Finite Group Databasebeta

← Group #11786170

Character table — Group #11786170

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order12442223344466661212121212123666666661212121212121212124444668812122424242424242424242424242424242444888812121212121212124444121212121212121224242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ41111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ911111-1-111-11-111-1-111-1-11111-1-1-1-111-111-1-111-1-1-111111-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i11-1-111-1-1i−i
χ1011111-1-111-11-111-1-111-1-11111-1-1-1-111-111-1-111-1-1-111111-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i-1-1-1-1111111-1-1-1-1i−i−iiii−i−i−i−iii-1-111-1-111−ii
χ1111111-1-111-11-111-1-111-1-11111-1-1-1-111-111-1-111-1-1-111111-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−ii
χ1211111-1-111-11-111-1-111-1-11111-1-1-1-111-111-1-111-1-1-111111-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii-1-1-1-1111111-1-1-1-1−iii−i−i−iiiii−i−i-1-111-1-111i−i
χ1311111-1-111-11-111-1-111-1-11111-1-1-1-111-111-1-111-1-1-1-1-1-1-11-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i1111-1-1-1-1-1-11111−iii−i−i−iiiii−i−i11-1-1-1-111−ii
χ1411111-1-111-11-111-1-111-1-11111-1-1-1-111-111-1-111-1-1-1-1-1-1-11-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i11-1-111-1-1-1-11111−ii−ii−i−iii−i−iii-1-11111-1-1i−i
χ1511111-1-111-11-111-1-111-1-11111-1-1-1-111-111-1-111-1-1-1-1-1-1-11-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii1111-1-1-1-1-1-11111i−i−iiii−i−i−i−iii11-1-1-1-111i−i
χ1611111-1-111-11-111-1-111-1-11111-1-1-1-111-111-1-111-1-1-1-1-1-1-11-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii11-1-111-1-1-1-11111i−ii−iii−i−iii−i−i-1-11111-1-1−ii
χ1722222222-12222-1222222-1-1-1-12-1-1-1-12-12-12-1-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022220000000000220000-1-1-1-1-1-1-1-1000000
χ1822222222-12222-1222222-1-1-1-12-1-1-1-12-12-12-1-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000-2-2000011111111000000
χ1922222222-12222-1222222-1-1-1-12-1-1-1-12-12-12-1-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-21111111111110022220000000000-2-200001111-1-1-1-1000000
χ2022222222-12222-1222222-1-1-1-12-1-1-1-12-12-12-1-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-211111111111100-2-2-2-20000000000220000-1-1-1-11111000000
χ212222222-12222-12-1-1-1-1-1-122-12-12-1-1-1-12-12-12-1-12-1-12222-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-12200-1-1-1-100000000000000
χ222222222-12222-12-1-1-1-1-1-122-12-12-1-1-1-12-12-12-1-12-1-12222-1-1-2-2-1-11111-2-21111-2-21111220000-1-1-1-1-1-1-1-1-2-200111100000000000000
χ232222222-12222-12-1-1-1-1-1-122-12-12-1-1-1-12-12-12-1-12-1-1-2-2-2-2-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2000011111111-2-200111100000000000000
χ242222222-12222-12-1-1-1-1-1-122-12-12-1-1-1-12-12-12-1-12-1-1-2-2-2-2-1-1-2-2-1-11111-2-21111-2-21111-2-20000111111112200-1-1-1-100000000000000
χ2522222-2-22-1-22-22-1-2-222-2-2-1-1-1-1-2111-1212-1-21-1-11110000-112i−2i-112i2i−2i−2i−i−i−i−i−i−iiiiiii0022-2-200000000002i−2i0000−i−iii-1-111000000
