Finite Group Databasebeta

← Group #11789733

Character table — Group #11789733

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order124422233444666612121212121236666666612121212121212121244446688121224242424242424242424242424242424448888121212121212121224446612121212121224242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111
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
χ911-1-11-1-111-1111-1-11-1-1-1-111111-1-1-1-11-11-1-1-1-11111ii−i−i1-11-11-111-1-1111111-1-1-1-1-1-1i−i11-1-1iiii−i−i−i−i1-1i−i11ii−i−i-1-111-1-1ii−i−ii−i
χ1011-1-11-1-111-1111-1-11-1-1-1-111111-1-1-1-11-11-1-1-1-11111ii−i−i1-11-11-111-1-1111111-1-1-1-1-1-1i−i-1-111iiii−i−i−i−i-11i−i-1-1ii−i−i11-1-111−i−iii−ii
χ1111-1-11-1-111-1111-1-11-1-1-1-111111-1-1-1-11-11-1-1-1-11111ii−i−i1-1-111-1-1-111-1-1-1-1-1-1111111i−i11-1-1iiii−i−i−i−i-11−ii-1-1−i−iii1111-1-1ii−i−i−ii
χ1211-1-11-1-111-1111-1-11-1-1-1-111111-1-1-1-11-11-1-1-1-11111ii−i−i1-1-111-1-1-111-1-1-1-1-1-1111111i−i-1-111iiii−i−i−i−i1-1−ii11−i−iii-1-1-1-111−i−iiii−i
χ1311-1-11-1-111-1111-1-11-1-1-1-111111-1-1-1-11-11-1-1-1-11111−i−iii1-11-11-111-1-1111111-1-1-1-1-1-1−ii11-1-1−i−i−i−iiiii1-1−ii11−i−iii-1-111-1-1−i−iii−ii
χ1411-1-11-1-111-1111-1-11-1-1-1-111111-1-1-1-11-11-1-1-1-11111−i−iii1-11-11-111-1-1111111-1-1-1-1-1-1−ii-1-111−i−i−i−iiiii-11−ii-1-1−i−iii11-1-111ii−i−ii−i
χ1511-1-11-1-111-1111-1-11-1-1-1-111111-1-1-1-11-11-1-1-1-11111−i−iii1-1-111-1-1-111-1-1-1-1-1-1111111−ii11-1-1−i−i−i−iiiii-11i−i-1-1ii−i−i1111-1-1−i−iiii−i
χ1611-1-11-1-111-1111-1-11-1-1-1-111111-1-1-1-11-11-1-1-1-11111−i−iii1-1-111-1-1-111-1-1-1-1-1-1111111−ii-1-111−i−i−i−iiiii1-1i−i11ii−i−i-1-1-1-111ii−i−i−ii
χ1722222222-1222222-122-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1002222000000002200-1-10000-1-1-1-1-1-1000000
χ1822222222-1222222-122-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-200000000-2-200110000111111000000
χ1922222222-1222222-122-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-211111111111100222200000000-2-20011000011-1-1-1-1000000
χ2022222222-1222222-122-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-211111111111100-2-2-2-2000000002200-1-10000-1-11111000000
χ212222222-12222-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-12-1-12-1-122222-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-1002200-1-1-1-1000000000000
χ222222222-12222-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-12-1-12-1-122222-1-1-2-2-1-11111-2-21111-2-21111220000-1-1-1-1-1-1-1-100-2-2001111000000000000
χ232222222-12222-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-12-1-12-1-12-2-2-2-2-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200001111111100-2-2001111000000000000
χ242222222-12222-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-12-1-12-1-12-2-2-2-2-1-1-2-2-1-11111-2-21111-2-21111-2-2000011111111002200-1-1-1-1000000000000
χ2522222-2-2222-2-22-2-222222-2-2222-2-2-2-22-2-22222-2-2-2-200002-200-220000000000000000002i−2i2i−2i000000000000000000002i−2i2i−2i000000
χ2622222-2-2222-2-22-2-222222-2-2222-2-2-2-22-2-22222-2-2-2-200002-200-22000000000000000000−2i2i−2i2i00000000000000000000−2i2i−2i2i000000
χ2722222-2-22-12-2-22-2-2-122-1-1-2-2-12-11111-1-2-22-1-1-111110000-11001-100003−333−3−33−333−3−3002i−2i2i−2i000000000000−i3i30000−i3i3−ii−ii000000
