Finite Group Databasebeta

← Group #11789727

Character table — Group #11789727

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order12442223344466661212121212123666666661212121212121212124444446612121212121212121212121212121212121244888812121212121212128888242424242424242424242424888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ911-1-11-1-111-11111-1-1-1-111-1-1111-1-11-1-1-111-1-111-1-11ii−i−ii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−ii−i11-1-1iiii−i−i−i−ii−i1-111-1-1ii−i−i11-1-1ii−i−i1-1
χ1011-1-11-1-111-11111-1-1-1-111-1-1111-1-11-1-1-111-1-111-1-11ii−i−ii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−ii−i-1-111iiii−i−i−i−i−ii1-111-1-1−i−iii-1-111−i−iii-11
χ1111-1-11-1-111-11111-1-1-1-111-1-1111-1-11-1-1-111-1-111-1-11ii−i−i−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiiii−i11-1-1iiii−i−i−i−i−ii-11-1-111−i−iii11-1-1ii−i−i-11
χ1211-1-11-1-111-11111-1-1-1-111-1-1111-1-11-1-1-111-1-111-1-11ii−i−i−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiiii−i-1-111iiii−i−i−i−ii−i-11-1-111ii−i−i-1-111−i−iii1-1
χ1311-1-11-1-111-11111-1-1-1-111-1-1111-1-11-1-1-111-1-111-1-11−i−iiii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i−ii11-1-1−i−i−i−iiiiii−i-11-1-111ii−i−i11-1-1−i−iii-11
χ1411-1-11-1-111-11111-1-1-1-111-1-1111-1-11-1-1-111-1-111-1-11−i−iiii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i−ii-1-111−i−i−i−iiiii−ii-11-1-111−i−iii-1-111ii−i−i1-1
χ1511-1-11-1-111-11111-1-1-1-111-1-1111-1-11-1-1-111-1-111-1-11−i−iii−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii−ii11-1-1−i−i−i−iiiii−ii1-111-1-1−i−iii11-1-1−i−iii1-1
χ1611-1-11-1-111-11111-1-1-1-111-1-1111-1-11-1-1-111-1-111-1-11−i−iii−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii−ii-1-111−i−i−i−iiiiii−i1-111-1-1ii−i−i-1-111ii−i−i-11
χ1722222222-12222-1222222-1-1-12-1-1-1-1-1-122-12-1-1-1-1-1-1000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10022220000000022000000-1-1-1-1-1-1-1-1000000
χ1822222222-12222-1222222-1-1-12-1-1-1-1-1-122-12-1-1-1-1-1-1000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-200000000-2-200000011111111000000
χ1922222222-12222-1222222-1-1-12-1-1-1-1-1-122-12-1-1-1-1-1-10000-2-2-1-1-2-2-2-2-1-111111111111100222200000000-2-20000001111-1-1-1-1000000
χ2022222222-12222-1222222-1-1-12-1-1-1-1-1-122-12-1-1-1-1-1-10000-2-2-1-1-2-2-2-2-1-111111111111100-2-2-2-20000000022000000-1-1-1-11111000000
χ212222222-12222-12-1-1-1-1-1-122-1-1222-1-1-1-1-12-12-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-10022-1-1-1-100000000000000
χ222222222-12222-12-1-1-1-1-1-122-1-1222-1-1-1-1-12-12-1-1-1-122222-2-2-1-11111-1-1-2-21111-2-21111220000-1-1-1-1-1-1-1-100-2-2111100000000000000
χ232222222-12222-12-1-1-1-1-1-122-1-1222-1-1-1-1-12-12-1-1-1-12-2-2-2-222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200001111111100-2-2111100000000000000
χ242222222-12222-12-1-1-1-1-1-122-1-1222-1-1-1-1-12-12-1-1-1-12-2-2-2-2-2-2-1-11111-1-1-2-21111-2-21111-2-20000111111110022-1-1-1-100000000000000
χ2522222-2-2222-2-222-2-222-2-222222-2-22-2-2-2-2-222-2-222-20000002-20000-22000000000000002i−2i2i−2i000000000000000000002i−2i2i−2i000000
χ2622222-2-2222-2-222-2-222-2-222222-2-22-2-2-2-2-222-2-222-20000002-20000-2200000000000000−2i2i−2i2i00000000000000000000−2i2i−2i2i000000
χ2722222-2-22-12-2-22-1-2-222-2-2-1-1-12-111-111-2-212-111-1-11000000-1100001-13−333−3−33−333−3−3002i−2i2i−2i0000000000000000−i3i3−i3i3−ii−ii000000
