Finite Group Databasebeta

← Group #11789726

Character table — Group #11789726

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order124422233444666612121212121236666666612121212121212121244444466121212121212121212121212121212121212448888121212121212121224668812122424242424242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111
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
χ911-1-11-1-111-1111-1-11-1-111-1-1111-1-11-1-1-11-111-111-1-1ii−i−ii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−ii−iii−i−iiiii−i−i−i−i1-1111-1-1-111-1-1ii−i−i11-1-1i−i
χ1011-1-11-1-111-1111-1-11-1-111-1-1111-1-11-1-1-11-111-111-1-1ii−i−ii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−ii−i−i−iiiiiii−i−i−i−i-11-1-11-11111-1-1−i−iii-1-111−ii
χ1111-1-11-1-111-1111-1-11-1-111-1-1111-1-11-1-1-11-111-111-1-1ii−i−i−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiiii−iii−i−iiiii−i−i−i−i-11-1-1-1111-1-111ii−i−i11-1-1−ii
χ1211-1-11-1-111-1111-1-11-1-111-1-1111-1-11-1-1-11-111-111-1-1ii−i−i−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiiii−i−i−iiiiiii−i−i−i−i1-111-11-1-1-1-111−i−iii-1-111i−i
χ1311-1-11-1-111-1111-1-11-1-111-1-1111-1-11-1-1-11-111-111-1-1−i−iiii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i−iiii−i−i−i−i−i−iiiii1-111-11-1-1-1-111ii−i−i-1-111−ii
χ1411-1-11-1-111-1111-1-11-1-111-1-1111-1-11-1-1-11-111-111-1-1−i−iiii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i−ii−i−iii−i−i−i−iiiii-11-1-1-1111-1-111−i−iii11-1-1i−i
χ1511-1-11-1-111-1111-1-11-1-111-1-1111-1-11-1-1-11-111-111-1-1−i−iii−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii−iiii−i−i−i−i−i−iiiii-11-1-11-11111-1-1ii−i−i-1-111i−i
χ1611-1-11-1-111-1111-1-11-1-111-1-1111-1-11-1-1-11-111-111-1-1−i−iii−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii−ii−i−iii−i−i−i−iiiii1-1111-1-1-111-1-1−i−iii11-1-1−ii
χ1722222222-1222222-12222-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10022220000000022-1-100-1-10000-1-1-1-1000000
χ1822222222-1222222-12222-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-200000000-2-211001100001111000000
χ1922222222-1222222-12222-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-10000-2-2-1-1-2-2-2-2-1-111111111111100222200000000-2-21100110000-1-1-1-1000000
χ2022222222-1222222-12222-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-10000-2-2-1-1-2-2-2-2-1-111111111111100-2-2-2-20000000022-1-100-1-100001111000000
χ212222222-12222-1-1-12-1-1-1-122-1-1222-1-1-1-1-1-1222-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-100002200-1-1-1-10000000000
χ222222222-12222-1-1-12-1-1-1-122-1-1222-1-1-1-1-1-1222-1-1-1-12222-2-2-1-11111-1-1-2-21111-2-21111220000-1-1-1-1-1-1-1-10000-2-20011110000000000
χ232222222-12222-1-1-12-1-1-1-122-1-1222-1-1-1-1-1-1222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-20000111111110000-2-20011110000000000
χ242222222-12222-1-1-12-1-1-1-122-1-1222-1-1-1-1-1-1222-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2-21111-2-21111-2-200001111111100002200-1-1-1-10000000000
χ2522222-2-2222-2-22-2-2222-2-222222-2-22-2-2-2-22-2-22-2-2220000002-20000-220000000000000000000000000000000000000000002i−2i2i−2i00
χ2622222-2-2222-2-22-2-2222-2-222222-2-22-2-2-2-22-2-22-2-2220000002-20000-22000000000000000000000000000000000000000000−2i2i−2i2i00
χ272222-22-222-22-222222222222-2-2-22222-2-2-22-2-22222000000-2-20000-2-2000000000000002-22-2000000000000000000002-22-2000000
