Finite Group Databasebeta

← Group #11789714

Character table — Group #11789714

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order124422233444666612121212121236666666612121212121212121244446688121224242424242424242424242424242424448888121212121212121224668812122424242424242424888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-11-111-1-1-1-11ii−i−i-1-1i−i11ii−i−iii−i−iiiii−i−i−i−ii−iii−i−iiiii−i−i−i−i1-1111-1-1-1ii−i−i11-1-111-1-1i−i
χ1011-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-11-111-1-1-1-11ii−i−i-1-1i−i11ii−i−iii−i−iiiii−i−i−i−ii−i−i−iiiiiii−i−i−i−i1-111-11-1-1−i−iii-1-111-1-111−ii
χ1111-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-11-111-1-1-1-11ii−i−i-1-1−ii11−i−iii−i−iii−i−i−i−iiiiii−iii−i−iiiii−i−i−i−i-11-1-1-1111ii−i−i-1-11111-1-1−ii
χ1211-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-11-111-1-1-1-11ii−i−i-1-1−ii11−i−iii−i−iii−i−i−i−iiiiii−i−i−iiiiiii−i−i−i−i-11-1-11-111−i−iii11-1-1-1-111i−i
χ1311-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-11-111-1-1-1-11−i−iii-1-1i−i11ii−i−iii−i−iiiii−i−i−i−i−iiii−i−i−i−i−i−iiiii-11-1-11-111ii−i−i11-1-1-1-111−ii
χ1411-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-11-111-1-1-1-11−i−iii-1-1i−i11ii−i−iii−i−iiiii−i−i−i−i−ii−i−iii−i−i−i−iiiii-11-1-1-1111−i−iii-1-11111-1-1i−i
χ1511-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-11-111-1-1-1-11−i−iii-1-1−ii11−i−iii−i−iii−i−i−i−iiiii−iiii−i−i−i−i−i−iiiii1-111-11-1-1ii−i−i-1-111-1-111i−i
χ1611-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-11-111-1-1-1-11−i−iii-1-1−ii11−i−iii−i−iii−i−i−i−iiiii−ii−i−iii−i−i−i−iiiii1-1111-1-1-1−i−iii11-1-111-1-1−ii
χ1722222222-1222-1-12-1-1-1-1-122-1222-1-1-1-1-122-1-1-1-1-1-122222-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1220000-1-1-1-1-1-1-1-122-1-100-1-100000000000000
χ1822222222-1222-1-12-1-1-1-1-122-1222-1-1-1-1-122-1-1-1-1-1-122222-1-1-2-2-1-11111-2-2-2-211111111220000-1-1-1-1-1-1-1-1-2-211001100000000000000
χ1922222222-1222-1-12-1-1-1-1-122-1222-1-1-1-1-122-1-1-1-1-1-12-2-2-2-2-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2000011111111-2-211001100000000000000
χ2022222222-1222-1-12-1-1-1-1-122-1222-1-1-1-1-122-1-1-1-1-1-12-2-2-2-2-1-1-2-2-1-11111-2-2-2-211111111-2-200001111111122-1-100-1-100000000000000
χ212222222-1222222-122222-1-1-1-1-1-12-1-1-12-1-122-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022220000000000002200-1-1-1-1-1-1-1-1000000
χ222222222-1222222-122222-1-1-1-1-1-12-1-1-12-1-122-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2000000000000-2-20011111111000000
χ232222222-1222222-122222-1-1-1-1-1-12-1-1-12-1-122-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-2111111111111002222000000000000-2-200-1-1-1-11111000000
χ242222222-1222222-122222-1-1-1-1-1-12-1-1-12-1-122-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-211111111111100-2-2-2-200000000000022001111-1-1-1-1000000
χ2522222-2-2222-2-2222222222222-2-2-2222-2-22-2-22222-20000-2-200-2-200000000000000000000000000000000000000000000002i−2i2i−2i00
χ2622222-2-2222-2-2222222222222-2-2-2222-2-22-2-22222-20000-2-200-2-20000000000000000000000000000000000000000000000−2i2i−2i2i00
χ272222-22-222-2-22-2-222-2-222222-22-2-2-2-2222-22-2-2-222-222222-2002-20000000000000000-2-2000022-2-222-2-20000000000000000000000
χ282222-22-222-2-22-2-222-2-222222-22-2-2-2-2222-22-2-2-222-2-2-2-2-22-2002-20000000000000000220000-2-222-2-2220000000000000000000000
χ292222-22-22-1-2-22112-111-1-122-1-22-2111-1-12-2-1111-1-1-22222-1100-11−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3-2-20000-1-111-1-11100−i3i300−i3i300000000000000
χ302222-22-22-1-2-22112-111-1-122-1-22-2111-1-12-2-1111-1-1-22222-1100-11i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3-2-20000-1-111-1-11100i3−i300i3−i300000000000000
