Finite Group Databasebeta

← Group #11771392

Character table — Group #11771392

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222224444444444444444444444448888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order12222233666666666634444446666666661212121212121212121212121212121212121212121212121212121244441212121212121212226666888824242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−iii−i−i
χ6111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−iii
χ7111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111ii−i−iiiii−i−i−i−i−i−iii
χ8111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−iii−i−i−i−iiiiiii−i−i
χ91-11-11-111-111-111-1-1-1-111-1i−ii−i1-111-1-1-11-111-1-1ii−i−i1-1iii−i−i−i11-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i1-111-1-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ101-11-11-111-111-111-1-1-1-111-1i−ii−i1-111-1-1-11-111-1-1ii−i−i1-1iii−i−i−i11-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i1-111-1-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ111-11-11-111-111-111-1-1-1-111-1i−ii−i1-111-1-1-11-111-1-1ii−i−i1-1iii−i−i−i11-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiii-11-1-111ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ121-11-11-111-111-111-1-1-1-111-1i−ii−i1-111-1-1-11-111-1-1ii−i−i1-1iii−i−i−i11-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiii-11-1-111−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ131-11-11-111-111-111-1-1-1-111-1−ii−ii1-111-1-1-11-111-1-1−i−iii1-1−i−i−iiii11-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11-1-111−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ141-11-11-111-111-111-1-1-1-111-1−ii−ii1-111-1-1-11-111-1-1−i−iii1-1−i−i−iiii11-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11-1-111ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ151-11-11-111-111-111-1-1-1-111-1−ii−ii1-111-1-1-11-111-1-1−i−iii1-1−i−i−iiii11-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii1-111-1-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ161-11-11-111-111-111-1-1-1-111-1−ii−ii1-111-1-1-11-111-1-1−i−iii1-1−i−i−iiii11-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii1-111-1-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
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χ202222222-12-1-1-12-12-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1222222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-211110000000000000000
χ212222222-12-1-1-12-12-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221-211-21-1-1-1-1111111112222-1-1-1-1-1-1-1-1-2-211110000000000000000
χ222222222-12-1-1-12-12-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221-211-21-1-1-1-111111111-2-2-2-21111111122-1-1-1-10000000000000000
χ232222222-12-1-1-12-12-1-1-1-1-2-222-2-222-1-1-1-1-1-1-111112222-2-2-1-21-1-211111-1-111-1-1110000−i3−i3i3i3−i3−i3i3i300−i3i3−i3i30000000000000000
χ242222222-12-1-1-12-12-1-1-1-1-2-222-2-222-1-1-1-1-1-1-111112222-2-2-1-21-1-211111-1-111-1-1110000i3i3−i3−i3i3i3−i3−i300i3−i3i3−i30000000000000000
χ252222222-12-1-1-12-12-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-11111-2-2-2-2-2-212-112-1111111-1-111-1-10000−i3−i3i3i3−i3−i3i3i300i3−i3i3−i30000000000000000
χ262222222-12-1-1-12-12-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-11111-2-2-2-2-2-212-112-1111111-1-111-1-10000i3i3−i3−i3i3i3−i3−i300−i3i3−i3i30000000000000000
χ27222222-12-1222-12-1222-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12-122-12-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-1-1-1-10000
χ28222222-12-1222-12-1222-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12-122-12-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2111111110000
χ29222222-12-1222-12-1222-122-2-2-2-2-1-1-1-1-1-1-1-1-122221111-1-1-21-2-21-2-1-1-1-1111111110000000000000000002i2i−2i−2i−i−i−i−iiiii0000
χ30222222-12-1222-12-1222-122-2-2-2-2-1-1-1-1-1-1-1-1-122221111-1-1-21-2-21-2-1-1-1-111111111000000000000000000−2i−2i2i2iiiii−i−i−i−i0000
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χ33222222-12-1222-12-1222-1-2-2-2-222-1-1-1-1-1-1-1-1-1-2-2-2-2111111-2-12-2-12111111-1-111-1-100000000000000000000003−33−3−33−330000
χ34222222-12-1222-12-1222-1-2-2-2-222-1-1-1-1-1-1-1-1-1-2-2-2-2111111-2-12-2-12111111-1-111-1-10000000000000000000000−33−333−33−30000