χ282222-22-222-22-222222222222-2-2-22222-2-2-22-2-22222000000-2-20000-2-200000000000000-22-2200000000000000000000-22-22000000
χ292222-22-22-1-22-2222-12222-1-1-1-211-1-1-1-1-2-2-2-111-1-1-1-100000011000011−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3002-22-20000000000−i3i300−i3i30000-11-11000000
χ302222-22-22-1-22-2222-12222-1-1-1-211-1-1-1-1-2-2-2-111-1-1-1-100000011000011−i3i3−i3−i3i3i3−i3i3−i3−i3i3i300-22-220000000000i3−i300i3−i300001-11-1000000
χ312222-22-22-1-22-2222-12222-1-1-1-211-1-1-1-1-2-2-2-111-1-1-1-100000011000011i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3002-22-20000000000i3−i300i3−i30000-11-11000000
χ322222-22-22-1-22-2222-12222-1-1-1-211-1-1-1-1-2-2-2-111-1-1-1-100000011000011i3−i3i3i3−i3−i3i3−i3i3i3−i3−i300-22-220000000000−i3i300−i3i300001-11-1000000
χ332222-2-2222-2-222-2-2222-2-2222-2-22-22-2-222-2-22-2-2-222222200-2200002-2000000000000-2-2000022-2-222-2-20000000000000000000000
χ342222-2-2222-2-222-2-2222-2-2222-2-22-22-2-222-2-22-2-2-222-2-2-2-200-2200002-2000000000000220000-2-222-2-2220000000000000000000000
χ352222-2-22-12-2-22-1112-1-11122-11-22-2-111-1-11-22-211-1-12222001-13−33−3-11003−33−3003−33−3-2-20000-1-111-1-111000000003−33−30000000000
χ362222-2-22-12-2-22-1112-1-11122-11-22-2-111-1-11-22-211-1-12222001-1−33−33-1100−33−3300−33−33-2-20000-1-111-1-11100000000−33−330000000000
χ372222-2-22-12-2-22-1112-1-11122-11-22-2-111-1-11-22-211-1-1-2-2-2-2001-13−33−3-11003−33−3003−33−322000011-1-111-1-100000000−33−330000000000
χ382222-2-22-12-2-22-1112-1-11122-11-22-2-111-1-11-22-211-1-1-2-2-2-2001-1−33−33-1100−33−3300−33−3322000011-1-111-1-1000000003−33−30000000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2000000220000-2-20000000000000000000000000000000000000000002i−2i−2i2i00
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2000000220000-2-2000000000000000000000000000000000000000000−2i2i2i−2i00
χ4122-2-22-2-22-1-2222-2-2-1-2-22211-12-111-111-22-2-1-11-1-11100002i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii002i2i−2i−2i000000002-2-1-100110000−i−iii000000
χ4222-2-22-2-22-1-2222-2-2-1-2-22211-12-111-111-22-2-1-11-1-11100002i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii00−2i−2i2i2i00000000-221100-1-10000ii−i−i000000
χ4322-2-22-2-22-1-2222-2-2-1-2-22211-12-111-111-22-2-1-11-1-1110000−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i002i2i−2i−2i00000000-221100-1-10000−i−iii000000
χ4422-2-22-2-22-1-2222-2-2-1-2-22211-12-111-111-22-2-1-11-1-1110000−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i00−2i−2i2i2i000000002-2-1-100110000ii−i−i000000
χ4522-2-22-2-2-12-222-111211-1-1-2-2-1-12-2-2-1111-1122-2-1-1112i2i−2i−2i2i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii2i−2i0000−i−i−i−iiiii00002-200-1-1110000000000
χ4622-2-22-2-2-12-222-111211-1-1-2-2-1-12-2-2-1111-1122-2-1-1112i2i−2i−2i−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i2i−2i0000−i−i−i−iiiii0000-220011-1-10000000000
χ4722-2-22-2-2-12-222-111211-1-1-2-2-1-12-2-2-1111-1122-2-1-111−2i−2i2i2i2i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii−2i2i0000iiii−i−i−i−i0000-220011-1-10000000000
χ4822-2-22-2-2-12-222-111211-1-1-2-2-1-12-2-2-1111-1122-2-1-111−2i−2i2i2i−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i−2i2i0000iiii−i−i−i−i00002-200-1-1110000000000
