Finite Group Databasebeta

← Group #11786162

Character table — Group #11786162

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order12442223344466661212121212123666666661212121212121212124444446612121212121212121212121212121212121244888812121212121212128888242424242424242424242424888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ91111-11-111-1-1111-1-11111-1-111-1-1-11-1-1111-1-111-1-1-11111i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i-1-111-1-11111-1-1-1-1i−ii−iii−i−i11-1-1ii−i−i11-1-1i−i
χ101111-11-111-1-1111-1-11111-1-111-1-1-11-1-1111-1-111-1-1-11111i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i-1-1-1-1111111-1-1-1-1i−i−iiii−i−i-1-111−i−iii-1-111−ii
χ111111-11-111-1-1111-1-11111-1-111-1-1-11-1-1111-1-111-1-1-11111−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii-1-111-1-11111-1-1-1-1−ii−ii−i−iii11-1-1−i−iii11-1-1−ii
χ121111-11-111-1-1111-1-11111-1-111-1-1-11-1-1111-1-111-1-1-11111−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii-1-1-1-1111111-1-1-1-1−iii−i−i−iii-1-111ii−i−i-1-111i−i
χ131111-11-111-1-1111-1-11111-1-111-1-1-11-1-1111-1-111-1-1-1-1-1-1-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i1111-1-1-1-1-1-11111−iii−i−i−iii11-1-1ii−i−i-1-111−ii
χ141111-11-111-1-1111-1-11111-1-111-1-1-11-1-1111-1-111-1-1-1-1-1-1-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i11-1-111-1-1-1-11111−ii−ii−i−iii-1-111−i−iii11-1-1i−i
χ151111-11-111-1-1111-1-11111-1-111-1-1-11-1-1111-1-111-1-1-1-1-1-1-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii1111-1-1-1-1-1-11111i−i−iiii−i−i11-1-1−i−iii-1-111i−i
χ161111-11-111-1-1111-1-11111-1-111-1-1-11-1-1111-1-111-1-1-1-1-1-1-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii11-1-111-1-1-1-11111i−ii−iii−i−i-1-111ii−i−i11-1-1−ii
χ1722222222-12222-12222-1-122-1-12-1-1-1-1-122-12-1-1-1-1-1-1000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10022220000000000220000-1-1-1-1-1-1-1-1000000
χ1822222222-12222-12222-1-122-1-12-1-1-1-1-122-12-1-1-1-1-1-1000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000-2-2000011111111000000
χ1922222222-12222-12222-1-122-1-12-1-1-1-1-122-12-1-1-1-1-1-10000-2-2-1-1-2-2-2-2-1-11111111111110022220000000000-2-20000-1-1-1-11111000000
χ2022222222-12222-12222-1-122-1-12-1-1-1-1-122-12-1-1-1-1-1-10000-2-2-1-1-2-2-2-2-1-111111111111100-2-2-2-200000000002200001111-1-1-1-1000000
χ212222222-12222-12-1-1-1-122-1-1-12-122-1-1-1-1-12-12-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-12200-1-1-1-100000000000000
χ222222222-12222-12-1-1-1-122-1-1-12-122-1-1-1-1-12-12-1-1-1-122222-2-2-1-11111-1-1-2-21111-2-21111220000-1-1-1-1-1-1-1-1-2-200111100000000000000
χ232222222-12222-12-1-1-1-122-1-1-12-122-1-1-1-1-12-12-1-1-1-12-2-2-2-222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2000011111111-2-200111100000000000000
χ242222222-12222-12-1-1-1-122-1-1-12-122-1-1-1-1-12-12-1-1-1-12-2-2-2-2-2-2-1-11111-1-1-2-21111-2-21111-2-20000111111112200-1-1-1-100000000000000
χ2522222-2-2222-2-222222222222-2-2-22222-2-2-2-222222-2000000-2-20000-2-20000000000000000000000000000000000000000002i−2i2i−2i00
χ2622222-2-2222-2-222222222222-2-2-22222-2-2-2-222222-2000000-2-20000-2-2000000000000000000000000000000000000000000−2i2i−2i2i00
χ272222-22-22-1-2-222-1-2-222-1-1-2-2-1-1-211-11122-1-21-1-111100002i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii0022-2-200000000002i−2i0000-1-111−i−iii000000
χ282222-22-22-1-2-222-1-2-222-1-1-2-2-1-1-211-11122-1-21-1-111100002i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii00-2-2220000000000−2i2i000011-1-1ii−i−i000000
χ292222-22-22-1-2-222-1-2-222-1-1-2-2-1-1-211-11122-1-21-1-11110000−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i0022-2-20000000000−2i2i0000-1-111ii−i−i000000
