Finite Group Databasebeta

← Group #11787652

Character table — Group #11787652

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order12442223344466661212121212123666666661212121212121212126688121224242424242424242424242424242424888888888888242424242424242444121212122424242424242424224424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1
χ911-1-11-1-11111-1-1-11111-1-1-1-1111-1-1-1-11-111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−ii−iii−i−iii−i−iii−i−i1-11-11-1
χ1011-1-11-1-11111-1-1-11111-1-1-1-1111-1-1-1-11-111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1ii−i−i−i−iiiii−i−iiiii−i−i−i−i−ii−i−iiiii−i−i−i−iii-11-11-11
χ1111-1-11-1-11111-1-1-11111-1-1-1-1111-1-1-1-11-111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1−i−iiiii−i−i−i−iii−i−i−i−iiiiii−iii−i−i−i−iiiii−i−i-11-11-11
χ1211-1-11-1-11111-1-1-11111-1-1-1-1111-1-1-1-11-111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii−ii−i−iii−i−iii−i−iii1-11-11-1
χ1311-1-11-1-11111-1-1-11111-1-1-1-1111-1-1-1-11-111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111ii−i−iii−i−i−i−iii−i−i−i−iiiii−ii−i−iiiii−i−iii−i−i1-11-1-11
χ1411-1-11-1-11111-1-1-11111-1-1-1-1111-1-1-1-11-111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111ii−i−i−i−iii−i−iii−i−i−i−iiiiii−iii−i−iii−i−i−i−iii-11-111-1
χ1511-1-11-1-11111-1-1-11111-1-1-1-1111-1-1-1-11-111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111−i−iiiii−i−iii−i−iiiii−i−i−i−i−ii−i−iii−i−iiiii−i−i-11-111-1
χ1611-1-11-1-11111-1-1-11111-1-1-1-1111-1-1-1-11-111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111−i−iii−i−iiiii−i−iiiii−i−i−i−ii−iii−i−i−i−iii−i−iii1-11-1-11
χ1722222222-1222222-12222-1-1-12-12-1-1-1-1-12-1-1-1-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000000022-1-1-1-10000-1-1-1-1000000
χ1822222222-1222222-12222-1-1-12-12-1-1-1-1-12-1-1-1-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000000000-2-2111100001111000000
χ1922222222-1222222-12222-1-1-12-12-1-1-1-1-12-1-1-1-1-1-1-12-1-1-2-2-1-1-2-2-2-211111111111100002222000000000000-2-211110000-1-1-1-1000000
χ2022222222-1222222-12222-1-1-12-12-1-1-1-1-12-1-1-1-1-1-1-12-1-1-2-2-1-1-2-2-2-21111111111110000-2-2-2-200000000000022-1-1-1-100001111000000
χ212222222-12222-1-1-12-1-1-1-122-1-12-12-1-1-12-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1222200002222-1-1-1-1-1-1-1-1000000-1-1-1-10000000000
χ222222222-12222-1-1-12-1-1-1-122-1-12-12-1-1-12-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20000-2-2-2-21111111100000011110000000000
χ232222222-12222-1-1-12-1-1-1-122-1-12-12-1-1-12-122-1-12-1-1-1-1-1-2-2-1-11111-2-21111-2-2111122220000-2-2-2-211111111000000-1-1-1-10000000000
χ242222222-12222-1-1-12-1-1-1-122-1-12-12-1-1-12-122-1-12-1-1-1-1-1-2-2-1-11111-2-21111-2-21111-2-2-2-200002222-1-1-1-1-1-1-1-100000011110000000000
χ2522222-2-222-2-22-2-222-2-22222222-2-2-2-22-2-2-2222-2-2-222-200-22000000000000000000002-22-200000000000000000000002-22-2000000
χ2622222-2-222-2-22-2-222-2-22222222-2-2-2-22-2-2-2222-2-2-222-200-2200000000000000000000-22-220000000000000000000000-22-22000000
χ2722222-2-22-1-2-22-2-22-1-2-222-1-1-12-1-2111-11-21-1-1-11112-11001-100003−333−3−33−333−3−300002-22-2000000000000003−33−30000-11-11000000
χ2822222-2-22-1-2-22-2-22-1-2-222-1-1-12-1-2111-11-21-1-1-11112-11001-100003−333−3−33−333−3−30000-22-2200000000000000−33−3300001-11-1000000
χ2922222-2-22-1-2-22-2-22-1-2-222-1-1-12-1-2111-11-21-1-1-11112-11001-10000−33−3−333−33−3−33300002-22-200000000000000−33−330000-11-11000000
χ3022222-2-22-1-2-22-2-22-1-2-222-1-1-12-1-2111-11-21-1-1-11112-11001-10000−33−3−333−33−3−3330000-22-22000000000000003−33−300001-11-1000000
χ312222-22-222-22-222222222222-2-2-22222-2-2-2-222222-2-2-200-2-2000000000000000000000000000000000000000000000000002-2-2200
χ322222-22-222-22-222222222222-2-2-22222-2-2-2-222222-2-2-200-2-200000000000000000000000000000000000000000000000000-222-200
