−ii3−3i−i−33000i3−i3000000000
χ4722-2-222-122-1-2-211-2-20-1-12−i3i3-1-12-21111-200−2i2i2i−2i-100−i3i3−i3i300-111−i3−i3i3i3-2-2220000000i−i−33−ii3−3−2i2i2i−2i000011-1-100000000i−i−33−ii3−3000i3−i3000000000
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χ4922-2-222-122-1-2-211-2-20-1-12i3−i3-1-12-21111-2002i−2i2i−2i-100i3−i3i3−i300-111i3i3−i3−i322-2-20000000−ii−33−ii−332i−2i2i−2i0000-1-11100000000−ii−33−ii−33000i3−i3000000000
χ5022-2-222-122-1-2-211-2-20-1-12i3−i3-1-12-21111-2002i−2i−2i2i-100i3−i3i3−i300-111i3i3−i3−i3-2-2220000000−ii−33i−i3−32i−2i−2i2i000011-1-100000000−ii−33i−i3−3000−i3i3000000000
χ5122-2-222-122-1-2-211-2-20-1-12i3−i3-1-12-21111-200−2i2i2i−2i-100i3−i3i3−i300-111i3i3−i3−i3-2-2220000000i−i3−3−ii−33−2i2i2i−2i000011-1-100000000i−i3−3−ii−33000−i3i3000000000
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χ532-22-2222-2-2-2-2-22-222022200-2-2-222-22-2-2000000200000000-22-200002-22-200000000000000000002-22-22-22-20000000000000000000002-22-200000
χ542-22-2222-2-2-2-2-22-222022200-2-2-222-22-2-2000000200000000-22-200002-22-20000000000000000000-22-222-22-2000000000000000000000-22-2200000
χ552-22-2222-2-2-2-2-22-222022200-2-2-222-22-2-2000000200000000-22-20000-22-2200000000000000000002-2-22-22-220000000000000000000002-2-2200000
χ562-22-2222-2-2-2-2-22-222022200-2-2-222-22-2-2000000200000000-22-20000-22-220000000000000000000-222-2-22-22000000000000000000000-222-200000
χ572-2-22222-2-2-222-22-2-2022200-2-2-2-2-22-2222-20000200000000-2-2200002-2-220002-22-200000000000000002-2-222-2000000000000000000000002-2000
χ582-2-22222-2-2-222-22-2-2022200-2-2-2-2-22-2222-20000200000000-2-220000-222-20002-22-20000000000000000-222-22-200000000000000000000000-22000
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χ6244444-2-24-2-24-2-2-24-24-21-2-2-2-21-2-2-2-211-20000-4-414-2-2-211-2-21111111000000-4000000002222002200000000000002000000-1-1-1-100000000000000
χ6344444-2-24-2-24-2-2-24-2-4-21-222-21-2-2-2-211-20000441-4222-1-122111-1-1-1-1000000-400000000-2-22200-2-20000000000000200000011-1-100000000000000
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χ8444-4-4-24-2-24-22-4222-401-2-22i3−2i31-2-22-1-122200−4i4i00100−i3i32i3−2i3001-1-1−i3−i3i3i3000000000002i−2i23−2300002i−2i000000000000000000−ii−33000000000000000000
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χ1004-4-44-2-2422-4-2-2-44220-2-210022-1-12-22-21-4400001000000-33-1-11-33-3300000002-22-200000000000000000000-1100003-30000000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222000000-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222000000-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-48-4-4844-8-8440-4-4200-4-42-24444-20000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-4-4-44444440222−4i34i3222-2-2-2-2-2-2000000-1002i3−2i32i3−2i300-111−i3−i3i3i30000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-4-4-4-444444402224i3−4i3222-2-2-2-2-2-2000000-100−2i32i3−2i32i300-111i3i3−i3−i30000000000000000000000000000000000000000000000000000000000000
χ1068-88-88-4-4-844-84-448-40-42-4004-24-4-442-24000000200000000-22-200000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-48-44-844-8-44-4802-4-400-244-42-2-444000000200000000-22-200000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4844-8448-8-4-40-4-420044-22-44-44-2000000200000000-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-444444-44-4-4022200-2-2-222-22-2-2000000-1000000001-11−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-444444-44-4-4022200-2-2-222-22-2-2000000-1000000001-113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-4-8448-44-4-840-42-4004-2444-4-22-4000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-44-84-484-44-802-4-400-2444-224-4-4000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-4-44-444022200-2-2-2-2-22-222000000-10000006-611-1-33-330000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-4-44-444022200-2-2-2-2-22-222000000-1000000-6611-13-33-30000000000000000000000000000000000000000000000000000000000000

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