χ312222-22-22-1-2-22112-111-1-122-1-22-2111-1-12-2-1111-1-1-2-2-2-2-2-1100-11−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i322000011-1-111-1-100i3−i300i3−i300000000000000
χ322222-22-22-1-2-22112-111-1-122-1-22-2111-1-12-2-1111-1-1-2-2-2-2-2-1100-11i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i322000011-1-111-1-100−i3i300−i3i300000000000000
χ332222-2-2222-22-2-2-222-2-222222-2-222-2-22-2-2-2-22-2-22220000-2200-220000000000000000002-22-200000000000000002-22-20000000000
χ342222-2-2222-22-2-2-222-2-222222-2-222-2-22-2-2-2-22-2-22220000-2200-22000000000000000000-22-220000000000000000-22-220000000000
χ352222-2-22-12-22-2-2-2-12-2-222-1-1-111-1211-1-211-2211-1-1-100001-1001-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3002-22-20000000000000000-11-11−i3i3−i3i3000000
χ362222-2-22-12-22-2-2-2-12-2-222-1-1-111-1211-1-211-2211-1-1-100001-1001-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300-22-2200000000000000001-11-1i3−i3i3−i3000000
χ372222-2-22-12-22-2-2-2-12-2-222-1-1-111-1211-1-211-2211-1-1-100001-1001-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3002-22-20000000000000000-11-11i3−i3i3−i3000000
χ382222-2-22-12-22-2-2-2-12-2-222-1-1-111-1211-1-211-2211-1-1-100001-1001-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300-22-2200000000000000001-11-1−i3i3−i3i3000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200002200-2-200000000000000000000000000000000000000000000002i−2i−2i2i00
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200002200-2-20000000000000000000000000000000000000000000000−2i2i2i−2i00
χ4122-2-22-2-22-1-222-1-12-11111-2-2-12-2-21-1-1-112-2-1-1111122i2i−2i−2i112i−2i-1-1−i−iii2i2i−2i−2i−i−i−i−iiiii2i−2i0000−i−i−i−iiiii2-2-1-1001100000000000000
χ4222-2-22-2-22-1-222-1-12-11111-2-2-12-2-21-1-1-112-2-1-1111122i2i−2i−2i11−2i2i-1-1ii−i−i−2i−2i2i2iiiii−i−i−i−i2i−2i0000−i−i−i−iiiii-221100-1-100000000000000
χ4322-2-22-2-22-1-222-1-12-11111-2-2-12-2-21-1-1-112-2-1-111112−2i−2i2i2i112i−2i-1-1−i−iii2i2i−2i−2i−i−i−i−iiiii−2i2i0000iiii−i−i−i−i-221100-1-100000000000000
χ4422-2-22-2-22-1-222-1-12-11111-2-2-12-2-21-1-1-112-2-1-111112−2i−2i2i2i11−2i2i-1-1ii−i−i−2i−2i2i2iiiii−i−i−i−i−2i2i0000iiii−i−i−i−i2-2-1-1001100000000000000
χ4522-2-22-2-2-12-22222-12-2-2-2-211-1-111-2-1-1-1-2-11221111-10000112i−2i-1-12i2i−2i−2i−i−iii−i−i−i−iiiii002i2i−2i−2i0000000000002-200−i−iii-1-111000000
χ4622-2-22-2-2-12-22222-12-2-2-2-211-1-111-2-1-1-1-2-11221111-10000112i−2i-1-12i2i−2i−2i−i−iii−i−i−i−iiiii00−2i−2i2i2i000000000000-2200ii−i−i11-1-1000000
χ4722-2-22-2-2-12-22222-12-2-2-2-211-1-111-2-1-1-1-2-11221111-1000011−2i2i-1-1−2i−2i2i2iii−i−iiiii−i−i−i−i002i2i−2i−2i000000000000-2200−i−iii11-1-1000000
χ4822-2-22-2-2-12-22222-12-2-2-2-211-1-111-2-1-1-1-2-11221111-1000011−2i2i-1-1−2i−2i2i2iii−i−iiiii−i−i−i−i00−2i−2i2i2i0000000000002-200ii−i−i-1-111000000
χ4922-2-2-22-22222-2-2-22222-2-2-2-22-22-2-2-2-222-22-2222-2-2200002-200-220000000000000000002i−2i−2i2i00000000000000002i−2i−2i2i0000000000
χ5022-2-2-22-22222-2-2-22222-2-2-2-22-22-2-2-2-222-22-2222-2-2200002-200-22000000000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000
χ5122-2-2-22-2-1222-2-2-2-1222-2-211-11-11-211-121-1-22-1-111-10000-11001-100003−3−333−33−3−33−33002i−2i−2i2i0000000000000000−iii−i−i3i3i3−i3000000
χ5222-2-2-22-2-1222-2-2-2-1222-2-211-11-11-211-121-1-22-1-111-10000-11001-100003−3−333−33−3−33−3300−2i2i2i−2i0000000000000000i−i−iii3−i3−i3i3000000
χ5322-2-2-22-2-1222-2-2-2-1222-2-211-11-11-211-121-1-22-1-111-10000-11001-10000−333−3−33−333−33−3002i−2i−2i2i0000000000000000−iii−ii3−i3−i3i3000000
χ5422-2-2-22-2-1222-2-2-2-1222-2-211-11-11-211-121-1-22-1-111-10000-11001-10000−333−3−33−333−33−300−2i2i2i−2i0000000000000000i−i−ii−i3i3i3−i3000000
