Finite Group Databasebeta

← Group #11775434

Character table — Group #11775434

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1111222222222222222244444444444444444668888888888888888888888812121212121212121212122424242424242424242424242424484872727272
order122222334466666612121212346666666121212121212121244668812121224242424242424242424242424242424444121212121212121224448812121212242424246122444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111
χ81111111111111111111111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ91111-1-111-1-1111111-1-1-1-111-1-1-1111-111-1-1-1-1-1-111-1-1i−i111ii−i−iiiiiii−i−i−i−i−i−i1-1-11111-1-1-1-11-1i−ii−iii−i−iii−i−i1-1-11i−i
χ101111-1-111-1-1111111-1-1-1-111-1-1-1111-111-1-1-1-1-1-111-1-1i−i111ii−i−iiiiiii−i−i−i−i−i−i1-1-11111-1-1-1-1-11−iii−i−i−iiiii−i−i-111-1−ii
χ111111-1-111-1-1111111-1-1-1-111-1-1-1111-111-1-1-1-1-1-111-1-1−ii111−i−iii−i−i−i−i−i−iiiiiii1-1-11111-1-1-1-11-1−ii−ii−i−iii−i−iii1-1-11−ii
χ121111-1-111-1-1111111-1-1-1-111-1-1-1111-111-1-1-1-1-1-111-1-1−ii111−i−iii−i−i−i−i−i−iiiiiii1-1-11111-1-1-1-1-11i−i−iiii−i−i−i−iii-111-1i−i
χ131111-1-111-1-1111111-1-1-1-111-1-1-1111-111-1-1-1-1-1-1-1-1-1-1i−i111ii−i−iiiiiii−i−i−i−i−i−i-111-1-1-1-111111-1i−i−iiii−i−i−i−iii1-11-1−ii
χ141111-1-111-1-1111111-1-1-1-111-1-1-1111-111-1-1-1-1-1-1-1-1-1-1i−i111ii−i−iiiiiii−i−i−i−i−i−i-111-1-1-1-11111-11−ii−ii−i−iii−i−iii-11-11i−i
χ151111-1-111-1-1111111-1-1-1-111-1-1-1111-111-1-1-1-1-1-1-1-1-1-1−ii111−i−iii−i−i−i−i−i−iiiiiii-111-1-1-1-111111-1−iii−i−i−iiiii−i−i1-11-1i−i
χ161111-1-111-1-1111111-1-1-1-111-1-1-1111-111-1-1-1-1-1-1-1-1-1-1−ii111−i−iii−i−i−i−i−i−iiiiiii-111-1-1-1-11111-11i−ii−iii−i−iii−i−i-11-11−ii
χ1722222222-2-2222222-2-2-2-22-22222222-2-2-2-2-2-2-2-2222200-2-2-20000000000000000-2-2222-2-222-2-200000000000000000000
χ1822222222-2-2222222-2-2-2-22-22222222-2-2-2-2-2-2-2-2-2-22200-2-2-2000000000000000022-2-2-222-2-22200000000000000000000
χ192222222-122-12-122-12222-1222-1-1-1-1-122-1-1-1-1-1-100-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000222200-1-1-1-10000-1-10000
χ202222222-122-12-122-12222-1222-1-1-1-1-122-1-1-1-1-1-100-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000-2-2-2-20011110000110000
χ212222222-122-12-122-12222-1222-1-1-1-1-122-1-1-1-1-1-100-1-1-2-2-1-1-1-2-2-2-21111111111110000000000022-2-20011110000-1-10000
χ222222222-122-12-122-12222-1222-1-1-1-1-122-1-1-1-1-1-100-1-1-2-2-1-1-1-2-2-2-211111111111100000000000-2-22200-1-1-1-10000110000
χ23222222-12222-12-1-12-1-1-1-1-12-1-12-1-1-12-1-122-1-1-1-122-1-1222-1-1-1-1-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-1-10000220000-1-1-1-1000000
χ24222222-12222-12-1-12-1-1-1-1-12-1-12-1-1-12-1-122-1-1-1-122-1-1-2-22-1-11111-2-21111-2-21111222-1-1-1-1-1-1-1-10000-2-200001111000000
χ25222222-12222-12-1-12-1-1-1-1-12-1-12-1-1-12-1-122-1-1-1-1-2-2-1-1222-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2111111110000-2-200001111000000
