Finite Group Databasebeta

← Group #13169333

Character table — Group #13169333

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121244441212121212121212121212121212121244444444121212121212121212121212121212121212121244121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111-1-11111-1-1111111-1-111-1-111111-11-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-11111-1-1111-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-111-1-1-1-1-11-1-111-1-11-111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-11111-1-11111-1-111-1-1-1-1-1-111-1-1-1-111-11-1-11111-1-11111-11-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1-1-111-1-11-1-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-11111-11-11-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-1-1-1111-11111-1-1-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1111-1-1111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-111-1-111-1-1-1-1111111111111-1-111-1-111-1-111-1-1-1-1-1-11111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-111-1-111-1-11111111111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-1-111-1-1-1-111-1-11111-111-1-1-1111111-1-1-1-111-1-1-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1111111-1111-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1-1111111-1-11-11111-1-1-11-11
χ17222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-12200222200-1-1-1-100-1-1-1-122002200-1-1-1-12020-1-1-1-100-1-1-1-10000-1-100000000
χ18222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-12-20022-2-200-1-11100-1-111-2-200-2-2001111-2020-1-11100-1-11100001100000000
χ19222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1-2200-2-2220011-1-10011-1-1-2-200-2-200111120-2011-1-10011-1-100001100000000
χ20222222-12222-1-1-1222-1-122-1-12-1-12-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-2-2-200111100111122002200-1-1-1-1-20-2011110011110000-1-100000000
χ21222222-12222-1-1-1222-1-1-22-1-12-1-12-1-1112222-1-1-1-1-2-2-2-211111111-2-200222200111100-1-1-1-12200-2-2001111-20-20-1-1-1-10011110000-1-100000000
χ22222222-12222-1-1-1222-1-1-22-1-12-1-12-1-11122-2-2-1-1-1-1-2-2-2-211111111-220022-2-20011-1-100-1-111-2-2002200-1-1-1-120-20-1-1110011-1-100001100000000
χ23222222-12222-1-1-1222-1-1-22-1-12-1-12-1-111-2-222-1-1-1-1-2-2-2-2111111112-200-2-22200-1-1110011-1-1-2-2002200-1-1-1-1-202011-1-100-1-11100001100000000
χ24222222-12222-1-1-1222-1-1-22-1-12-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-2111111112200-2-2-2-200-1-1-1-10011112200-2-20011112020111100-1-1-1-10000-1-100000000
χ2522222-1222-1-1222-12-12-12-12-1-12-1-12-1220022-1-1-1-1-12-1-122-1-1-1-1-1-1022200-1-1220022-1-10022000000220000-1-10200-1-1-1-100-1-1-1-10200-1-100-1000
χ2622222-1222-1-1222-12-12-12-12-1-12-1-12-1220022-1-1-1-1-12-1-122-1-1-1-1-1-102-2-200-1-1-2-20022110022000000-2-20000-110-200-1-11100-1-1110-20011001000
χ2722222-1222-1-1222-12-12-12-12-1-12-1-12-12200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10-22200112200-2-2-1-100-2-2000000-2-200001-1020011-1-10011-1-10-20011001000
χ2822222-1222-1-1222-12-12-12-12-1-12-1-12-12200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10-2-2-20011-2-200-2-21100-2-2000000220000110-20011110011110200-1-100-1000
χ2922222-1222-1-1222-12-12-1-2-12-1-12-1-12-1-2-20022-1-1-1-11-211-2-21111110-22-200-1-1-2-200-2-2-1-10022000000220000110200-1-1110011-1-10-200-1-1001000
χ3022222-1222-1-1222-12-12-1-2-12-1-12-1-12-1-2-20022-1-1-1-11-211-2-21111110-2-2200-1-12200-2-2110022000000-2-200001-10-200-1-1-1-100111102001100-1000
χ3122222-1222-1-1222-12-12-1-2-12-1-12-1-12-1-2-200-2-2-1-1-1-11-211-2-2111111022-20011-2-20022-1-100-2-2000000-2-20000-110200111100-1-1-1-102001100-1000
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χ332222-122-1-1222222-1-1-122-1-12-1-12-1-12222200-1-1-1-12-1-1-1-1-122-1-1-1-12022-1-100-1-1220022220000220000000002-1-1-1-100-1-1-1-100-1-1200000-1-10-100
χ342222-122-1-1222222-1-1-122-1-12-1-12-1-12222200-1-1-1-12-1-1-1-1-122-1-1-1-120-2-2-1-100112200-2-2220000-2-2000000000-2-11-1-10011-1-10011-200000110100