χ2622222-2-22-1-22-22-1-2-222-2-2-1-1-1-1-2111-1212-1-21-1-11110000-112i−2i-112i2i−2i−2i−i−i−i−i−i−iiiiiii00-2-2220000000000−2i2i0000ii−i−i11-1-1000000
χ2722222-2-22-1-22-22-1-2-222-2-2-1-1-1-1-2111-1212-1-21-1-11110000-11−2i2i-11−2i−2i2i2iiiiiii−i−i−i−i−i−i0022-2-20000000000−2i2i0000ii−i−i-1-111000000
χ2822222-2-22-1-22-22-1-2-222-2-2-1-1-1-1-2111-1212-1-21-1-11110000-11−2i2i-11−2i−2i2i2iiiiiii−i−i−i−i−i−i00-2-22200000000002i−2i0000−i−iii11-1-1000000
χ2922222-2-2-12-22-2-1211-1-11122-121-211-1-1-2-121-2-1-1-2112222-112i−2i-11−i−iii2i2i−i−i−i−i−2i−2iiiii-2-20000-1-1-1-111112i−2i00−i−iii00000000000000
χ3022222-2-2-12-22-2-1211-1-11122-121-211-1-1-2-121-2-1-1-2112222-11−2i2i-11ii−i−i−2i−2iiiii2i2i−i−i−i−i-2-20000-1-1-1-11111−2i2i00ii−i−i00000000000000
χ3122222-2-2-12-22-2-1211-1-11122-121-211-1-1-2-121-2-1-1-211-2-2-2-2-112i−2i-11−i−iii2i2i−i−i−i−i−2i−2iiiii2200001111-1-1-1-1−2i2i00ii−i−i00000000000000
χ3222222-2-2-12-22-2-1211-1-11122-121-211-1-1-2-121-2-1-1-211-2-2-2-2-11−2i2i-11ii−i−i−2i−2iiiii2i2i−i−i−i−i2200001111-1-1-1-12i−2i00−i−iii00000000000000
χ332222-22-2222-2-222222222222-2-22222-2-2-2-2-2-2222220000-2-200-2-200000000000000000000000000000000000000000000002i−2i2i−2i00
χ342222-22-2222-2-222222222222-2-22222-2-2-2-2-2-2222220000-2-200-2-20000000000000000000000000000000000000000000000−2i2i−2i2i00
χ352222-2-2222-2-2222-2-222-2-2222-22-2-2-22-22-2-22222-2-2-20000-2200-2200000000000000000000000000000000000000000000002i−2i−2i2i00
χ362222-2-2222-2-2222-2-222-2-2222-22-2-2-22-22-2-22222-2-2-20000-2200-220000000000000000000000000000000000000000000000−2i2i2i−2i00
χ3722-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200002200-2-20000000000000000002i−2i2i−2i000000000000000000002i−2i2i−2i000000
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χ3922-2-22222-1-2-2-22-122-2-2-2-211-1-12-1-1-1-12-1-21-21111110000-1-1001100003−333−3−33−333−3−3002i−2i2i−2i0000000000000000−i3i3−i3i3−ii−ii000000
χ4022-2-22222-1-2-2-22-122-2-2-2-211-1-12-1-1-1-12-1-21-21111110000-1-1001100003−333−3−33−333−3−300−2i2i−2i2i0000000000000000i3−i3i3−i3i−ii−i000000
χ4122-2-22222-1-2-2-22-122-2-2-2-211-1-12-1-1-1-12-1-21-21111110000-1-100110000−33−3−333−33−3−333002i−2i2i−2i0000000000000000i3−i3i3−i3−ii−ii000000
χ4222-2-22222-1-2-2-22-122-2-2-2-211-1-12-1-1-1-12-1-21-21111110000-1-100110000−33−3−333−33−3−33300−2i2i−2i2i0000000000000000−i3i3−i3i3i−ii−i000000
χ4322-2-22-2-2222-2222-2-2-2-222-2-222-2-2-2-222-2-2-222-2-222200002-200-220000000000000000002i−2i−2i2i000000000000000000002i−2i−2i2i000000
χ4422-2-22-2-2222-2222-2-2-2-222-2-222-2-2-2-222-2-2-222-2-222200002-200-22000000000000000000−2i2i2i−2i00000000000000000000−2i2i2i−2i000000
χ4522-2-22-2-22-12-222-1-2-2-2-22211-1-1-2111-121-212-111-1-1-10000-11001-10000−i3i3−i3−i3i3i3i3−i3i3i3−i3−i3002i−2i−2i2i0000000000000000−333−3−iii−i000000
χ4622-2-22-2-22-12-222-1-2-2-2-22211-1-1-2111-121-212-111-1-1-10000-11001-10000−i3i3−i3−i3i3i3i3−i3i3i3−i3−i300−2i2i2i−2i00000000000000003−3−33i−i−ii000000
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χ4822-2-22-2-22-12-222-1-2-2-2-22211-1-1-2111-121-212-111-1-1-10000-11001-10000i3−i3i3i3−i3−i3−i3i3−i3−i3i3i300−2i2i2i−2i0000000000000000−333−3i−i−ii000000