χ26222222-12222-12-1-12-1-1-1-1-12-1-12-1-1-12-1-122-1-1-1-1-2-2-1-1-2-22-1-11111-2-21111-2-21111-2-2-2111111110000220000-1-1-1-1000000
χ27222222-12-2-22-12-1-121111-1-2-1-12-1-1-1211-2-2111122-1-100-2113−33−30033−3−30033−3−3-2-22-1-111-1-11100000000003−33−3000000
χ28222222-12-2-22-12-1-121111-1-2-1-12-1-1-1211-2-2111122-1-100-211−33−3300−3−33300−3−333-2-22-1-111-1-1110000000000−33−33000000
χ29222222-12-2-22-12-1-121111-1-2-1-12-1-1-1211-2-21111-2-2-1-100-2113−33−30033−3−30033−3−322-211-1-111-1-10000000000−33−33000000
χ30222222-12-2-22-12-1-121111-1-2-1-12-1-1-1211-2-21111-2-2-1-100-211−33−3300−3−33300−3−33322-211-1-111-1-100000000003−33−3000000
χ312222-2-2222222222222222-2-2-2-2222-2-2-222222222-2-200-2-2-20000000000000000-22-222-2-2-2-22200000000000000000000
χ322222-2-2222222222222222-2-2-2-2222-2-2-2222222-2-2-2-200-2-2-200000000000000002-22-2-22222-2-200000000000000000000
χ332222-2-22-1-2-2-12-122-1-2-2-2-2-12-2-21-1-1-112211111100112i−2i-1-1-12i2i−2i−2i−i−i−i−i−i−iiiiiii000000000002-22i−2i00−i−iii0000-110000
χ342222-2-22-1-2-2-12-122-1-2-2-2-2-12-2-21-1-1-112211111100112i−2i-1-1-12i2i−2i−2i−i−i−i−i−i−iiiiiii00000000000-22−2i2i00ii−i−i00001-10000
χ352222-2-22-1-2-2-12-122-1-2-2-2-2-12-2-21-1-1-11221111110011−2i2i-1-1-1−2i−2i2i2iiiiiii−i−i−i−i−i−i000000000002-2−2i2i00ii−i−i0000-110000
χ362222-2-22-1-2-2-12-122-1-2-2-2-2-12-2-21-1-1-11221111110011−2i2i-1-1-1−2i−2i2i2iiiiiii−i−i−i−i−i−i00000000000-222i−2i00−i−iii00001-10000
χ372222-2-2-12222-12-1-12-1-1-1-1-1-211-2-1-1-1-21122-1-1-1-1221100-211−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3-22-2-1-11111-1-10000000000−i3i3i3−i3000000
χ382222-2-2-12222-12-1-12-1-1-1-1-1-211-2-1-1-1-21122-1-1-1-1221100-211i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3-22-2-1-11111-1-10000000000i3−i3−i3i3000000
χ392222-2-2-12222-12-1-12-1-1-1-1-1-211-2-1-1-1-21122-1-1-1-1-2-21100-211−i3i3i3−i300−i3−i3i3i300i3i3−i3−i32-2211-1-1-1-1110000000000i3−i3−i3i3000000
χ402222-2-2-12222-12-1-12-1-1-1-1-1-211-2-1-1-1-21122-1-1-1-1-2-21100-211i3−i3−i3i300i3i3−i3−i300−i3−i3i3i32-2211-1-1-1-1110000000000−i3i3i3−i3000000
χ412222-2-2-12-2-22-12-1-121111-1211-2-1-1-1-2-1-1-2-2111122112i−2i2-1-1−i−iii2i2i−i−i−i−i−2i−2iiiii2-2-2-1-1-1-1111100002i−2i0000−i−iii000000
χ422222-2-2-12-2-22-12-1-121111-1211-2-1-1-1-2-1-1-2-211112211−2i2i2-1-1ii−i−i−2i−2iiiii2i2i−i−i−i−i2-2-2-1-1-1-111110000−2i2i0000ii−i−i000000
χ432222-2-2-12-2-22-12-1-121111-1211-2-1-1-1-2-1-1-2-21111-2-2112i−2i2-1-1−i−iii2i2i−i−i−i−i−2i−2iiiii-2221111-1-1-1-10000−2i2i0000ii−i−i000000
χ442222-2-2-12-2-22-12-1-121111-1211-2-1-1-1-2-1-1-2-21111-2-211−2i2i2-1-1ii−i−i−2i−2iiiii2i2i−i−i−i−i-2221111-1-1-1-100002i−2i0000−i−iii000000
χ454444444-2-4-4-24-244-2-4-4-4-4-2-444-2-2-2-2-2-4-422222200-2-20022200000000000000000000000000000000000000000000000
χ46444444-2-244-2-2-2-2-2-2-2-2-2-214-2-2-2111-2-2-2-2-21111001144-211-2-2-2-2-2-21111-2-211110000000000000000000000000000000
