Finite Group Databasebeta

← Group #11787633

Character table — Group #11787633

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order124422233444666612121212121236666666612121212121212121244661212121212121212121212121212121212122244888888882424242424242424668812122424242424242424888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1
χ911-1-11-1-11111-11-1-1111-1-1-1-111-11-1-11-1-11-1111-1-11-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i1-11-1ii−i−iii−i−iiiii−i−i−i−i1-11-11-1ii−i−i11-1-1ii−i−i1-1
χ1011-1-11-1-11111-11-1-1111-1-1-1-111-11-1-11-1-11-1111-1-11-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i1-11-1−i−iiiii−i−iiiii−i−i−i−i1-1-111-1−i−iii-1-111−i−iii-11
χ1111-1-11-1-11111-11-1-1111-1-1-1-111-11-1-11-1-11-1111-1-11-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i-11-11ii−i−i−i−iii−i−i−i−iiiii-111-1-11ii−i−i11-1-1−i−iii-11
χ1211-1-11-1-11111-11-1-1111-1-1-1-111-11-1-11-1-11-1111-1-11-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i-11-11−i−iii−i−iii−i−i−i−iiiii-11-11-11−i−iii-1-111ii−i−i1-1
χ1311-1-11-1-11111-11-1-1111-1-1-1-111-11-1-11-1-11-1111-1-11-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii1-11-1ii−i−i−i−iii−i−i−i−iiiii1-1-111-1ii−i−i-1-111ii−i−i-11
χ1411-1-11-1-11111-11-1-1111-1-1-1-111-11-1-11-1-11-1111-1-11-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii1-11-1−i−iii−i−iii−i−i−i−iiiii1-11-11-1−i−iii11-1-1−i−iii1-1
χ1511-1-11-1-11111-11-1-1111-1-1-1-111-11-1-11-1-11-1111-1-11-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii-11-11ii−i−iii−i−iiiii−i−i−i−i-11-11-11ii−i−i-1-111−i−iii1-1
χ1611-1-11-1-11111-11-1-1111-1-1-1-111-11-1-11-1-11-1111-1-11-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii-11-11−i−iiiii−i−iiiii−i−i−i−i-111-1-11−i−iii11-1-1ii−i−i-11
χ1722222222-12222-1-1-1-1-1-1-122-122-1-12-1-1-122-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1222200002222-1-1-1-1-1-1-1-1-1-100-1-100000000000000
χ1822222222-12222-1-1-1-1-1-1-122-122-1-12-1-1-122-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20000-2-2-2-21111111111001100000000000000
χ1922222222-12222-1-1-1-1-1-1-122-122-1-12-1-1-122-1-1-1-1-12-1-2-2-1-11111-1-1-2-21111-2-2111122220000-2-2-2-211111111-1-100-1-100000000000000
χ2022222222-12222-1-1-1-1-1-1-122-122-1-12-1-1-122-1-1-1-1-12-1-2-2-1-11111-1-1-2-21111-2-21111-2-2-2-200002222-1-1-1-1-1-1-1-111001100000000000000
χ212222222-12222-12222222-1-1-1-1-122-1-1-1-1-1-12-1-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100002222000000000000002200-1-1-1-1-1-1-1-1000000
χ222222222-12222-12222222-1-1-1-1-122-1-1-1-1-1-12-1-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000000000-2-20011111111000000
χ232222222-12222-12222222-1-1-1-1-122-1-1-1-1-1-12-1-1-1-1-12-2-2-1-1-2-2-2-2-1-11111111111110000222200000000000000-2-200-1-1-1-11111000000
χ242222222-12222-12222222-1-1-1-1-122-1-1-1-1-1-12-1-1-1-1-12-2-2-1-1-2-2-2-2-1-11111111111110000-2-2-2-20000000000000022001111-1-1-1-1000000
χ2522222-2-222-2-222-2-22-2-2222222-22-2-22-2-2-22-2-2-222-22002-20000-2200000000000000002-22-20000000000000000002-22-20000000000
χ2622222-2-222-2-222-2-22-2-2222222-22-2-22-2-2-22-2-2-222-22002-20000-220000000000000000-22-22000000000000000000-22-220000000000
χ2722222-2-2-12-2-22-1-2-22-2-222-1-1-1-112-21-1111-1-211-1-11200-1100001-13−333−3−33−333−3−300002-22-2000000000000000000-11-113−33−3000000