χ4922-2-2-22-222-2222222-2-2-2-2-2-22-2-22222-2-22222-2-2-2-2-22i2i−2i−2i-2-2002200000000000000002i−2i00002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ5022-2-2-22-222-2222222-2-2-2-2-2-22-2-22222-2-22222-2-2-2-2-2−2i−2i2i2i-2-200220000000000000000−2i2i0000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ5122-2-2-22-2-12-222-12-1-11111-2-2-1-212-1-1-11-2-12-1211-2112i2i−2i−2i1100-1-13−33−3003−33−3003−33−32i−2i0000−i−iii−i−iii0000−i3i3−i3i300000000000000
χ5222-2-2-22-2-12-222-12-1-11111-2-2-1-212-1-1-11-2-12-1211-2112i2i−2i−2i1100-1-1−33−3300−33−3300−33−332i−2i0000−i−iii−i−iii0000i3−i3i3−i300000000000000
χ5322-2-2-22-2-12-222-12-1-11111-2-2-1-212-1-1-11-2-12-1211-211−2i−2i2i2i1100-1-13−33−3003−33−3003−33−3−2i2i0000ii−i−iii−i−i0000i3−i3i3−i300000000000000
χ5422-2-2-22-2-12-222-12-1-11111-2-2-1-212-1-1-11-2-12-1211-211−2i−2i2i2i1100-1-1−33−3300−33−3300−33−33−2i2i0000ii−i−iii−i−i0000−i3i3−i3i300000000000000
χ5522-2-2-2-222222-222-2-2-2-222-2-22-22-2-2-22-2222-2-2-2-22222i2i−2i−2i-22002-20000000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ5622-2-2-2-222222-222-2-2-2-222-2-22-22-2-2-22-2222-2-2-2-2222−2i−2i2i2i-22002-200000000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
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χ884-44i−4i000-240002-4−2i32i3−2i2i23−234i−4i-2000−2i32i32000000−2i2i023−23−2−2i2+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−4i000-240002-42i3−2i3−2i2i−23234i−4i-20002i3−2i32000000−2i2i0−23232+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−4i000-240002-42i3−2i3−2i2i−23234i−4i-20002i3−2i32000000−2i2i0−2323−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−i1−i−1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000
χ914-4−4i4i00044000-4-400−4i4i00−4i4i400000-4000000−4i4i0002−2i−2+2i2+2i−2−2i00000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ924-4−4i4i00044000-4-400−4i4i00−4i4i400000-4000000−4i4i000−2+2i2−2i−2−2i2+2i0000000000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ934-4−4i4i000-240002-4−2i32i32i−2i−2323−4i4i-2000−2i32i320000002i−2i0−23232−2i−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−2323−4i4i-2000−2i32i320000002i−2i0−2323−2+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−2i23−23−4i4i-20002i3−2i320000002i−2i023−232−2i−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−2i23−23−4i4i-20002i3−2i320000002i−2i023−23−2+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−8i00−4i4i-4000004000000−4i4i00000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-400044−4i34i3−4i4i43−43−4i4i20002i3−2i3-20000002i−2i0−232300000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-4000444i3−4i3−4i4i−4343−4i4i2000−2i32i3-20000002i−2i023−2300000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-4000-8400−8i8i004i−4i-40000040000004i−4i00000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-400044−4i34i34i−4i−43434i−4i20002i3−2i3-2000000−2i2i023−2300000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-4000444i3−4i34i−4i43−434i−4i2000−2i32i3-2000000−2i2i0−232300000000000000000000000000000000000000000000000000000000000000

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