Finite Group Databasebeta

← Group #11787777

Character table — Group #11787777

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order124422233444666612121212121236666666612121212121212121244661212121212121212121212121212121212124444888888881212121212121212246612122424242424242424224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ61111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ81111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ911-1-1-11-11111-11-1-1111-1-1-1-11-11-1-11-1-111-111-111-1-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i11-1-1ii−i−iii−i−i1111-1-1-1-11-111-1-1ii−i−iii−i−i11-1-1i−i
χ1011-1-1-11-11111-11-1-1111-1-1-1-11-11-1-11-1-111-111-111-1-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i11-1-1ii−i−i−i−iii1111-1-1-1-1-11-1-111ii−i−i−i−iii-1-111−ii
χ1111-1-1-11-11111-11-1-1111-1-1-1-11-11-1-11-1-111-111-111-1-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i-1-111−i−iiiii−i−i-1-1-1-111111-111-1-1−i−iiiii−i−i-1-111−ii
χ1211-1-1-11-11111-11-1-1111-1-1-1-11-11-1-11-1-111-111-111-1-1i−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i-1-111−i−iii−i−iii-1-1-1-11111-11-1-111−i−iii−i−iii11-1-1i−i
χ1311-1-1-11-11111-11-1-1111-1-1-1-11-11-1-11-1-111-111-111-1-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii11-1-1−i−iiiii−i−i1111-1-1-1-1-11-1-111−i−iiiii−i−i-1-111i−i
χ1411-1-1-11-11111-11-1-1111-1-1-1-11-11-1-11-1-111-111-111-1-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii11-1-1−i−iii−i−iii1111-1-1-1-11-111-1-1−i−iii−i−iii11-1-1−ii
χ1511-1-1-11-11111-11-1-1111-1-1-1-11-11-1-11-1-111-111-111-1-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii-1-111ii−i−iii−i−i-1-1-1-11111-11-1-111ii−i−iii−i−i11-1-1−ii
χ1611-1-1-11-11111-11-1-1111-1-1-1-11-11-1-11-1-111-111-111-1-1−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii-1-111ii−i−i−i−iii-1-1-1-111111-111-1-1ii−i−i−i−iii-1-111i−i
χ1722222222-1222222-12222-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022220000000022-1-1-1-10000-1-1-1-1000000
χ1822222222-1222222-12222-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-200000000-2-2111100001111000000
χ1922222222-1222222-12222-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-1-1-2-2-2-2-1-111111111111100000000222200000000-2-211110000-1-1-1-1000000
χ2022222222-1222222-12222-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-1-1-2-2-2-2-1-111111111111100000000-2-2-2-20000000022-1-1-1-100001111000000
χ212222222-12222-1-1-12-1-1-1-122-1-1222-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1222222220000-1-1-1-1-1-1-1-1000000-1-1-1-10000000000
χ222222222-12222-1-1-12-1-1-1-122-1-1222-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-200001111111100000011110000000000
χ232222222-12222-1-1-12-1-1-1-122-1-1222-1-1-1-1-1-1222-1-1-1-1-2-2-1-11111-1-1-2-21111-2-211112222-2-2-2-20000-1-1-1-1-1-1-1-100000011110000000000
χ242222222-12222-1-1-12-1-1-1-122-1-1222-1-1-1-1-1-1222-1-1-1-1-2-2-1-11111-1-1-2-21111-2-21111-2-2-2-22222000011111111000000-1-1-1-10000000000
χ2522222-2-2222-2-222222222222-2-2-22222-2-2-22-2-2222200-2-20000-2-2000000000000000000002-22-20000000000000000002-22-2000000
χ2622222-2-2222-2-222222222222-2-2-22222-2-2-22-2-2222200-2-20000-2-200000000000000000000-22-22000000000000000000-22-22000000