χ332222-2-22222-2-2-2-222-2-222222-2-22-2-2-22222-222-2-2-2-2-22002-200000000000000002-22-200000000000000000000002-22-20000000000
χ342222-2-22222-2-2-2-222-2-222222-2-22-2-2-22222-222-2-2-2-2-22002-20000000000000000-22-220000000000000000000000-22-220000000000
χ352222-2-22-122-2-211-1211-1-122-11-2-1-211-12-12-2-1-1-21111-100-113−33−3003−33−3003−33−32-22-20000000033−3−333−3−3000000-11-110000000000
χ362222-2-22-122-2-211-1211-1-122-11-2-1-211-12-12-2-1-1-21111-100-113−33−3003−33−3003−33−3-22-2200000000−3−333−3−3330000001-11-10000000000
χ372222-2-22-122-2-211-1211-1-122-11-2-1-211-12-12-2-1-1-21111-100-11−33−3300−33−3300−33−332-22-200000000−3−333−3−333000000-11-110000000000
χ382222-2-22-122-2-211-1211-1-122-11-2-1-211-12-12-2-1-1-21111-100-11−33−3300−33−3300−33−33-22-220000000033−3−333−3−30000001-11-10000000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-2000000000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-200000000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i000000
χ4122-2-22222-1-2-2-2222-1-2-2-2-211-12-12-1-1-1-1-1-21111111-2-1-1001100003−333−3−3−33−3−33300002i−2i−2i2i00000000000000i3−i3−i3i30000−iii−i000000
χ4222-2-22222-1-2-2-2222-1-2-2-2-211-12-12-1-1-1-1-1-21111111-2-1-1001100003−333−3−3−33−3−3330000−2i2i2i−2i00000000000000−i3i3i3−i30000i−i−ii000000
χ4322-2-22222-1-2-2-2222-1-2-2-2-211-12-12-1-1-1-1-1-21111111-2-1-100110000−33−3−3333−333−3−300002i−2i−2i2i00000000000000−i3i3i3−i30000−iii−i000000
χ4422-2-22222-1-2-2-2222-1-2-2-2-211-12-12-1-1-1-1-1-21111111-2-1-100110000−33−3−3333−333−3−30000−2i2i2i−2i00000000000000i3−i3−i3i30000i−i−ii000000
χ4522-2-22-2-22-122-2-2-22-122-2-211-12-1-2111-112-1111-1-1-1-2-112-2-1122-2-2-1-1-1-1-1-111111100002i2i−2i−2i0000000000002i−2i−i−iii0000−i−iii000000
χ4622-2-22-2-22-122-2-2-22-122-2-211-12-1-2111-112-1111-1-1-1-2-112-2-1122-2-2-1-1-1-1-1-11111110000−2i−2i2i2i000000000000−2i2iii−i−i0000ii−i−i000000
χ4722-2-22-2-22-122-2-2-22-122-2-211-12-1-2111-112-1111-1-1-1-2-11-22-11-2-222111111-1-1-1-1-1-100002i2i−2i−2i000000000000−2i2iii−i−i0000−i−iii000000
χ4822-2-22-2-22-122-2-2-22-122-2-211-12-1-2111-112-1111-1-1-1-2-11-22-11-2-222111111-1-1-1-1-1-10000−2i−2i2i2i0000000000002i−2i−i−iii0000ii−i−i000000
χ4922-2-22-2-2-1222-211-12-1-111-2-2-1-121-211-1-2-12-2112-1-11-112-2-11-1-11122-1-1-1-1-2-211112i2i−2i−2i00002i2i−2i−2i−i−i−i−iiiii000000−i−iii0000000000
χ5022-2-22-2-2-1222-211-12-1-111-2-2-1-121-211-1-2-12-2112-1-11-112-2-11-1-11122-1-1-1-1-2-21111−2i−2i2i2i0000−2i−2i2i2iiiii−i−i−i−i000000ii−i−i0000000000
χ5122-2-22-2-2-1222-211-12-1-111-2-2-1-121-211-1-2-12-2112-1-11-11-22-1111-1-1-2-2111122-1-1-1-12i2i−2i−2i0000−2i−2i2i2iiiii−i−i−i−i000000−i−iii0000000000
χ5222-2-22-2-2-1222-211-12-1-111-2-2-1-121-211-1-2-12-2112-1-11-11-22-1111-1-1-2-2111122-1-1-1-1−2i−2i2i2i00002i2i−2i−2i−i−i−i−iiiii000000ii−i−i0000000000
χ5322-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22222-2222-2-2-2-2-22-2-2002200000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i0000000000
χ5422-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22222-2222-2-2-2-2-22-2-200220000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i0000000000
χ5522-2-2-22-2-122-22-1-1-121111-2-2-11-212-1-1-1-2-12211-211-11100-1-13−3−33003−33−300−33−332i−2i−2i2i00000000i3i3−i3−i3−i3−i3i3i3000000−iii−i0000000000
χ5622-2-2-22-2-122-22-1-1-121111-2-2-11-212-1-1-1-2-12211-211-11100-1-13−3−33003−33−300−33−33−2i2i2i−2i00000000−i3−i3i3i3i3i3−i3−i3000000i−i−ii0000000000
χ5722-2-2-22-2-122-22-1-1-121111-2-2-11-212-1-1-1-2-12211-211-11100-1-1−333−300−33−33003−33−32i−2i−2i2i00000000−i3−i3i3i3i3i3−i3−i3000000−iii−i0000000000
χ5822-2-2-22-2-122-22-1-1-121111-2-2-11-212-1-1-1-2-12211-211-11100-1-1−333−300−33−33003−33−3−2i2i2i−2i00000000i3i3−i3−i3−i3−i3i3i3000000i−i−ii0000000000
χ5922-2-2-2-2222-222-2-22222-2-2-2-22-2-22-2-2-222-2-22-2-22222-2200-220000000000000000000000000000000000000000000000000022-2-200
χ6022-2-2-2-2222-222-2-22222-2-2-2-22-2-22-2-2-222-2-22-2-22222-2200-2200000000000000000000000000000000000000000000000000-2-22200