χ2822222-2-2-12-2-22-1-2-22-2-222-1-1-1-112-21-1111-1-211-1-11200-1100001-13−333−3−33−333−3−30000-22-220000000000000000001-11-1−33−33000000
χ2922222-2-2-12-2-22-1-2-22-2-222-1-1-1-112-21-1111-1-211-1-11200-1100001-1−33−3−333−33−3−33300002-22-2000000000000000000-11-11−33−33000000
χ3022222-2-2-12-2-22-1-2-22-2-222-1-1-1-112-21-1111-1-211-1-11200-1100001-1−33−3−333−33−3−3330000-22-220000000000000000001-11-13−33−3000000
χ312222-22-222-22-22-2-22-2-222222-22-22-22-2-2-2-22-2-2222-200-2200002-20000000000002-2-2200000000000000002-200-2200000000000000
χ322222-22-222-22-22-2-22-2-222222-22-22-22-2-2-2-22-2-2222-200-2200002-2000000000000-222-20000000000000000-22002-200000000000000
χ332222-22-22-1-22-2211-111-1-122-1-221-1-2-111-2-2-111-1-121001-13−33−3-11003−33−3003−33−32-2-220000000033−3−333−3−3-11001-100000000000000
χ342222-22-22-1-22-2211-111-1-122-1-221-1-2-111-2-2-111-1-121001-13−33−3-11003−33−3003−33−3-222-200000000−3−333−3−3331-100-1100000000000000
χ352222-22-22-1-22-2211-111-1-122-1-221-1-2-111-2-2-111-1-121001-1−33−33-1100−33−3300−33−332-2-2200000000−3−333−3−333-11001-100000000000000
χ362222-22-22-1-22-2211-111-1-122-1-221-1-2-111-2-2-111-1-121001-1−33−33-1100−33−3300−33−33-222-20000000033−3−333−3−31-100-1100000000000000
χ372222-2-22222-2-222222222222-2-2-2-222222-2-22222-2-200-2-20000-2-200000000000000000000000000000000000000000000002-22-200
χ382222-2-22222-2-222222222222-2-2-2-222222-2-22222-2-200-2-20000-2-20000000000000000000000000000000000000000000000-22-2200
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200220000-2-200000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i0000000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200220000-2-20000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i0000000000
χ4122-2-2222-12-2-2-2-1222-2-2-2-211-1-1-122-1-1-1-111-211111-200-1-1000011−i3i3−i3−i3i3i3i3−i3i3i3−i3−i300002i−2i−2i2i000000000000000000−iii−i−333−3000000
χ4222-2-2222-12-2-2-2-1222-2-2-2-211-1-1-122-1-1-1-111-211111-200-1-1000011−i3i3−i3−i3i3i3i3−i3i3i3−i3−i30000−2i2i2i−2i000000000000000000i−i−ii3−3−33000000
χ4322-2-2222-12-2-2-2-1222-2-2-2-211-1-1-122-1-1-1-111-211111-200-1-1000011i3−i3i3i3−i3−i3−i3i3−i3−i3i3i300002i−2i−2i2i000000000000000000−iii−i3−3−33000000
χ4422-2-2222-12-2-2-2-1222-2-2-2-211-1-1-122-1-1-1-111-211111-200-1-1000011i3−i3i3i3−i3−i3−i3i3−i3−i3i3i30000−2i2i2i−2i000000000000000000i−i−ii−333−3000000
χ4522-2-22-2-22-122-2211-1-1-111-2-2-12-2-11-2-1112-2-1-1-111212i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii2-22-200002i2i−2i−2i−i−i−i−iiiii-1100-1100000000000000
χ4622-2-22-2-22-122-2211-1-1-111-2-2-12-2-11-2-1112-2-1-1-111212i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii-22-220000−2i−2i2i2iiiii−i−i−i−i1-1001-100000000000000
χ4722-2-22-2-22-122-2211-1-1-111-2-2-12-2-11-2-1112-2-1-1-11121−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i2-22-20000−2i−2i2i2iiiii−i−i−i−i-1100-1100000000000000
χ4822-2-22-2-22-122-2211-1-1-111-2-2-12-2-11-2-1112-2-1-1-11121−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i-22-2200002i2i−2i−2i−i−i−i−iiiii1-1001-100000000000000
χ4922-2-22-2-2-1222-2-1-2-2222-2-211-1-112-21-111-112-1-111-1-22i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii00002i2i−2i−2i000000000000002-200−i−iii-1-111000000