χ2822222-2-22-12-2-22-1-2-222-2-2-1-1-12-111-111-2-212-111-1-11000000-1100001-13−333−3−33−333−3−300−2i2i−2i2i0000000000000000i3−i3i3−i3i−ii−i000000
χ2922222-2-22-12-2-22-1-2-222-2-2-1-1-12-111-111-2-212-111-1-11000000-1100001-1−33−3−333−33−3−333002i−2i2i−2i0000000000000000i3−i3i3−i3−ii−ii000000
χ3022222-2-22-12-2-22-1-2-222-2-2-1-1-12-111-111-2-212-111-1-11000000-1100001-1−33−3−333−33−3−33300−2i2i−2i2i0000000000000000−i3i3−i3i3i−ii−i000000
χ312222-22-222-22-222222222222-2-2-22222-2-22-2-22222-2000000-2-20000-2-20000000000000000000000000000000000000000002-22-200
χ322222-22-222-22-222222222222-2-2-22222-2-22-2-22222-2000000-2-20000-2-2000000000000000000000000000000000000000000-22-2200
χ332222-2-2222-2-2222-2-222-2-2222-2-22-22-2-222-2-2-2-2-2222222200-2200002-2000000000000-2-2000022-2-222-2-20000000000000000000000
χ342222-2-2222-2-2222-2-222-2-2222-2-22-22-2-222-2-2-2-2-2222-2-2-2-200-2200002-2000000000000220000-2-222-2-2220000000000000000000000
χ352222-2-22-12-2-22-1211-1-11122-11-22-2-111-1-1-21-211-1-122222001-13−33−3-11003−33−3003−33−3-2-20000-1-111-1-11100003−33−300000000000000
χ362222-2-22-12-2-22-1211-1-11122-11-22-2-111-1-1-21-211-1-122222001-1−33−33-1100−33−3300−33−33-2-20000-1-111-1-1110000−33−3300000000000000
χ372222-2-22-12-2-22-1211-1-11122-11-22-2-111-1-1-21-211-1-12-2-2-2-2001-13−33−3-11003−33−3003−33−322000011-1-111-1-10000−33−3300000000000000
χ382222-2-22-12-2-22-1211-1-11122-11-22-2-111-1-1-21-211-1-12-2-2-2-2001-1−33−33-1100−33−3300−33−3322000011-1-111-1-100003−33−300000000000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2000000220000-2-2000000000000002i−2i−2i2i000000000000000000002i−2i−2i2i000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2000000220000-2-200000000000000−2i2i2i−2i00000000000000000000−2i2i2i−2i000000
χ4122-2-22222-1-2-2-22-122-2-2-2-211-12-1-1-1-1-1-12-21-2111111000000-1-1000011−i3i3−i3−i3i3i3i3−i3i3i3−i3−i3002i−2i−2i2i0000000000000000−333−3−iii−i000000
χ4222-2-22222-1-2-2-22-122-2-2-2-211-12-1-1-1-1-1-12-21-2111111000000-1-1000011−i3i3−i3−i3i3i3i3−i3i3i3−i3−i300−2i2i2i−2i00000000000000003−3−33i−i−ii000000
χ4322-2-22222-1-2-2-22-122-2-2-2-211-12-1-1-1-1-1-12-21-2111111000000-1-1000011i3−i3i3i3−i3−i3−i3i3−i3−i3i3i3002i−2i−2i2i00000000000000003−3−33−iii−i000000
χ4422-2-22222-1-2-2-22-122-2-2-2-211-12-1-1-1-1-1-12-21-2111111000000-1-1000011i3−i3i3i3−i3−i3−i3i3−i3−i3i3i300−2i2i2i−2i0000000000000000−333−3i−i−ii000000
χ4522-2-22-2-22-1-2222-1-2-2-2-22211-12-111-111-22-1-21-1-111-100002i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii0022-2-2000000002i−2i000000−i−iii-1-111000000
χ4622-2-22-2-22-1-2222-1-2-2-2-22211-12-111-111-22-1-21-1-111-100002i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii00-2-22200000000−2i2i000000ii−i−i11-1-1000000
χ4722-2-22-2-22-1-2222-1-2-2-2-22211-12-111-111-22-1-21-1-111-10000−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i0022-2-200000000−2i2i000000ii−i−i-1-111000000
χ4822-2-22-2-22-1-2222-1-2-2-2-22211-12-111-111-22-1-21-1-111-10000−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i00-2-222000000002i−2i000000−i−iii11-1-1000000
χ4922-2-22-2-2-12-222-121111-1-1-2-2-1-12-2-2-1111-121-2-1-11122i2i−2i−2i2i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii2i−2i0000−i−i−i−iiiii002-2-1-11100000000000000
χ5022-2-22-2-2-12-222-121111-1-1-2-2-1-12-2-2-1111-121-2-1-11122i2i−2i−2i−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i2i−2i0000−i−i−i−iiiii00-2211-1-100000000000000
