Finite Group Databasebeta

← Group #11774780

Character table — Group #11774780

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222444444444444444488888888181818181818181818181818181818181818181818181818242424242424242424242424242424242424242424242424
order12224444444433666666121212121212121212121212121212122244444488888888888888884444888812121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ511111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ711111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1
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χ101111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii11-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii11-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-1-11111-1-1−i−iiiii−i−i
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-1-11111-1-1ii−i−i−i−iii
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χ2722-2-2-2-22200002222-2-2-2-2-2-2-2-2222200000000-222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
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χ302-22-22i−2i2i−2i000022-2-22-22-22i2i−2i−2i2i−2i2i−2i0000000000002-22i−2i00000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
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χ332-22-2−2i2i−2i2i000022-2-22-22-2−2i−2i2i2i−2i2i−2i2i0000000000002-2−2i2i00000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ342-22-2−2i2i−2i2i000022-2-22-22-2−2i−2i2i2i−2i2i−2i2i0000000000002-2−2i2i000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ352-22-2−2i2i−2i2i000022-2-22-22-2−2i−2i2i2i−2i2i−2i2i000000000000-222i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ362-22-2−2i2i−2i2i000022-2-22-22-2−2i−2i2i2i−2i2i−2i2i000000000000-222i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ372-2-222i−2i−2i2i2i−2i2-222-2-2-22-222i2i−2i−2i−2i2i−2i2i2i−2i2-22i−2i2-2000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000000000
χ382-2-222i−2i−2i2i2i−2i2-222-2-2-22-222i2i−2i−2i−2i2i−2i2i2i−2i2-22i−2i2-200000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000000000
χ392-2-222i−2i−2i2i−2i2i-2222-2-2-22-222i2i−2i−2i−2i2i−2i2i−2i2i-22−2i2i-22000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000000000
χ402-2-222i−2i−2i2i−2i2i-2222-2-2-22-222i2i−2i−2i−2i2i−2i2i−2i2i-22−2i2i-2200000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000000000
χ412-2-22−2i2i2i−2i2i−2i-2222-2-2-22-22−2i−2i2i2i2i−2i2i−2i2i−2i-222i−2i-22000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000000000
χ422-2-22−2i2i2i−2i2i−2i-2222-2-2-22-22−2i−2i2i2i2i−2i2i−2i2i−2i-222i−2i-2200000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000000000
χ432-2-22−2i2i2i−2i−2i2i2-222-2-2-22-22−2i−2i2i2i2i−2i2i−2i−2i2i2-2−2i2i2-2000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000000000
χ442-2-22−2i2i2i−2i−2i2i2-222-2-2-22-22−2i−2i2i2i2i−2i2i−2i−2i2i2-2−2i2i2-200000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000000000
χ454444444444441-21-211-2-21-21-2-2-2111111-2-2-2-20000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
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χ48444444444444-21-21-2-211-21-2111-2-2-2-2-2-21111000000000000000000000000-2-2-2-200001111111100000000
χ4944444444-4-4-4-41-21-211-2-21-21-2-2-211-1-1-1-12222000000000000000000000000000022-2-200000000-1-1-1-11111
χ5044444444-4-4-4-41-21-211-2-21-21-2-2-211-1-1-1-122220000000000000000000000000000-2-222000000001111-1-1-1-1
χ5144444444-4-4-4-4-21-21-2-211-21-2111-2-22222-1-1-1-100000000000000000000000022-2-20000-1-1-1-1111100000000
χ5244444444-4-4-4-4-21-21-2-211-21-2111-2-22222-1-1-1-1000000000000000000000000-2-22200001111-1-1-1-100000000
χ534444-4-4-4-444-4-41-21-211-2-2-12-1222-1-111-1-1-2-22200000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii
χ544444-4-4-4-444-4-41-21-211-2-2-12-1222-1-111-1-1-2-2220000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i
χ554444-4-4-4-444-4-4-21-21-2-2112-12-1-1-122-2-22211-1-10000000000000000000000002-22-20000-1-111-1-11100000000
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χ584444-4-4-4-4-4-4441-21-211-2-2-12-1222-1-1-1-11122-2-20000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii
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χ604444-4-4-4-4-4-444-21-21-2-2112-12-1-1-12222-2-2-1-111000000000000000000000000-222-2000011-1-1-1-11100000000
χ614-4-444i−4i−4i4i4i−4i4-41-2-12-112-2i−2i−i2i2i−2i−iii−i1-1−2i2i-220000000000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ624-4-444i−4i−4i4i4i−4i4-41-2-12-112-2i−2i−i2i2i−2i−iii−i1-1−2i2i-220000000000000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
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χ714-4-44−4i4i4i−4i4i−4i-44-212-12-2-112i−i−2iii−i−2i2i−2i2i2-2i−i-11000000000000000000000000000000003−3i3−i3−i3i3−3300000000
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χ828-88-88i−8i8i−8i0000-424-2-442-2−4i2i4i−2i2i−2i−4i4i00000000000000000000000000000000000000000000000000000000
χ838-88-8−8i8i−8i8i00002-4-242-2-44−2i4i2i−4i4i−4i−2i2i00000000000000000000000000000000000000000000000000000000
χ848-88-8−8i8i−8i8i0000-424-2-442-24i−2i−4i2i−2i2i4i−4i00000000000000000000000000000000000000000000000000000000

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