χ302222-22-22-1-2-222-1-2-222-1-1-2-2-1-1-211-11122-1-21-1-11110000−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i00-2-22200000000002i−2i000011-1-1−i−iii000000
χ312222-22-2-12-2-22-1211-1-12211-121-2-2-111-1-121-2-1-111-222222i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii-2-20000-1-1-1-111112i−2i00−i−iii00000000000000
χ322222-22-2-12-2-22-1211-1-12211-121-2-2-111-1-121-2-1-111-22222−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i-2-20000-1-1-1-11111−2i2i00ii−i−i00000000000000
χ332222-22-2-12-2-22-1211-1-12211-121-2-2-111-1-121-2-1-111-2-2-2-2-22i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii2200001111-1-1-1-1−2i2i00ii−i−i00000000000000
χ342222-22-2-12-2-22-1211-1-12211-121-2-2-111-1-121-2-1-111-2-2-2-2-2−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i2200001111-1-1-1-12i−2i00−i−iii00000000000000
χ352222-2-2222-22-222-2-22222-2-22-222-22-2-2-2-2-22-222-2-22000000-220000-220000000000000000000000000000000000000000002i−2i−2i2i00
χ362222-2-2222-22-222-2-22222-2-22-222-22-2-2-2-2-22-222-2-22000000-220000-22000000000000000000000000000000000000000000−2i2i2i−2i00
χ3722-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2000000220000-2-2000000000000002i−2i2i−2i00000000000000002i−2i2i−2i0000000000
χ3822-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2000000220000-2-200000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i0000000000
χ3922-2-22222-1-2-2-22-122-2-211-2-2-1-12-1-1-1-1-12-21-2111111000000-1-1000011−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3002i−2i2i−2i0000000000000000−ii−ii3−33−3000000
χ4022-2-22222-1-2-2-22-122-2-211-2-2-1-12-1-1-1-1-12-21-2111111000000-1-1000011−i3i3−i3−i3i3i3−i3i3−i3−i3i3i300−2i2i−2i2i0000000000000000i−ii−i−33−33000000
χ4122-2-22222-1-2-2-22-122-2-211-2-2-1-12-1-1-1-1-12-21-2111111000000-1-1000011i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3002i−2i2i−2i0000000000000000−ii−ii−33−33000000
χ4222-2-22222-1-2-2-22-122-2-211-2-2-1-12-1-1-1-1-12-21-2111111000000-1-1000011i3−i3i3i3−i3−i3i3−i3i3i3−i3−i300−2i2i−2i2i0000000000000000i−ii−i3−33−3000000
χ4322-2-22-2-222-2222222-2-2-2-2-2-22-2-2-22222-2222-2-2-2-2-222i2i−2i−2i00-2-20000220000000000002i−2i00002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ4422-2-22-2-222-2222222-2-2-2-2-2-22-2-2-22222-2222-2-2-2-2-22−2i−2i2i2i00-2-2000022000000000000−2i2i0000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ4522-2-22-2-2-12-222-12-1-111-2-211-1-21-22-1-1-11-12-1-2111122i2i−2i−2i0011−i3i3−i3i3-1-100−i3i3−i3i300−i3i3−i3i32i−2i0000−i−iii−i−iii00003−33−300000000000000
χ4622-2-22-2-2-12-222-12-1-111-2-211-1-21-22-1-1-11-12-1-2111122i2i−2i−2i0011i3−i3i3−i3-1-100i3−i3i3−i300i3−i3i3−i32i−2i0000−i−iii−i−iii0000−33−3300000000000000
χ4722-2-22-2-2-12-222-12-1-111-2-211-1-21-22-1-1-11-12-1-211112−2i−2i2i2i0011−i3i3−i3i3-1-100−i3i3−i3i300−i3i3−i3i3−2i2i0000ii−i−iii−i−i0000−33−3300000000000000
χ4822-2-22-2-2-12-222-12-1-111-2-211-1-21-22-1-1-11-12-1-211112−2i−2i2i2i0011i3−i3i3−i3-1-100i3−i3i3−i300i3−i3i3−i3−2i2i0000ii−i−iii−i−i00003−33−300000000000000
χ4922-2-2-22-22222-222-2-2-2-2-2-22222-2-2-22-2-22-2-222-2-22220000002-20000-22000000000000002i−2i−2i2i00000000000000002i−2i−2i2i0000000000
χ5022-2-2-22-22222-222-2-2-2-2-2-22222-2-2-22-2-22-2-222-2-22220000002-20000-2200000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000
χ5122-2-2-22-22-122-22-1-2-2-2-21122-1-1-211-1112-212-111-1-1-1000000-1100001-13−333−3−3−33−3−333002i−2i−2i2i0000000000000000−iii−ii3−i3−i3i3000000
χ5222-2-2-22-22-122-22-1-2-2-2-21122-1-1-211-1112-212-111-1-1-1000000-1100001-13−333−3−3−33−3−33300−2i2i2i−2i0000000000000000i−i−ii−i3i3i3−i3000000