χ2722222-2-22-12-2-2222-12222-1-1-1-211-1-1-1-1-2-2-2-111-1-1-1-10011000011−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3000000002-22-20000000000−i3i3−i3i30000-11-11000000
χ2822222-2-22-12-2-2222-12222-1-1-1-211-1-1-1-1-2-2-2-111-1-1-1-10011000011−i3i3−i3−i3i3i3−i3i3−i3−i3i3i300000000-22-220000000000i3−i3i3−i300001-11-1000000
χ2922222-2-22-12-2-2222-12222-1-1-1-211-1-1-1-1-2-2-2-111-1-1-1-10011000011i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3000000002-22-20000000000i3−i3i3−i30000-11-11000000
χ3022222-2-22-12-2-2222-12222-1-1-1-211-1-1-1-1-2-2-2-111-1-1-1-10011000011i3−i3i3i3−i3−i3i3−i3i3i3−i3−i300000000-22-220000000000−i3i3−i3i300001-11-1000000
χ312222-22-222-2-222-2-22-2-222222-22-2-22-2-22-22-2-22-2-222002-20000-2200000000000000000000000000000000000000000000002-22-200
χ322222-22-222-2-222-2-22-2-222222-22-2-22-2-22-22-2-22-2-222002-20000-220000000000000000000000000000000000000000000000-22-2200
χ332222-2-2222-22-22-2-22-2-2222222-22-22-2-2-22-2-22-2-2-22200-2200002-200000000000000002-22-20000000000000000002-22-20000000000
χ342222-2-2222-22-22-2-22-2-2222222-22-22-2-2-22-2-22-2-2-22200-2200002-20000000000000000-22-22000000000000000000-22-220000000000
χ352222-2-22-12-22-2-111211-1-122-1-1-22-2-1111-11-22-211-1-1001-13−33−3-11003−33−3003−33−300002-22-2000033−3−333−3−3000000-11-110000000000
χ362222-2-22-12-22-2-111211-1-122-1-1-22-2-1111-11-22-211-1-1001-13−33−3-11003−33−3003−33−30000-22-220000−3−333−3−3330000001-11-10000000000
χ372222-2-22-12-22-2-111211-1-122-1-1-22-2-1111-11-22-211-1-1001-1−33−33-1100−33−3300−33−3300002-22-20000−3−333−3−333000000-11-110000000000
χ382222-2-22-12-22-2-111211-1-122-1-1-22-2-1111-11-22-211-1-1001-1−33−33-1100−33−3300−33−330000-22-22000033−3−333−3−30000001-11-10000000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200220000-2-200000000000000000000000000000000000000000000002-2-2200
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200220000-2-20000000000000000000000000000000000000000000000-222-200
χ4122-2-22-2-222-2222222-2-2-2-2-2-22-2-2-22222-222-222-2-2-2-200-2-200002200000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i0000000000
χ4222-2-22-2-222-2222222-2-2-2-2-2-22-2-2-22222-222-222-2-2-2-200-2-20000220000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i0000000000
χ4322-2-22-2-2-12-222-1-1-121111-2-2-11-2-22-1-1-11-1-1-22211110011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i300002i−2i−2i2i0000−3−33333−3−3000000−iii−i0000000000
χ4422-2-22-2-2-12-222-1-1-121111-2-2-11-2-22-1-1-11-1-1-22211110011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i30000−2i2i2i−2i000033−3−3−3−333000000i−i−ii0000000000
χ4522-2-22-2-2-12-222-1-1-121111-2-2-11-2-22-1-1-11-1-1-22211110011i3−i3−i3i3-1-100i3−i3i3−i300−i3i3−i3i300002i−2i−2i2i000033−3−3−3−333000000−iii−i0000000000
χ4622-2-22-2-2-12-222-1-1-121111-2-2-11-2-22-1-1-11-1-1-22211110011i3−i3−i3i3-1-100i3−i3i3−i300−i3i3−i3i30000−2i2i2i−2i0000−3−33333−3−3000000i−i−ii0000000000
χ4722-2-2-22-22-122-22-2-2-122-2-211-1-2-111-11122-2-1-11-1-1112i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii000000002i2i−2i−2i000000002-2-1-1110000−i−iii000000
χ4822-2-2-22-22-122-22-2-2-122-2-211-1-2-111-11122-2-1-11-1-1112i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii00000000−2i−2i2i2i00000000-2211-1-10000ii−i−i000000
