Finite Group Databasebeta

← Group #13168440

Character table — Group #13168440

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order1222333666666666333466666666612121212121212124444441212121236661212121212121212122246612121212121212121212121212121212121212124444666666612121212122244661212121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11-1-111111111111111111111-1-111-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111111111111111111111-1111111-1-1-1-111-1-111111111-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-11
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1111111111111-11-1-1-1-1-1-111-1-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-111-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-11-1-1-11111-1-111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-11-1-111-1-1-111-1-11-11-111-1-11111-11-1-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-111-1-111-111-1-111-1111-1-1-1-1-1-11-111
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111-1-11-1-111-111-1-1-111-1-1-1-111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-111-1-1-11-1-1111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1111111-1-1-1-1111111111-1-111-1-1-111-1-1-1-1-11-1-11111-1-1-1-111
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1111111-1-1-1-11111-1-111-111-1-111-111-1-1-111-1-1-111-1-11111-1-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11-1-111-1-11-1-11111-1111-1-1-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-111-1-1111-1-1111-11-111-1-111-1-1-11-11
χ17222222-1-1222-122-122-1-12-1-1-12-122-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-10000222200-1-100000000220022-1-1-1-1-1-1-1-1-1-102000000-1-100-1000
χ18222222-1-1222-122-122-1-12-1-1-12-122-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22110000222200-1-100000000-2-200-2-211111-1-1-1-1-10-200000011001000
χ19222222-1-1222-122-122-1-12-1-1-12-122-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-122-2-1-10000-2-2-2-2001100000000-2-20022-1-1-1-1-1111110-200000011001000
χ20222222-1-1222-122-122-1-12-1-1-12-122-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2110000-2-2-2-20011000000002200-2-2111111111102000000-1-100-1000
χ21222222-1-1222-122-122-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-11111111112-2-2-1-10000-2-22200-1-10000000022002-21-1-1111-1-1110-2000000-1-1001000
χ22222222-1-1222-122-122-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-1111111111-22-2110000-2-22200-1-100000000-2-200-22-111-1-11-1-111020000001100-1000
χ23222222-1-1222-122-122-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-11111111112-22-1-1000022-2-2001100000000-2-2002-21-1-111-111-1-1020000001100-1000
χ24222222-1-1222-122-122-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-1111111111-22211000022-2-20011000000002200-22-111-1-1-111-1-10-2000000-1-1001000
χ2522222-12222-12-1-122-1-122-122-12-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1002002222-1-1-1-1-1-122-1-1-1-1-1-1-1-1002200000002-1-1-1-12000-1-1-1-100000000
χ2622222-12222-12-1-122-1-122-122-12-1-1-1-1-1-122-1-1-1-122-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-100-20022221111-1-1-2-2-1-1-1-1-1-1-1-100-2-20000000-21111-2000111100000000
