Finite Group Databasebeta

← Group #11788576

Character table — Group #11788576

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order124422233444666612121212121236666666612121212121212121244444466121212121212121212121212121212121212444444121212121212121224668812121212121224242424224488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
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
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1
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
χ81111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911-1-11-1-1111-111-1-11-1-1-1-111111-11-1-1-1-11-111-111-1-1ii−i−ii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−ii−iii−i−iiiii−i−i−i−i1-1111-1-1-1ii−i−i11-1-11-11-1i−i
χ1011-1-11-1-1111-111-1-11-1-1-1-111111-11-1-1-1-11-111-111-1-1ii−i−ii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−ii−i−i−iiiiiii−i−i−i−i-11-1-11-111−i−iii11-1-1-11-11−ii
χ1111-1-11-1-1111-111-1-11-1-1-1-111111-11-1-1-1-11-111-111-1-1ii−i−i−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiiii−iii−i−iiiii−i−i−i−i-11-1-1-1111ii−i−i-1-1111-11-1−ii
χ1211-1-11-1-1111-111-1-11-1-1-1-111111-11-1-1-1-11-111-111-1-1ii−i−i−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiiii−i−i−iiiiiii−i−i−i−i1-111-11-1-1−i−iii-1-111-11-11i−i
χ1311-1-11-1-1111-111-1-11-1-1-1-111111-11-1-1-1-11-111-111-1-1−i−iiii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i−iiii−i−i−i−i−i−iiiii1-111-11-1-1ii−i−i-1-111-11-11−ii
χ1411-1-11-1-1111-111-1-11-1-1-1-111111-11-1-1-1-11-111-111-1-1−i−iiii−i1-1ii−i−i1-1iiiiii−i−i−i−i−i−i−ii−i−iii−i−i−i−iiiii-11-1-1-1111−i−iii-1-1111-11-1i−i
χ1511-1-11-1-1111-111-1-11-1-1-1-111111-11-1-1-1-11-111-111-1-1−i−iii−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii−iiii−i−i−i−i−i−iiiii-11-1-11-111ii−i−i11-1-1-11-11i−i
χ1611-1-11-1-1111-111-1-11-1-1-1-111111-11-1-1-1-11-111-111-1-1−i−iii−ii1-1−i−iii1-1−i−i−i−i−i−iiiiiii−ii−i−iii−i−i−i−iiiii1-1111-1-1-1−i−iii11-1-11-11-1−ii
χ1722222222-1222222-122-1-122-12-1-1-1-1-12-122-1-1-1-1-1-1-1000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10022220000000022-1-100-1-1-1-1-1-10000000000
χ1822222222-1222222-122-1-122-12-1-1-1-1-12-122-1-1-1-1-1-1-1000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-200000000-2-211001111110000000000
χ1922222222-1222222-122-1-122-12-1-1-1-1-12-122-1-1-1-1-1-1-10000-2-2-1-1-2-2-2-2-1-111111111111100222200000000-2-2110011-1-1-1-10000000000
χ2022222222-1222222-122-1-122-12-1-1-1-1-12-122-1-1-1-1-1-1-10000-2-2-1-1-2-2-2-2-1-111111111111100-2-2-2-20000000022-1-100-1-111110000000000
χ212222222-12222-1-1-12-1-122-1-1-1-122-1-1-1-12-1-1222-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-1000022000000-1-1-1-1000000
χ222222222-12222-1-1-12-1-122-1-1-1-122-1-1-1-12-1-1222-1-1-1-12222-2-2-1-11111-1-1-2-21111-2-21111220000-1-1-1-1-1-1-1-10000-2-20000001111000000
χ232222222-12222-1-1-12-1-122-1-1-1-122-1-1-1-12-1-1222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-20000111111110000-2-20000001111000000
χ242222222-12222-1-1-12-1-122-1-1-1-122-1-1-1-12-1-1222-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2-21111-2-21111-2-2000011111111000022000000-1-1-1-1000000
χ2522222-2-222-22-22-2-222222-2-2222-22-2-2-2-2-22-2-22-2-2220000002-20000-22000000000000002i−2i2i−2i00000000000000002i−2i2i−2i0000000000
χ2622222-2-222-22-22-2-222222-2-2222-22-2-2-2-2-22-2-22-2-2220000002-20000-2200000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i0000000000
χ2722222-2-22-1-22-22-2-2-122-1-1-2-2-12-11-111-21-2211-111-1-1000000-1100001-13−333−3−33−333−3−3002i−2i2i−2i0000000000−i3i300−i3i3−ii−ii0000000000
χ2822222-2-22-1-22-22-2-2-122-1-1-2-2-12-11-111-21-2211-111-1-1000000-1100001-13−333−3−33−333−3−300−2i2i−2i2i0000000000i3−i300i3−i3i−ii−i0000000000