χ5522-2-2-2-22222-22-2-22222-2-2-2-22-2-222-2-22-2222-222-2-2-22i2i−2i−2i-22002-20000000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ5622-2-2-2-22222-22-2-22222-2-2-2-22-2-222-2-22-2222-222-2-2-2−2i−2i2i2i-22002-200000000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ5722-2-2-2-222-12-22112-1-1-111-2-2-1-2-22-111-1122-11-1-111-22i2i−2i−2i1-100-113−3−33000033−3−3−3−333−2i2i0000−i−iiiii−i−i00−i3i300i3−i300000000000000
χ5822-2-2-2-222-12-22112-1-1-111-2-2-1-2-22-111-1122-11-1-111-22i2i−2i−2i1-100-11−333−30000−3−33333−3−3−2i2i0000−i−iiiii−i−i00i3−i300−i3i300000000000000
χ5922-2-2-2-222-12-22112-1-1-111-2-2-1-2-22-111-1122-11-1-111-2−2i−2i2i2i1-100-113−3−33000033−3−3−3−3332i−2i0000ii−i−i−i−iii00i3−i300−i3i300000000000000
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χ614444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-2-21111-20000114411-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000
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χ7844-4-44-4-4-2-2-444-2-2-2-22222221-22221112-22-2-2-1-1-1-1-20000-1-1−4i4i112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000
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χ884-44i−4i0004-2000−2i32i3-4223−23−2i2i4i−4i-20000−2i32i320000023−23−2i2i0−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ111−i−1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000
χ894-44i−4i0004-20002i3−2i3-42−2323−2i2i4i−4i-200002i3−2i3200000−2323−2i2i02+2i−2−2i2−2i−2+2i0000000000000000000000000000−1−i1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−1+i1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000
χ904-44i−4i0004-20002i3−2i3-42−2323−2i2i4i−4i-200002i3−2i3200000−2323−2i2i0−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ111−i−1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000
χ914-4−4i4i0004400000-4-400−4i4i−4i4i4000000-40000000−4i4i02−2i−2+2i2+2i−2−2i00000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ924-4−4i4i0004400000-4-400−4i4i−4i4i4000000-40000000−4i4i0−2+2i2−2i−2−2i2+2i0000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ934-4−4i4i0004-2000−2i32i3-42−23232i−2i−4i4i-20000−2i32i3200000−23232i−2i02−2i−2+2i2+2i−2−2i0000000000000000000000000000−1+i1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−1−i1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000
χ944-4−4i4i0004-2000−2i32i3-42−23232i−2i−4i4i-20000−2i32i3200000−23232i−2i0−2+2i2−2i−2−2i2+2i00000000000000000000000000001−i−1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ111+i−1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000
χ954-4−4i4i0004-20002i3−2i3-4223−232i−2i−4i4i-200002i3−2i320000023−232i−2i02−2i−2+2i2+2i−2−2i0000000000000000000000000000−1+i1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−1−i1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000
χ964-4−4i4i0004-20002i3−2i3-4223−232i−2i−4i4i-200002i3−2i320000023−232i−2i0−2+2i2−2i−2−2i2+2i00000000000000000000000000001−i−1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ111+i−1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000
χ978-88i−8i000-48000004-8008i−8i−4i4i-400000040000000−4i4i000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-4000−4i34i34443−43−4i4i−4i4i200002i3−2i3-200000−23232i−2i000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-40004i3−4i344−4343−4i4i−4i4i20000−2i32i3-20000023−232i−2i000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i000-48000004-800−8i8i4i−4i-4000000400000004i−4i000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-4000−4i34i344−43434i−4i4i−4i200002i3−2i3-20000023−23−2i2i000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-40004i3−4i34443−434i−4i4i−4i20000−2i32i3-200000−2323−2i2i000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.