χ2722222-12222-12-1-122-1-122-122-12-1-1-1-1-1-122-1-1-1-1-2-222-2-21111-1-1-1-1222-1-1-1-1-1-100200-2-2-2-2-1-1-1-111221111111100-2-200000002-1-1-1-1-2000111100000000
χ2822222-12222-12-1-122-1-122-122-12-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-21111-1-1-1-1222-1-1-1-1-1-100-200-2-2-2-2111111-2-21111111100220000000-211112000-1-1-1-100000000
χ2922222-12222-12-1-122-1-12-2-122-12-1-1-1-111-2-211112222-2-2-1-1-1-1-1-1-1-1-2-2-211111100-20022-2-211-1-11122-1-1-1-1111100-2-20000000-2-1-1112000-1-11100000000
χ3022222-12222-12-1-122-1-12-2-122-12-1-1-1-111-2-2111122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-21111110020022-2-2-1-11111-2-2-1-1-1-1111100220000000211-1-1-200011-1-100000000
χ3122222-12222-12-1-122-1-12-2-122-12-1-1-1-111-2-21111-2-222221111-1-1-1-1-2-2-211111100-200-2-22211-1-1-1-1221111-1-1-1-100220000000-2-1-111-200011-1-100000000
χ3222222-12222-12-1-122-1-12-2-122-12-1-1-1-111-2-21111-2-2-2-2221111-1-1-1-1-2-2-211111100200-2-222-1-111-1-1-2-21111-1-1-1-100-2-20000000211-1-12000-1-11100000000
χ332222-1222-1-122222-1-12-122-1-1-1-1-1-12222-1-1-1-1-1-12200222222-1-1-1-12-1-122-1-1-1-122022-1-1-1-100002200-1-1-1-1-1-1-1-10000-1-12-1-1-1-1000000022000000000-1-10
χ342222-1222-1-122222-1-12-122-1-1-1-1-1-12222-1-1-1-1-1-12200222222-1-1-1-12-1-122-1-1-1-1-2-20-2-2-1-1-1-100002200-1-1-1-1-1-1-1-1000011-211110000000-2-2000000000110
χ352222-1222-1-122222-1-12-122-1-1-1-1-1-12222-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-12202211110000-2-200111111110000-1-12-1-1-1-10000000-2-2000000000110
χ362222-1222-1-122222-1-12-122-1-1-1-1-1-12222-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-20-2-211110000-2-20011111111000011-21111000000022000000000-1-10
χ372222-1222-1-122222-1-12-1-22-1-1-1-1-1-122-2-21111112200-2-22222-1-1-1-1-211-2-211112-2022-1-1110000-2-200-1-1-1-111110000-11-2-1-11100000002-2000000000-110
χ382222-1222-1-122222-1-12-1-22-1-1-1-1-1-122-2-21111112200-2-22222-1-1-1-1-211-2-21111-220-2-2-1-1110000-2-200-1-1-1-1111100001-1211-1-10000000-220000000001-10
χ392222-1222-1-122222-1-12-1-22-1-1-1-1-1-122-2-2111111-2-20022-2-2-2-2-1-1-1-1-211-2-211112-202211-1-1000022001111-1-1-1-10000-11-2-1-1110000000-220000000001-10
χ402222-1222-1-122222-1-12-1-22-1-1-1-1-1-122-2-2111111-2-20022-2-2-2-2-1-1-1-1-211-2-21111-220-2-211-1-1000022001111-1-1-1-100001-1211-1-100000002-2000000000-110
χ4122-2-2222-22-2-2-22-22-22220-22-2-2-22-22-200000000002-22i−2i000022-2-200000000000000002i−2i002-22i−2i2-200002i2i−2i−2i002i−2i000000002-2000000002i−2i00000000
χ4222-2-2222-22-2-2-22-22-22220-22-2-2-22-22-200000000002-2−2i2i000022-2-20000000000000000−2i2i002-2−2i2i2-20000−2i−2i2i2i00−2i2i000000002-200000000−2i2i00000000
χ4322-2-2222-22-2-2-22-22-22220-22-2-2-22-22-20000000000-222i−2i000022-2-200000000000000002i−2i00-222i−2i-2200002i2i−2i−2i00−2i2i00000000-2200000000−2i2i00000000
χ4422-2-2222-22-2-2-22-22-22220-22-2-2-22-22-20000000000-22−2i2i000022-2-20000000000000000−2i2i00-22−2i2i-220000−2i−2i2i2i002i−2i00000000-22000000002i−2i00000000
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χ4722-2-22-12-22-21-2-112-2-1-12012-21-2-11-113−30033−3−300-222i−2i−i3−i3i3i3-1-1110003−333−3−300000002i−2i−331-1−ii-22−i3−i3i3i3−i−iii00−2i2i000000001-1−330000i3−i3i−i00000000
χ4822-2-22-12-22-21-2-112-2-1-12012-21-2-11-113−30033−3−300-22−2i2ii3i3−i3−i3-1-1110003−333−3−30000000−2i2i−331-1i−i-22i3i3−i3−i3ii−i−i002i−2i000000001-1−330000−i3i3−ii00000000