χ2822222-2-22-12-2-22-2-2-122-1-1-2-2-12-11111-1-2-22-1-1-111110000-11001-100003−333−3−33−333−3−300−2i2i−2i2i000000000000i3−i30000i3−i3i−ii−i000000
χ2922222-2-22-12-2-22-2-2-122-1-1-2-2-12-11111-1-2-22-1-1-111110000-11001-10000−33−3−333−33−3−333002i−2i2i−2i000000000000i3−i30000i3−i3−ii−ii000000
χ3022222-2-22-12-2-22-2-2-122-1-1-2-2-12-11111-1-2-22-1-1-111110000-11001-10000−33−3−333−33−3−33300−2i2i−2i2i000000000000−i3i30000−i3i3i−ii−i000000
χ312222-22-222-22-222222222222-2-22-2222-2-2-2-222222-20000-2-200-2-200000000000000000000000000000000000000000000002-22-200
χ322222-22-222-22-222222222222-2-22-2222-2-2-2-222222-20000-2-200-2-20000000000000000000000000000000000000000000000-22-2200
χ332222-2-2222-2-222-2-222222-2-22-2-2-22-2-2222-2-222-2-2-222222-22002-20000000000000000-2-2000022-2-222-2-20000000000000000000000
χ342222-2-2222-2-222-2-222222-2-22-2-2-22-2-2222-2-222-2-2-22-2-2-2-2-22002-20000000000000000220000-2-222-2-2220000000000000000000000
χ352222-2-22-12-2-22-1112-1-12211-11-2-2211-1-1-11-2-1-1-211222221-100-113−33−3003−33−3003−33−3-2-20000-1-111-1-1110000003−33−3000000000000
χ362222-2-22-12-2-22-1112-1-12211-11-2-2211-1-1-11-2-1-1-211222221-100-11−33−3300−33−3300−33−33-2-20000-1-111-1-111000000−33−33000000000000
χ372222-2-22-12-2-22-1112-1-12211-11-2-2211-1-1-11-2-1-1-2112-2-2-2-21-100-113−33−3003−33−3003−33−322000011-1-111-1-1000000−33−33000000000000
χ382222-2-22-12-2-22-1112-1-12211-11-2-2211-1-1-11-2-1-1-2112-2-2-2-21-100-11−33−3300−33−3300−33−3322000011-1-111-1-10000003−33−3000000000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200002200-2-20000000000000000002i−2i−2i2i000000000000000000002i−2i−2i2i000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200002200-2-2000000000000000000−2i2i2i−2i00000000000000000000−2i2i2i−2i000000
χ4122-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-1-12-2-211111110000-1-1001100003−333−3−3−33−3−333002i−2i−2i2i000000000000−i3i30000i3−i3−iii−i000000
χ4222-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-1-12-2-211111110000-1-1001100003−333−3−3−33−3−33300−2i2i2i−2i000000000000i3−i30000−i3i3i−i−ii000000
χ4322-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-1-12-2-211111110000-1-100110000−33−3−3333−333−3−3002i−2i−2i2i000000000000i3−i30000−i3i3−iii−i000000
χ4422-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-1-12-2-211111110000-1-100110000−33−3−3333−333−3−300−2i2i2i−2i000000000000−i3i30000i3−i3i−i−ii000000
χ4522-2-22-2-22-1-2222-2-2-1-2-21122-12-11111-1-22-2111-1-1-1-10000-112-2-1122-2-2-1-1-1-1-1-11111110022-2-2000000002-200-1-1000011-1-111000000
χ4622-2-22-2-22-1-2222-2-2-1-2-21122-12-11111-1-22-2111-1-1-1-10000-112-2-1122-2-2-1-1-1-1-1-111111100-2-22200000000-2200110000-1-111-1-1000000
χ4722-2-22-2-22-1-2222-2-2-1-2-21122-12-11111-1-22-2111-1-1-1-10000-11-22-11-2-222111111-1-1-1-1-1-10022-2-200000000-2200110000-1-1-1-111000000
χ4822-2-22-2-22-1-2222-2-2-1-2-21122-12-11111-1-22-2111-1-1-1-10000-11-22-11-2-222111111-1-1-1-1-1-100-2-222000000002-200-1-100001111-1-1000000
χ4922-2-22-2-2-12-222-111211-2-2-1-1-1-12-2-211-11-11-2112-1-122i2i−2i−2i-112-2-11-1-11122-1-1-1-1-2-211112i−2i0000−i−i−i−iiiii002i−2i00−i−iii000000000000