χ5022-2-22-2-2-1222-2-1-2-2222-2-211-1-112-21-111-112-1-111-1-22i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii0000−2i−2i2i2i00000000000000-2200ii−i−i11-1-1000000
χ5122-2-22-2-2-1222-2-1-2-2222-2-211-1-112-21-111-112-1-111-1-2−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i00002i2i−2i−2i00000000000000-2200−i−iii11-1-1000000
χ5222-2-22-2-2-1222-2-1-2-2222-2-211-1-112-21-111-112-1-111-1-2−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i0000−2i−2i2i2i000000000000002-200ii−i−i-1-111000000
χ5322-2-2-22-2222-222-2-2222-2-2-2-22-22-22-22-2-222-222-2-2-2200-220000-2200000000000000000000000000000000000000000000002i−2i−2i2i00
χ5422-2-2-22-2222-222-2-2222-2-2-2-22-22-22-22-2-222-222-2-2-2200-220000-220000000000000000000000000000000000000000000000−2i2i2i−2i00
χ5522-2-2-2-2222-2222222-2-2-2-2-2-22-2-2-2-22222-222-2-2-2-22200-2-200002200000000000022-2-200000000000000002200-2-200000000000000
χ5622-2-2-2-2222-2222222-2-2-2-2-2-22-2-2-2-22222-222-2-2-2-22200-2-2000022000000000000-2-2220000000000000000-2-2002200000000000000
χ5722-2-2-2-222-1-2222-1-1-11111-2-2-1-2-2112-1-1-1-22-111112-10011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i322-2-200000000−i3−i3i3i3i3i3−i3−i3-1-1001100000000000000
χ5822-2-2-2-222-1-2222-1-1-11111-2-2-1-2-2112-1-1-1-22-111112-10011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i3-2-22200000000i3i3−i3−i3−i3−i3i3i31100-1-100000000000000
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χ614444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2111-2-2-21111-2-24411-2-2-2-211-2-21111-2-211110000000000000000000000000000000000000000
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χ854-44i−4i00044000-400-4004i−4i4i−4i400000-400000004i−4i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
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χ894-44i−4i0004-2000-42i3−2i32−2323−2i2i4i−4i-20000022i3−2i3000−2323−2i2i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ2300000000000000000000
χ904-44i−4i0004-2000-42i3−2i32−2323−2i2i4i−4i-20000022i3−2i3000−2323−2i2i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ2300000000000000000000
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χ944-4−4i4i0004-2000-4−2i32i32−23232i−2i−4i4i-2000002−2i32i3000−23232i−2i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ2300000000000000000000
χ954-4−4i4i0004-2000-42i3−2i3223−232i−2i−4i4i-20000022i3−2i300023−232i−2i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ2300000000000000000000
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χ978-88i−8i000-48000400-8008i−8i−4i4i-40000040000000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-40004−4i34i3443−43−4i4i−4i4i200000-22i3−2i3000−23232i−2i0000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-400044i3−4i34−4343−4i4i−4i4i200000-2−2i32i300023−232i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i000-48000400-800−8i8i4i−4i-400000400000004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-40004−4i34i34−43434i−4i4i−4i200000-22i3−2i300023−23−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-400044i3−4i3443−434i−4i4i−4i200000-2−2i32i3000−2323−2i2i0000000000000000000000000000000000000000000000000000000000000000

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