χ47444444-2-244-2-2-2-2-2-2-2-2-2-214-2-2-2111-2-2-2-2-211110011-4-4-211222222-1-1-1-122-1-1-1-10000000000000000000000000000000
χ48444444-2-2-4-4-2-2-2-2-2-222221-4-2-2-2111-22222-1-1-1-10011002-1-123−2323−2300−3−33300−3−3330000000000000000000000000000000
χ49444444-2-2-4-4-2-2-2-2-2-222221-4-2-2-2111-22222-1-1-1-10011002-1-1−2323−23230033−3−30033−3−30000000000000000000000000000000
χ504444-4-44-244-24-244-24444-2-4-4-42-2-2-22-4-4-2-2-2-2-2-200220022200000000000000000000000000000000000000000000000
χ514444-4-4-2-244-2-2-2-2-2-2-2-2-2-21-4222111222-2-2111100-1-1002-1-1−2i32i32i3−2i300i3i3−i3−i300−i3−i3i3i30000000000000000000000000000000
χ524444-4-4-2-244-2-2-2-2-2-2-2-2-2-21-4222111222-2-2111100-1-1002-1-12i3−2i3−2i32i300−i3−i3i3i300i3i3−i3−i30000000000000000000000000000000
χ534444-4-4-2-2-4-4-2-2-2-2-2-22222142221112-2-222-1-1-1-100-1-14i−4i-211−2i−2i2i2i−2i−2iiiii2i2i−i−i−i−i0000000000000000000000000000000
χ544444-4-4-2-2-4-4-2-2-2-2-2-22222142221112-2-222-1-1-1-100-1-1−4i4i-2112i2i−2i−2i2i2i−i−i−i−i−2i−2iiiii0000000000000000000000000000000
χ5544-4-4004400-444-4-4-4000040000-4-440000000004i−4i000000000000000000000000004i−4i00000000000000000000000000
χ5644-4-4004400-444-4-4-4000040000-4-44000000000−4i4i00000000000000000000000000−4i4i00000000000000000000000000
χ5744-4-400-2400-4-2422-4−2i3−2i32i32i3-2000022-200000−2i3−2i32i32i34i−4i00000000000000000000000000−2i2i000023−2300000000000000000000
χ5844-4-400-2400-4-2422-4−2i3−2i32i32i3-2000022-200000−2i3−2i32i32i3−4i4i000000000000000000000000002i−2i0000−232300000000000000000000
χ5944-4-400-2400-4-2422-42i32i3−2i3−2i3-2000022-2000002i32i3−2i3−2i34i−4i00000000000000000000000000−2i2i0000−232300000000000000000000
χ6044-4-400-2400-4-2422-42i32i3−2i3−2i3-2000022-2000002i32i3−2i3−2i3−4i4i000000000000000000000000002i−2i000023−2300000000000000000000
χ614-44-400444i−4i4-4-44-4-44i−4i4i−4i400004-4-40004i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000
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χ634-44-4004-24i−4i-2-424-424i−4i4i−4i-20000-222000−2i2i−2i2i−2i2i000000000000000000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000
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χ664-44-4004-2−4i4i-2-424-42−4i4i−4i4i-20000-2220002i−2i2i−2i2i−2i000000000000000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000
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χ874-4-44-44-2-2002222-2-2−232323−23102-2-2-11-1223−23003−3−3300-11000−3300006−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ230000000000000000000000000000000
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χ9188-8-800-4-4004-4-44444i34i3−4i3−4i320000-2-2200000−2i3−2i32i32i300000000000000000000000000000000000000000000000000000000
χ928-88-800-4-48i−8i-444-444−4i4i−4i4i200002-2-2000−4i4i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000
χ938-88-800-4-4−8i8i-444-4444i−4i4i−4i200002-2-20004i−4i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.