χ4922-2-22-12-22-21-2-112-2-1-12012-21-2-11-11−3300−3−333002-22i−2ii3i3−i3−i3-1-111000−33−3−33300000002i−2i−33-11−ii2-2i3i3−i3−i3−i−iii002i−2i00000000-11−330000i3−i3−ii00000000
χ5022-2-22-12-22-21-2-112-2-1-12012-21-2-11-11−3300−3−333002-2−2i2i−i3−i3i3i3-1-111000−33−3−3330000000−2i2i−33-11i−i2-2−i3−i3i3i3ii−i−i00−2i2i00000000-11−330000−i3i3i−i00000000
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χ532-22-22222-22-2-2-22-2-222202-22-2-2-22-2-2000000002i−2i00002i−2i2i−2i2-22-2000000000000002i−2i00000000002i−2i2i−2i00002i−2i00000000000000000000002i−2i2-20000
χ542-22-22222-22-2-2-22-2-222202-22-2-2-22-2-2000000002i−2i00002i−2i2i−2i2-22-2000000000000002i−2i00000000002i−2i2i−2i0000−2i2i0000000000000000000000−2i2i-220000
χ552-22-22222-22-2-2-22-2-222202-22-2-2-22-2-200000000−2i2i0000−2i2i−2i2i2-22-200000000000000−2i2i0000000000−2i2i−2i2i00002i−2i00000000000000000000002i−2i-220000
χ562-22-22222-22-2-2-22-2-222202-22-2-2-22-2-200000000−2i2i0000−2i2i−2i2i2-22-200000000000000−2i2i0000000000−2i2i−2i2i0000−2i2i0000000000000000000000−2i2i2-20000
χ5744444-2-2-244-2-2-2-2-24-21-241-2-2-2-2-2-211-2-244-2-2-2-200440000001111-2-2-2111111004000000-2-2-2-200-2-20000000000000000000-211110000000000000000
χ5844444-2-2-244-2-2-2-2-24-21-241-2-2-2-2-2-211-2-244-2-2-2-200-4-40000001111-2-2-211111100-40000002222002200000000000000000002-1-1-1-10000000000000000
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χ664444-2-244-2-2-24-2-24-21-2-24-2-2-21-211-2-2-2-2-2-21111-4-400-4-4222211114-2-2-2-2111100000222200002200-1-1-1-1-1-1-1-100000000000000000000000000000000
χ674444-2-244-2-2-24-2-24-21-2-2-4-2-2-21-211-2-22222-1-1-1-14400-4-4-2-2-2-21111-42222-1-1-1-100000-2-222000022001111-1-1-1-100000000000000000000000000000000
χ684444-2-244-2-2-24-2-24-21-2-2-4-2-2-21-211-2-22222-1-1-1-1-4-4004422221111-42222-1-1-1-10000022-2-20000-2-200-1-1-1-1111100000000000000000000000000000000
χ6944-4-444-224-4-424-4-2-44-2-202-22-424-4-2200000000004-4000000-2-222000000000000000000004-400-2200000000000000000000-22000000000000000000
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χ7344-4-44-2-224-422-22-2-4-21-20-1-2222-221-1−232300−23−232323004-400000011-1-10003−333−3−3000000000−2323-2200-22000000000000000000001-13−30000000000000000
χ7444-4-44-2-224-422-22-2-4-21-20-1-2222-221-1−232300−23−23232300-4400000011-1-10003−333−3−300000000023−232-2002-200000000000000000000-11−330000000000000000
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χ814-44-444-2-2-44-42-442-44-2-20-22-2-42-4422000000000000000000-22-2200000000000000000000000000000000004i−4i0000000000000000000000−2i2i000000
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χ854-44-4-24442-2-4-4-44-42-24-2042-2222-2-4-4000000004i−4i00004i−4i4i−4i-22-2200000000000000−2i2i0000000000−2i2i−2i2i000000000000000000000000000000000000
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χ884-44-4-2-2442-22-42-2-421-2-20-22-2-12-112200003i−3i3i−3i−4i4i00002i−2i2i−2i1-11-1000003i−3i3i−3i000002i−2i0000000000−ii−ii-33-3300000000000000000000000000000000
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χ904-44-4-2-2442-22-42-2-421-2-20-22-2-12-11220000−3i3i−3i3i−4i4i00002i−2i2i−2i1-11-100000−3i3i−3i3i000002i−2i0000000000−ii−ii3-33-300000000000000000000000000000000