χ352222-122-1-1222222-1-1-122-1-12-1-12-1-1222-2-200-1-1-1-12-1-1-1-1-122-1-1-1-1-20221100-1-1-2-20022-2-20000-2-200000000021-11100-1-11100-1-1-200000110100
χ362222-122-1-1222222-1-1-122-1-12-1-12-1-1222-2-200-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-2110011-2-200-2-2-2-2000022000000000-211110011110011200000-1-10-100
χ372222-122-1-1222222-1-1-12-2-1-12-1-12-1-12-2-22200-1-1-1-1-211111-2-21111-202-2-1-10011-2-20022220000-2-2000000000-21-1-1-100111100-1-1200000110-100
χ382222-122-1-1222222-1-1-12-2-1-12-1-12-1-12-2-22200-1-1-1-1-211111-2-21111-20-22-1-100-1-1-2-200-2-222000022000000000211-1-100-1-1110011-200000-1-10100
χ392222-122-1-1222222-1-1-12-2-1-12-1-12-1-12-2-2-2-200-1-1-1-1-211111-2-21111202-2110011220022-2-2000022000000000-2-1-1110011-1-100-1-1-200000-1-10100
χ402222-122-1-1222222-1-1-12-2-1-12-1-12-1-12-2-2-2-200-1-1-1-1-211111-2-2111120-221100-1-12200-2-2-2-20000-2-20000000002-111100-1-1-1-10011200000110-100
χ4122-2-22222-22-2-2-22-2-222202-2-2-222-2-2-2002-22-222-2-200000000000000002-22-2000000002-22-22-2000000000000002-22-200000000002-200000000
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χ4322-2-22222-22-2-2-22-2-222202-2-2-222-2-2-200-222-222-2-20000000000000000-222-200000000-222-2-2200000000000000-222-20000000000-2200000000
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χ4622-2-222-12-22-211-1-2-22-1-10211-2-1-1-2113−32-2-22-1-11100003−33−333−3−300002-2-22003−3−3300-111-1-22000000−3−3330000-111-1003−3−3300001-100000000
χ4722-2-222-12-22-211-1-2-22-1-10211-2-1-1-2113−3-222-2-1-11100003−33−333−3−30000-222-200−333−3001-1-11-22000000−3−33300001-1-1100−333−300001-100000000
χ4822-2-222-12-22-211-1-2-22-1-10211-2-1-1-2113−3-22-22-1-11100003−33−333−3−30000-22-2200−33−33001-11-12-200000033−3−300001-11-100−33−330000-1100000000
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χ5122-2-222-12-22-211-1-2-22-1-10211-2-1-1-211−33-222-2-1-1110000−33−33−3−3330000-222-2003−3−33001-1-11-2200000033−3−300001-1-11003−3−3300001-100000000
χ5222-2-222-12-22-211-1-2-22-1-10211-2-1-1-211−33-22-22-1-1110000−33−33−3−3330000-22-22003−33−3001-11-12-2000000−3−33300001-11-1003−33−30000-1100000000
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χ934-4-44-2442-2-4-4-44-442-2-2402-24-22-422-4000000-22-22000000000000000000002i3−2i30000000000000000000000000000002i3−2i3000000000000000000
χ944-4-44-2-242-222-44-4-221-2-20-1-2-2122-1220000001-11-1003i−3i00003i−3i3i−3i00000000−2i32i3000023−23000000000000000000000000i3−i30000−33000000000000
χ954-4-44-2-242-222-44-4-221-2-20-1-2-2122-1220000001-11-1003i−3i00003i−3i3i−3i000000002i3−2i30000−2323000000000000000000000000−i3i300003−3000000000000
χ964-4-44-2-242-222-44-4-221-2-20-1-2-2122-1220000001-11-100−3i3i0000−3i3i−3i3i00000000−2i32i30000−2323000000000000000000000000i3−i300003−3000000000000
χ974-4-44-2-242-222-44-4-221-2-20-1-2-2122-1220000001-11-100−3i3i0000−3i3i−3i3i000000002i3−2i3000023−23000000000000000000000000−i3i30000−33000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-48-44-44-8-88442-4-40244-2-4-4-24400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-44-4444-44422202-2-2-222-2-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-44-4444-44422202-2-2-222-2-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-4-8-84-4-44448-4-42044-244-2-4-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-444-88-444-8-4-42-404-244-24-42-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-48444-48-8-84-42-4-40-244-2442-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4444-4-4444-42220-2-2-2-2-2-2222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4444-4-4444-42220-2-2-2-2-2-2222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-4-88444-44-4-8-4-4204-42-44-244-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-44-4-8-84-4484-42-4042-4-4-244-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44-4444-44-442220-2222-2-2-2-2-2000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44-4444-44-442220-2222-2-2-2-2-2000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000

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