χ2922222-2-22-1-22-22-2-2-122-1-1-2-2-12-11-111-21-2211-111-1-1000000-1100001-1−33−3−333−33−3−333002i−2i2i−2i0000000000i3−i300i3−i3−ii−ii0000000000
χ3022222-2-22-1-22-22-2-2-122-1-1-2-2-12-11-111-21-2211-111-1-1000000-1100001-1−33−3−333−33−3−33300−2i2i−2i2i0000000000−i3i300−i3i3i−ii−i0000000000
χ312222-22-222-2-2222222222222-2-22222-2-2-2-22-2-22222000000-2-20000-2-20000000000000000000000000000000000000000002-2-2200
χ322222-22-222-2-2222222222222-2-22222-2-2-2-22-2-22222000000-2-20000-2-2000000000000000000000000000000000000000000-222-200
χ332222-2-22222-2-22-2-222222-2-22-2-2-22-2-2222-2-22-2-2-222222200-2200002-2000000000000-2-2000022-2-222-2-20000000000000000000000
χ342222-2-22222-2-22-2-222222-2-22-2-2-22-2-2222-2-22-2-2-222-2-2-2-200-2200002-2000000000000220000-2-222-2-2220000000000000000000000
χ352222-2-22-122-2-2-1112-1-12211-11-2-2-111-12-11-22-211-1-12222001-13−33−3-11003−33−3003−33−3-2-20000-1-111-1-1110000000000003−33−3000000
χ362222-2-22-122-2-2-1112-1-12211-11-2-2-111-12-11-22-211-1-12222001-1−33−33-1100−33−3300−33−33-2-20000-1-111-1-111000000000000−33−33000000
χ372222-2-22-122-2-2-1112-1-12211-11-2-2-111-12-11-22-211-1-1-2-2-2-2001-13−33−3-11003−33−3003−33−322000011-1-111-1-1000000000000−33−33000000
χ382222-2-22-122-2-2-1112-1-12211-11-2-2-111-12-11-22-211-1-1-2-2-2-2001-1−33−33-1100−33−3300−33−3322000011-1-111-1-10000000000003−33−3000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2000000220000-2-2000000000000002-2-2200000000000000002-2-220000000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2000000220000-2-200000000000000-222-20000000000000000-222-20000000000
χ4122-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-12-1-2-21111111000000-1-1000011−i3i3−i3−i3i3i3i3−i3i3i3−i3−i3002-2-220000000000−i3i300i3−i3-111-10000000000
χ4222-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-12-1-2-21111111000000-1-1000011−i3i3−i3−i3i3i3i3−i3i3i3−i3−i300-222-20000000000i3−i300−i3i31-1-110000000000
χ4322-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-12-1-2-21111111000000-1-1000011i3−i3i3i3−i3−i3−i3i3−i3−i3i3i3002-2-220000000000i3−i300−i3i3-111-10000000000
χ4422-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-12-1-2-21111111000000-1-1000011i3−i3i3i3−i3−i3−i3i3−i3−i3i3i300-222-20000000000−i3i300i3−i31-1-110000000000
χ4522-2-22-2-22-12-222-2-2-1-2-21122-12-11-111-212-2-1-11-1-11100002i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii002i2i−2i−2i000000002-2-1-10011−i−iii0000000000
χ4622-2-22-2-22-12-222-2-2-1-2-21122-12-11-111-212-2-1-11-1-11100002i−2i-112i2i−2i−2i-11−i−i−i−i−i−iiiiiii00−2i−2i2i2i00000000-221100-1-1ii−i−i0000000000
χ4722-2-22-2-22-12-222-2-2-1-2-21122-12-11-111-212-2-1-11-1-1110000−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i002i2i−2i−2i00000000-221100-1-1−i−iii0000000000
χ4822-2-22-2-22-12-222-2-2-1-2-21122-12-11-111-212-2-1-11-1-1110000−2i2i-11−2i−2i2i2i-11iiiiii−i−i−i−i−i−i00−2i−2i2i2i000000002-2-1-10011ii−i−i0000000000
χ4922-2-22-2-2-122-22-111211-2-2-1-1-1-12-2-1111-2-1122-2-1-1112i2i−2i−2i2i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii2i−2i0000−i−i−i−iiiii00002-2000000-1-111000000
χ5022-2-22-2-2-122-22-111211-2-2-1-1-1-12-2-1111-2-1122-2-1-1112i2i−2i−2i−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i2i−2i0000−i−i−i−iiiii0000-2200000011-1-1000000
χ5122-2-22-2-2-122-22-111211-2-2-1-1-1-12-2-1111-2-1122-2-1-111−2i−2i2i2i2i−2i-11−i−iii-112i2i−i−i−i−i−2i−2iiiii−2i2i0000iiii−i−i−i−i0000-2200000011-1-1000000
χ5222-2-22-2-2-122-22-111211-2-2-1-1-1-12-2-1111-2-1122-2-1-111−2i−2i2i2i−2i2i-11ii−i−i-11−2i−2iiiii2i2i−i−i−i−i−2i2i0000iiii−i−i−i−i00002-2000000-1-111000000