χ5122-2-22-2-2-12-222-121111-1-1-2-2-1-12-2-2-1111-121-2-1-1112−2i−2i2i2i2i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii−2i2i0000iiii−i−i−i−i00-2211-1-100000000000000
χ5222-2-22-2-2-12-222-121111-1-1-2-2-1-12-2-2-1111-121-2-1-1112−2i−2i2i2i−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i−2i2i0000iiii−i−i−i−i002-2-1-11100000000000000
χ5322-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22222-22-222-2-2-2-222i2i−2i−2i00-2-2000022000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ5422-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22222-22-222-2-2-2-22−2i−2i2i2i00-2-20000220000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ5522-2-2-22-2-122-22-12-1-11111-2-2-11-2-22-1-1-11-1-2-12111122i2i−2i−2i0011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i3−2i2i0000−i−iiiii−i−i0000−333−300000000000000
χ5622-2-2-22-2-122-22-12-1-11111-2-2-11-2-22-1-1-11-1-2-12111122i2i−2i−2i0011i3−i3−i3i3-1-100i3−i3i3−i300−i3i3−i3i3−2i2i0000−i−iiiii−i−i00003−3−3300000000000000
χ5722-2-2-22-2-122-22-12-1-11111-2-2-11-2-22-1-1-11-1-2-1211112−2i−2i2i2i0011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i32i−2i0000ii−i−i−i−iii00003−3−3300000000000000
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χ874-44i−4i000-240002-4−2i32i3−2i2i23−234i−4i-200002−2i32i30000023−23−2i2i02+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
χ884-44i−4i000-240002-4−2i32i3−2i2i23−234i−4i-200002−2i32i30000023−23−2i2i0−2−2i2+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−4i000-240002-42i3−2i3−2i2i−23234i−4i-2000022i3−2i300000−2323−2i2i02+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−4i000-240002-42i3−2i3−2i2i−23234i−4i-2000022i3−2i300000−2323−2i2i0−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ111−i−1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000
χ914-4−4i4i00044000-4-400−4i4i00−4i4i40000-4000000000−4i4i02−2i−2+2i2+2i−2−2i00000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ924-4−4i4i00044000-4-400−4i4i00−4i4i40000-4000000000−4i4i0−2+2i2−2i−2−2i2+2i0000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ934-4−4i4i000-240002-4−2i32i32i−2i−2323−4i4i-200002−2i32i300000−23232i−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
χ944-4−4i4i000-240002-4−2i32i32i−2i−2323−4i4i-200002−2i32i300000−23232i−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
χ954-4−4i4i000-240002-42i3−2i32i−2i23−23−4i4i-2000022i3−2i30000023−232i−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
χ964-4−4i4i000-240002-42i3−2i32i−2i23−23−4i4i-2000022i3−2i30000023−232i−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−8i0008-4000-84008i−8i00−4i4i-400004000000000−4i4i000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-400044−4i34i3−4i4i43−43−4i4i20000-22i3−2i300000−23232i−2i000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-4000444i3−4i3−4i4i−4343−4i4i20000-2−2i32i30000023−232i−2i000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-4000-8400−8i8i004i−4i-4000040000000004i−4i000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-400044−4i34i34i−4i−43434i−4i20000-22i3−2i30000023−23−2i2i000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-4000444i3−4i34i−4i43−434i−4i20000-2−2i32i300000−2323−2i2i000000000000000000000000000000000000000000000000000000000000000

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