χ5322-2-2-22-22-122-22-1-2-2-2-21122-1-1-211-1112-212-111-1-1-1000000-1100001-1−33−3−3333−333−3−3002i−2i−2i2i0000000000000000−iii−i−i3i3i3−i3000000
χ5422-2-2-22-22-122-22-1-2-2-2-21122-1-1-211-1112-212-111-1-1-1000000-1100001-1−33−3−3333−333−3−300−2i2i2i−2i0000000000000000i−i−iii3−i3−i3i3000000
χ5522-2-2-2-22222-2222-2-2-2-2-2-2222-222-22-2-2-222-22-2-222-22i2i−2i−2i00-2200002-2000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ5622-2-2-2-22222-2222-2-2-2-2-2-2222-222-22-2-2-222-22-2-222-2−2i−2i2i2i00-2200002-20000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ5722-2-2-2-22-122-22-121111-2-2-1-1-1-2-12-2-1111-121211-1-1-22i2i−2i−2i001-13−3−33-11003−33−300−33−33−2i2i0000−i−iiiii−i−i0000i3−i3−i3i300000000000000
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χ6022-2-2-2-22-122-22-121111-2-2-1-1-1-2-12-2-1111-121211-1-1-2−2i−2i2i2i001-1−333−3-1100−33−33003−33−32i−2i0000ii−i−i−i−iii0000i3−i3−i3i300000000000000
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χ864-44i−4i00044000-4-4004i−4i4i−4i0040000-400000004i−4i000−2−2i2+2i−2+2i2−2i0000000000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ874-44i−4i000-240002-4−2i32i3−2i2i4i−4i23−23-200002−2i32i300000−2i2i23−2302+2i−2−2i2−2i−2+2i0000000000000000000000000000−1−i1+i−1+i1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000
χ884-44i−4i000-240002-4−2i32i3−2i2i4i−4i23−23-200002−2i32i300000−2i2i23−230−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−i1−i−1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000
χ894-44i−4i000-240002-42i3−2i3−2i2i4i−4i−2323-2000022i3−2i300000−2i2i−232302+2i−2−2i2−2i−2+2i0000000000000000000000000000−1−i1+i−1+i1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000
χ904-44i−4i000-240002-42i3−2i3−2i2i4i−4i−2323-2000022i3−2i300000−2i2i−23230−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−i1−i−1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000
χ914-4−4i4i00044000-4-400−4i4i−4i4i0040000-40000000−4i4i0002−2i−2+2i2+2i−2−2i00000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ924-4−4i4i00044000-4-400−4i4i−4i4i0040000-40000000−4i4i000−2+2i2−2i−2−2i2+2i0000000000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ934-4−4i4i000-240002-4−2i32i32i−2i−4i4i−2323-200002−2i32i3000002i−2i−232302−2i−2+2i2+2i−2−2i0000000000000000000000000000−1+i1−i−1−i1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000
χ944-4−4i4i000-240002-4−2i32i32i−2i−4i4i−2323-200002−2i32i3000002i−2i−23230−2+2i2−2i−2−2i2+2i00000000000000000000000000001−i−1+i1+i−1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000
χ954-4−4i4i000-240002-42i3−2i32i−2i−4i4i23−23-2000022i3−2i3000002i−2i23−2302−2i−2+2i2+2i−2−2i0000000000000000000000000000−1+i1−i−1−i1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000
χ964-4−4i4i000-240002-42i3−2i32i−2i−4i4i23−23-2000022i3−2i3000002i−2i23−230−2+2i2−2i−2−2i2+2i00000000000000000000000000001−i−1+i1+i−1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000
χ978-88i−8i0008-4000-84008i−8i−4i4i00-4000040000000−4i4i00000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-400044−4i34i3−4i4i−4i4i43−4320000-22i3−2i3000002i−2i−2323000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-4000444i3−4i3−4i4i−4i4i−434320000-2−2i32i3000002i−2i23−23000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-4000-8400−8i8i4i−4i00-40000400000004i−4i00000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-400044−4i34i34i−4i4i−4i−434320000-22i3−2i300000−2i2i23−23000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-4000444i3−4i34i−4i4i−4i43−4320000-2−2i32i300000−2i2i−2323000000000000000000000000000000000000000000000000000000000000000

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