χ352-22-22-222-222-222-2-2-2-22-222i−2i−2i2i2-222-2-2-22-2-2-2222i2i−2i−2i-222i−2i−2i−2i2i2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ362-22-22-222-222-222-2-2-2-22-22−2i2i2i−2i2-222-2-2-22-2-2-222−2i−2i2i2i-22−2i2i2i2i−2i−2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ372-22-22-22-1-2-1-112-1-2111-12-22i−2i2i−2i2-2-1-1111-11-1-1112i2i−2i−2i2-2−i2i−ii−2ii-1-111−i−i−i−iiiii2i2i−2i−2i−i−i−i−iiiii2-2-1-1110000000000000000
χ382-22-22-22-1-2-1-112-1-2111-12-22i−2i2i−2i2-2-1-1111-11-1-1112i2i−2i−2i2-2−i2i−ii−2ii-1-111−i−i−i−iiiii−2i−2i2i2iiiii−i−i−i−i-2211-1-10000000000000000
χ392-22-22-22-1-2-1-112-1-2111-12-2−2i2i−2i2i2-2-1-1111-11-1-111−2i−2i2i2i2-2i−2ii−i2i−i-1-111iiii−i−i−i−i2i2i−2i−2i−i−i−i−iiiii-2211-1-10000000000000000
χ402-22-22-22-1-2-1-112-1-2111-12-2−2i2i−2i2i2-2-1-1111-11-1-111−2i−2i2i2i2-2i−2ii−i2i−i-1-111iiii−i−i−i−i−2i−2i2i2iiiii−i−i−i−i2-2-1-1110000000000000000
χ412-22-22-22-1-2-1-112-1-2111-1-222i−2i−2i2i2-2-1-1111-1111-1-12i2i−2i−2i-22−i−2iii2i−i11-1-1−i−iiiii−i−i000033−3−3−3−33300−i3i3i3−i30000000000000000
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χ442-22-22-22-1-2-1-112-1-2111-1-22−2i2i2i−2i2-2-1-1111-1111-1-1−2i−2i2i2i-22i2i−i−i−2ii11-1-1ii−i−i−i−iii0000−3−33333−3−300−i3i3i3−i30000000000000000
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χ462-22-22-2-12122-2-121-2-2-2-12-22i−2i2i−2i-11-1-1111-1122-2-2−i−iii-112i−i2i−2ii−2i-1-111−i−i−i−iiiii000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ130000
χ472-22-22-2-12122-2-121-2-2-2-12-2−2i2i−2i2i-11-1-1111-1122-2-2ii−i−i-11−2ii−2i2i−i2i-1-111iiii−i−i−i−i000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ230000
χ482-22-22-2-12122-2-121-2-2-2-12-2−2i2i−2i2i-11-1-1111-1122-2-2ii−i−i-11−2ii−2i2i−i2i-1-111iiii−i−i−i−i0000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ230000
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χ764-44-4-4444-4-4-4-444-4-4444000000-44-4-4-4444-400000000000000000000000000000000000000000000000000000000000000
χ774-44-4-444-2-42224-2-42-2-2-2000000-44222-2-2-22−2i32i32i3−2i3000000000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ784-44-4-444-2-42224-2-42-2-2-2000000-44222-2-2-222i3−2i3−2i32i30000000000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ794-44-4-44-242-4-4-4-242-444-20000002-2222-2-2-22000023−23−232300000000000023−2300−2323000000000000000000000000000000000000
χ804-44-4-44-242-4-4-4-242-444-20000002-2222-2-2-220000−232323−23000000000000−23230023−23000000000000000000000000000000000000
χ814-44-4-44-2-22222-2-222-2-210000002-2-1-1-1111-1−2i32i32i3−2i323−23−232300000000i3−i3−i3i3−333i−3i3−3−3i3i0000000000000000000000000000000000
χ824-44-4-44-2-22222-2-222-2-210000002-2-1-1-1111-1−2i32i32i3−2i3−232323−2300000000i3−i3−i3i33−3−3i3i−333i−3i0000000000000000000000000000000000
χ834-44-4-44-2-22222-2-222-2-210000002-2-1-1-1111-12i3−2i3−2i32i323−23−232300000000−i3i3i3−i3−33−3i3i3−33i−3i0000000000000000000000000000000000
χ844-44-4-44-2-22222-2-222-2-210000002-2-1-1-1111-12i3−2i3−2i32i3−232323−2300000000−i3i3i3−i33−33i−3i−33−3i3i0000000000000000000000000000000000
χ854-4-440044-400-4-4-4440040000000000-400-4400000000000000000000000000002-2-222-22-2-22-220000000000000000000000
χ864-4-440044-400-4-4-4440040000000000-400-440000000000000000000000000000-222-2-22-222-22-20000000000000000000000
χ874-4-44004-2-4−2i32i32-424-22i3−2i3-200000000−2i32i322i3−2i32-200000000000000000000000000002-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000
χ884-4-44004-2-4−2i32i32-424-22i3−2i3-200000000−2i32i322i3−2i32-20000000000000000000000000000-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000
χ894-4-44004-2-42i3−2i32-424-2−2i32i3-2000000002i3−2i32−2i32i32-200000000000000000000000000002-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000
χ904-4-44004-2-42i3−2i32-424-2−2i32i3-2000000002i3−2i32−2i32i32-20000000000000000000000000000-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000
χ9188-8-800-48-40084-84-800-40000000000-4004400000000000000000000000000000000000000000000000000000000000000
χ9288-8-800-4-4-4−4i34i3-44444−4i34i32000000002i3−2i322i3−2i3-2-200000000000000000000000000000000000000000000000000000000000000
χ9388-8-800-4-4-44i3−4i3-444444i3−4i3200000000−2i32i32−2i32i3-2-200000000000000000000000000000000000000000000000000000000000000
χ948-8-8800-48400-84-8-4800-400000000004004-400000000000000000000000000000000000000000000000000000000000000
χ958-8-8800-4-44−4i34i3444-4-44i3−4i32000000002i3−2i3-2−2i32i3-2200000000000000000000000000000000000000000000000000000000000000
χ968-8-8800-4-444i3−4i3444-4-4−4i34i3200000000−2i32i3-22i3−2i3-2200000000000000000000000000000000000000000000000000000000000000

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