χ914-4-44444-4-4-444-4-4-444440-4-4-444-4-4-440000000000000000004-4-44000000000000000000000000000000000000000000000000000000000000000000
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χ964-4-44-244-42244-4-4-4-2-24-20-422-2-222-4400−2i32i3−2i32i32i3−2i30000000000-222-20−2i32i300−2i32i32i3−2i3000000000000000000000000000000000000000000000000000000000
χ974-4-44-244-42244-4-4-4-2-24-20-422-2-222-44002i3−2i32i3−2i3−2i32i30000000000-222-202i3−2i3002i3−2i3−2i32i3000000000000000000000000000000000000000000000000000000000
χ984-4-44-24-22224-2-4-42-2-2-2102-1-1-21222-200−2i32i3−2i32i32i3−2i300000000001-1-110i3−i300i3−i3−i3i3000−2i32i3000000000000000000000000000i3−i33-3000000000000000000000
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χ1004-4-44-24-22224-2-4-42-2-2-2102-1-1-21222-2002i3−2i32i3−2i3−2i32i300000000001-1-110−i3i300−i3i3i3−i3000−2i32i3000000000000000000000000000i3−i3-33000000000000000000000
χ1014-4-44-24-22224-2-4-42-2-2-2102-1-1-21222-2002i3−2i32i3−2i3−2i32i300000000001-1-110−i3i300−i3i3i3−i30002i3−2i3000000000000000000000000000−i3i33-3000000000000000000000
χ1024-4-44-2-24-422-2422-4-21-2-202221-2-1-12-200−2i32i3i3−i3−i3i300000023−23−23231-1-110−2i32i300i3−i3−i3i300000000000000000−333−33i−3i−3i3i00000000000000000000000000000000
χ1034-4-44-2-24-422-2422-4-21-2-202221-2-1-12-200−2i32i3i3−i3−i3i3000000−232323−231-1-110−2i32i300i3−i3−i3i3000000000000000003−3−33−3i3i3i−3i00000000000000000000000000000000
χ1044-4-44-2-24-422-2422-4-21-2-202221-2-1-12-2002i3−2i3−i3i3i3−i300000023−23−23231-1-1102i3−2i300−i3i3i3−i300000000000000000−333−3−3i3i3i−3i00000000000000000000000000000000
χ1054-4-44-2-24-422-2422-4-21-2-202221-2-1-12-2002i3−2i3−i3i3i3−i3000000−232323−231-1-1102i3−2i300−i3i3i3−i3000000000000000003−3−333i−3i−3i3i00000000000000000000000000000000
χ1068888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-422220000000000-1-1-1-1-42222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-20000000000-1-1-1-14-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ10888-8-8-48-44-44-848-8-44-4-42042-24-2-44-4400000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-44-4444-44-442220-22-2-2-22-22-243−4300−23−2323230000000000-1-111000−232333−3−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-44-4444-44-442220-22-2-2-22-22-2−4343002323−23−230000000000-1-11100023−23−3−333000000000000000000000000000000000000000000000000000000000
χ1118-88-88-4-4-4-88444-44-8-42-4024-4444-4-2-20000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-48-4-44-4-84-8844-4-420-4-224-24-4440000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4-44-4444-44422202-22-2-2-22-2-200006i−6i6i−6i0000000000-11-1100000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-4-44-4444-44422202-22-2-2-22-2-20000−6i6i−6i6i0000000000-11-11000003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1158-8-888-4-44-8-8-4-44448-42-40-244-4-444-220000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-4444-4-4444-42220-2-2-222-2-2-2200−4i34i32i3−2i3−2i32i30000000000-111-102i3−2i300−i3i3i3−i3000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4444-4-4444-42220-2-2-222-2-2-22004i3−4i3−2i32i32i3−2i30000000000-111-10−2i32i300i3−i3−i3i3000000000000000000000000000000000000000000000000000000000

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