χ4922-2-2-22-22-122-22-2-2-122-2-211-1-2-111-11122-2-1-11-1-111−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i000000002i2i−2i−2i00000000-2211-1-10000−i−iii000000
χ5022-2-2-22-22-122-22-2-2-122-2-211-1-2-111-11122-2-1-11-1-111−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i00000000−2i−2i2i2i000000002-2-1-1110000ii−i−i000000
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χ5322-2-2-22-2-1222-2-1112-1-111-2-2-112-2-2-111-1-1122-2-1-111−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i22-2-2−2i−2i2i2i0000-1-1-1-11111000000ii−i−i0000000000
χ5422-2-2-22-2-1222-2-1112-1-111-2-2-112-2-2-111-1-1122-2-1-111−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i-2-2222i2i−2i−2i00001111-1-1-1-1000000−i−iii0000000000
χ5522-2-2-2-22222-222-2-2222-2-2-2-222-22-22-2-2-2-222-2222-2-200-220000-22000000000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i000000
χ5622-2-2-2-22222-222-2-2222-2-2-2-222-22-22-2-2-2-222-2222-2-200-220000-2200000000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i000000
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χ884-44i−4i000-240002−2i32i3-423−23−2i2i4i−4i-200002−2i32i300000023−23−2i2i0000000000000000000000-22−2i2i000000001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000
χ894-44i−4i000-2400022i3−2i3-4−2323−2i2i4i−4i-2000022i3−2i3000000−2323−2i2i00000000000000000000002-22i−2i00000000−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000
χ904-44i−4i000-2400022i3−2i3-4−2323−2i2i4i−4i-2000022i3−2i3000000−2323−2i2i0000000000000000000000-22−2i2i000000001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000
χ914-4−4i4i00044000-400-400−4i4i−4i4i40000-40000000000−4i4i00000000000000000000002-2−2i2i000000002-22-2−2i2i−2i2i00000000000000000000
χ924-4−4i4i00044000-400-400−4i4i−4i4i40000-40000000000−4i4i0000000000000000000000-222i−2i00000000-22-222i−2i2i−2i00000000000000000000
χ934-4−4i4i000-240002−2i32i3-4−23232i−2i−4i4i-200002−2i32i3000000−23232i−2i00000000000000000000002-2−2i2i00000000−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000
χ944-4−4i4i000-240002−2i32i3-4−23232i−2i−4i4i-200002−2i32i3000000−23232i−2i0000000000000000000000-222i−2i000000001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000
χ954-4−4i4i000-2400022i3−2i3-423−232i−2i−4i4i-2000022i3−2i300000023−232i−2i00000000000000000000002-2−2i2i00000000−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000
χ964-4−4i4i000-2400022i3−2i3-423−232i−2i−4i4i-2000022i3−2i300000023−232i−2i0000000000000000000000-222i−2i000000001−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000
χ978-88i−8i0008-4000-8004008i−8i−4i4i-4000040000000000−4i4i00000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-40004−4i34i3443−43−4i4i−4i4i20000-22i3−2i3000000−23232i−2i00000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-400044i3−4i34−4343−4i4i−4i4i20000-2−2i32i300000023−232i−2i00000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-4000-800400−8i8i4i−4i-40000400000000004i−4i00000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-40004−4i34i34−43434i−4i4i−4i20000-22i3−2i300000023−23−2i2i00000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-400044i3−4i3443−434i−4i4i−4i20000-2−2i32i3000000−2323−2i2i00000000000000000000000000000000000000000000000000000000000000

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