χ5322-2-2-22-22222-22222-2-2-2-2-2-22-2-22222-2-222-222-2-2-2-22i2i−2i−2i00-2-2000022000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ5422-2-2-22-22222-22222-2-2-2-2-2-22-2-22222-2-222-222-2-2-2-2−2i−2i2i2i00-2-20000220000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ5522-2-2-22-2-1222-2-1-1-1211-2-211-11-22-1-1-11-2-1-1-22211112i2i−2i−2i0011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i3−2i2i0000−i−iiiii−i−i000000000000−333−3000000
χ5622-2-2-22-2-1222-2-1-1-1211-2-211-11-22-1-1-11-2-1-1-22211112i2i−2i−2i0011i3−i3−i3i3-1-100i3−i3i3−i300−i3i3−i3i3−2i2i0000−i−iiiii−i−i0000000000003−3−33000000
χ5722-2-2-22-2-1222-2-1-1-1211-2-211-11-22-1-1-11-2-1-1-2221111−2i−2i2i2i0011−i3i3i3−i3-1-100−i3i3−i3i300i3−i3i3−i32i−2i0000ii−i−i−i−iii0000000000003−3−33000000
χ5822-2-2-22-2-1222-2-1-1-1211-2-211-11-22-1-1-11-2-1-1-2221111−2i−2i2i2i0011i3−i3−i3i3-1-100i3−i3i3−i300−i3i3−i3i32i−2i0000ii−i−i−i−iii000000000000−333−3000000
χ5922-2-2-2-2222-2222-2-22-2-2-2-2222-2-2-22-2-222-222-2222-2-2000000-220000-2200000000000000000000000000000000000000000022-2-200
χ6022-2-2-2-2222-2222-2-22-2-2-2-2222-2-2-22-2-222-222-2222-2-2000000-220000-22000000000000000000000000000000000000000000-2-22200
χ614444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2111-2-2-2-2-2-2-2111100004411-2-2-2-211-2-21111-2-21111000000000000000000000000000000000000
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χ6544444-4-4-2-2-44-4-222-2-2-2-2-2221-2-221-1-1222-222-2-1-1110000001-10000-11−232333−3−3−232333−3−3000000000000000000000000000000000000
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χ7744-4-44-4-4-2-24-44-222-22222-2-21-2-221-1-122-22-2-2211-1-10000−4i4i1-12i2i−2i−2i1-12i2i−i−i−i−i−2i−2iiiii000000000000000000000000000000000000
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χ8444-4-4-4-44-2-2-444-222-22222-2-212221-1-1-2-22-2-22-211-1-1000000-110000-1100−3i3i3i−3i003i−3i−3i3i000000000000000000000000000000000000
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χ874-44i−4i000-240002−2i32i3-4−2i2i4i−4i23−23-20002−2i32i3000000023−23−2i2i2+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−4i000-240002−2i32i3-4−2i2i4i−4i23−23-20002−2i32i3000000023−23−2i2i−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−4i000-2400022i3−2i3-4−2i2i4i−4i−2323-200022i3−2i30000000−2323−2i2i2+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−4i000-2400022i3−2i3-4−2i2i4i−4i−2323-200022i3−2i30000000−2323−2i2i−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
χ914-4−4i4i00044000-400-4−4i4i−4i4i004000-400000000000−4i4i2−2i−2+2i2+2i−2−2i00000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ924-4−4i4i00044000-400-4−4i4i−4i4i004000-400000000000−4i4i−2+2i2−2i−2−2i2+2i0000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ934-4−4i4i000-240002−2i32i3-42i−2i−4i4i−2323-20002−2i32i30000000−23232i−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−4i4i−2323-20002−2i32i30000000−23232i−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−2i−4i4i23−23-200022i3−2i3000000023−232i−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−2i−4i4i23−23-200022i3−2i3000000023−232i−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−8i−4i4i00-4000400000000000−4i4i00000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-40004−4i34i34−4i4i−4i4i43−432000-22i3−2i30000000−23232i−2i00000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-400044i3−4i34−4i4i−4i4i−43432000-2−2i32i3000000023−232i−2i00000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-4000-8004−8i8i4i−4i00-40004000000000004i−4i00000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-40004−4i34i344i−4i4i−4i−43432000-22i3−2i3000000023−23−2i2i00000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-400044i3−4i344i−4i4i−4i43−432000-2−2i32i30000000−2323−2i2i00000000000000000000000000000000000000000000000000000000000000

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