χ5022-2-22-2-2-12-222-111211-2-2-1-1-1-12-2-211-11-11-2112-1-122i2i−2i−2i-11-22-1111-1-1-2-2111122-1-1-1-12i−2i0000−i−i−i−iiiii00−2i2i00ii−i−i000000000000
χ5122-2-22-2-2-12-222-111211-2-2-1-1-1-12-2-211-11-11-2112-1-12−2i−2i2i2i-112-2-11-1-11122-1-1-1-1-2-21111−2i2i0000iiii−i−i−i−i00−2i2i00ii−i−i000000000000
χ5222-2-22-2-2-12-222-111211-2-2-1-1-1-12-2-211-11-11-2112-1-12−2i−2i2i2i-11-22-1111-1-1-2-2111122-1-1-1-1−2i2i0000iiii−i−i−i−i002i−2i00−i−iii000000000000
χ5322-2-2-22-2222-222222-2-2-2-2-2-22-2-22-2222-2222-2-2-2-2-222i2i−2i−2i-2-200220000000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ5422-2-2-22-2222-222222-2-2-2-2-2-22-2-22-2222-2222-2-2-2-2-22−2i−2i2i2i-2-2002200000000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ5522-2-2-22-2-122-22-1-1-1211-2-211-11-22-2-1-1-11-1-1211-21122i2i−2i−2i1100-1-13−3−33003−33−300−33−33−2i2i0000−i−iiiii−i−i000000i3−i3−i3i3000000000000
χ5622-2-2-22-2-122-22-1-1-1211-2-211-11-22-2-1-1-11-1-1211-21122i2i−2i−2i1100-1-1−333−300−33−33003−33−3−2i2i0000−i−iiiii−i−i000000−i3i3i3−i3000000000000
χ5722-2-2-22-2-122-22-1-1-1211-2-211-11-22-2-1-1-11-1-1211-2112−2i−2i2i2i1100-1-13−3−33003−33−300−33−332i−2i0000ii−i−i−i−iii000000−i3i3i3−i3000000000000
χ5822-2-2-22-2-122-22-1-1-1211-2-211-11-22-2-1-1-11-1-1211-2112−2i−2i2i2i1100-1-1−333−300−33−33003−33−32i−2i0000ii−i−i−i−iii000000i3−i3−i3i3000000000000
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χ614444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-211-211-20000114411-2-2-2-2-2-21111-2-21111000000000000000000000000000000000000
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χ894-44i−4i000-2400022i3−2i3-4−2i2i4i−4i−2323-200002i3−2i320000−2i2i0−232302+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−4i000-2400022i3−2i3-4−2i2i4i−4i−2323-200002i3−2i320000−2i2i0−23230−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ111−i−1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000
χ914-4−4i4i00044000-400-4−4i4i−4i4i004000000-40000−4i4i00002−2i−2+2i2+2i−2−2i00000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ924-4−4i4i00044000-400-4−4i4i−4i4i004000000-40000−4i4i0000−2+2i2−2i−2−2i2+2i0000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ934-4−4i4i000-240002−2i32i3-42i−2i−4i4i−2323-20000−2i32i3200002i−2i0−232302−2i−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−4i4i−2323-20000−2i32i3200002i−2i0−23230−2+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−2i−4i4i23−23-200002i3−2i3200002i−2i023−2302−2i−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−2i−4i4i23−23-200002i3−2i3200002i−2i023−230−2+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−8i−4i4i00-400000040000−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-40004−4i34i34−4i4i−4i4i43−43200002i3−2i3-200002i−2i0−2323000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-400044i3−4i34−4i4i−4i4i−434320000−2i32i3-200002i−2i023−23000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-4000-8004−8i8i4i−4i00-4000000400004i−4i000000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-40004−4i34i344i−4i4i−4i−4343200002i3−2i3-20000−2i2i023−23000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-400044i3−4i344i−4i4i−4i43−4320000−2i32i3-20000−2i2i0−2323000000000000000000000000000000000000000000000000000000000000000

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