χ614444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-211-211-2114411-2-2-2-2-2-21111-2-211110000000000000000000000000000000000000000
χ624444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-211-211-211-4-411222222-1-1-1-122-1-1-1-10000000000000000000000000000000000000000
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χ6444444-4-4-2-2-4-4422-2-222-2-2-2-21-2-222-1-11222-2112-1-1-21-100-11000023−23−3−33323−23−3−3330000000000000000000000000000000000000000
χ6544444-4-4-2-2-4-4422-2-222-2-2-2-21-2-222-1-11222-2112-1-1-21-100-110000−232333−3−3−232333−3−30000000000000000000000000000000000000000
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χ704444-4-444-24-4-4-4-44-2-4-444-2-2-2-424222-2-24-22-2-2222-42-200-2200000000000000000000000000000000000000000000000000000000
χ714444-4-44-2-24-4-422-2-222-2-2-2-2122-22-1-11-2-2-22112-1-12-11001-123−2323−2300−33−3300−33−330000000000000000000000000000000000000000
χ724444-4-44-2-24-4-422-2-222-2-2-2-2122-22-1-11-2-2-22112-1-12-11001-1−2323−2323003−33−3003−33−30000000000000000000000000000000000000000
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χ7544-4-4444-2-2-4-4-4-2-2-2-22222221-2-2-2-2111-2222-1-12-1-121100-1-10000−232333−3−323−23−3−3330000000000000000000000000000000000000000
χ7644-4-44-4-4-2-244-422-2-2-2-222221-2-222-1-112-2-22-1-1-21121-14-41-1-2-222-2-2111122-1-1-1-10000000000000000000000000000000000000000
χ7744-4-44-4-4-2-244-422-2-2-2-222221-2-222-1-112-2-22-1-1-21121-1-441-122-2-222-1-1-1-1-2-211110000000000000000000000000000000000000000
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χ8044-4-4-44-4-2-24-44-2-2-2-22222221222-21112-2-2-2-1-12-1-1-2-1-10011−232323−23003−33−300−33−330000000000000000000000000000000000000000
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χ884-44i−4i000-24000−2i32i32-423−23−2i2i4i−4i-20000−2i32i320000−2i2i023−230000000000000000000000000000000−2ζ7−2ζ232ζ7+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
χ894-44i−4i000-240002i3−2i32-4−2323−2i2i4i−4i-200002i3−2i320000−2i2i0−232300000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ2300000000000000000000
χ904-44i−4i000-240002i3−2i32-4−2323−2i2i4i−4i-200002i3−2i320000−2i2i0−23230000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ2300000000000000000000
χ914-4−4i4i0004400000-4-400−4i4i−4i4i4000000-40000−4i4i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ924-4−4i4i0004400000-4-400−4i4i−4i4i4000000-40000−4i4i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ934-4−4i4i000-24000−2i32i32-4−23232i−2i−4i4i-20000−2i32i3200002i−2i0−23230000000000000000000000000000000−2ζ5−2ζ132ζ5+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
χ944-4−4i4i000-24000−2i32i32-4−23232i−2i−4i4i-20000−2i32i3200002i−2i0−232300000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ2300000000000000000000
χ954-4−4i4i000-240002i3−2i32-423−232i−2i−4i4i-200002i3−2i3200002i−2i023−230000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ2300000000000000000000
χ964-4−4i4i000-240002i3−2i32-423−232i−2i−4i4i-200002i3−2i3200002i−2i023−2300000000000000000000000000000002ζ5+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
χ978-88i−8i0008-400000-84008i−8i−4i4i-400000040000−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-4000−4i34i34443−43−4i4i−4i4i200002i3−2i3-200002i−2i0−2323000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-40004i3−4i344−4343−4i4i−4i4i20000−2i32i3-200002i−2i023−23000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-400000-8400−8i8i4i−4i-4000000400004i−4i000000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-4000−4i34i344−43434i−4i4i−4i200002i3−2i3-20000−2i2i023−23000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-40004i3−4i34443−434i−4i4i−4i20000−2i32i3-20000−2i2i0−2323000000000000000000000000000000000000000000000000000000000000000

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