χ4922-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22222-222-222-2-2-2-22i2i−2i−2i00-2-2000022000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ5022-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22222-222-222-2-2-2-2−2i−2i2i2i00-2-20000220000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ5122-2-2-22-2-122-22-1-1-121111-2-2-11-2-22-1-1-11-1-1-22211112i2i−2i−2i0011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i3−2i2i0000−i−iiiii−i−i00000000−333−30000000000
χ5222-2-2-22-2-122-22-1-1-121111-2-2-11-2-22-1-1-11-1-1-22211112i2i−2i−2i0011i3−i3−i3i3-1-100i3−i3i3−i300−i3i3−i3i3−2i2i0000−i−iiiii−i−i000000003−3−330000000000
χ5322-2-2-22-2-122-22-1-1-121111-2-2-11-2-22-1-1-11-1-1-2221111−2i−2i2i2i0011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i32i−2i0000ii−i−i−i−iii000000003−3−330000000000
χ5422-2-2-22-2-122-22-1-1-121111-2-2-11-2-22-1-1-11-1-1-2221111−2i−2i2i2i0011i3−i3−i3i3-1-100i3−i3i3−i300−i3i3−i3i32i−2i0000ii−i−i−i−iii00000000−333−30000000000
χ5522-2-2-2-222222-22-2-22-2-222-2-22-2-22-22-2-22-222-2222-2-2000000-220000-22000000000000002i−2i−2i2i000000000000000000002i−2i−2i2i000000
χ5622-2-2-2-222222-22-2-22-2-222-2-22-2-22-22-2-22-222-2222-2-2000000-220000-2200000000000000−2i2i2i−2i00000000000000000000−2i2i2i−2i000000
χ5722-2-2-2-222-122-22-2-2-1-2-22211-1-21-11-1112-22-11-1-1-1110000001-100001-13−333−3−3−33−3−333002i−2i−2i2i0000000000−i3i300i3−i30000−iii−i000000
χ5822-2-2-2-222-122-22-2-2-1-2-22211-1-21-11-1112-22-11-1-1-1110000001-100001-13−333−3−3−33−3−33300−2i2i2i−2i0000000000i3−i300−i3i30000i−i−ii000000
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χ874-44i−4i000-240002−2i32i3-4−2i2i23−234i−4i-200002−2i32i300000023−23−2i2i2+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−4i000-240002−2i32i3-4−2i2i23−234i−4i-200002−2i32i300000023−23−2i2i−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−4i000-2400022i3−2i3-4−2i2i−23234i−4i-2000022i3−2i3000000−2323−2i2i2+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−4i000-2400022i3−2i3-4−2i2i−23234i−4i-2000022i3−2i3000000−2323−2i2i−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
χ914-4−4i4i00044000-400-4−4i4i00−4i4i40000-40000000000−4i4i2−2i−2+2i2+2i−2−2i00000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ924-4−4i4i00044000-400-4−4i4i00−4i4i40000-40000000000−4i4i−2+2i2−2i−2−2i2+2i0000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ934-4−4i4i000-240002−2i32i3-42i−2i−2323−4i4i-200002−2i32i3000000−23232i−2i2−2i−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
χ944-4−4i4i000-240002−2i32i3-42i−2i−2323−4i4i-200002−2i32i3000000−23232i−2i−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
χ954-4−4i4i000-2400022i3−2i3-42i−2i23−23−4i4i-2000022i3−2i300000023−232i−2i2−2i−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
χ964-4−4i4i000-2400022i3−2i3-42i−2i23−23−4i4i-2000022i3−2i300000023−232i−2i−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−8i0008-4000-80048i−8i00−4i4i-4000040000000000−4i4i00000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-40004−4i34i34−4i4i43−43−4i4i20000-22i3−2i3000000−23232i−2i00000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-400044i3−4i34−4i4i−4343−4i4i20000-2−2i32i300000023−232i−2i00000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-4000-8004−8i8i004i−4i-40000400000000004i−4i00000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-40004−4i34i344i−4i−43434i−4i20000-22i3−2i300000023−23−2i2i00000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-400044i3−4i344i−4i43−434i−4i20000-2−2i32i3000000−2323−2i2i00000000000000000000000000000000000000000000000000000000000000

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