Finite Group Databasebeta

← Group #13017060

Character table — Group #13017060

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size111144444888888810101010202020202020202040111144444888888810101010202020202020202040111144444888888810101010202020202020202040111144444888888810101010202020202020202040
order12224510101042020202020204444888888882444442020202042020202020204444888888884222241010101042020202020204444888888882444442020202042020202020204444888888884
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11
χ31111111111111111-1-1-1-1iiii−i−i−i−i-11111111111111111-1-1-1-1iiii−i−i−i−i-11111111111111111-1-1-1-1iiii−i−i−i−i-11111111111111111-1-1-1-1iiii−i−i−i−i-1
χ41111111111111111-1-1-1-1−i−i−i−iiiii-11111111111111111-1-1-1-1−i−i−i−iiiii-11111111111111111-1-1-1-1−i−i−i−iiiii-11111111111111111-1-1-1-1−i−i−i−iiiii-1
χ5111111111-111-1-1-1-1111111-1-111-1-1-1111111111-111-1-1-1-1111111-1-111-1-1-1111111111-111-1-1-1-1111111-1-111-1-1-1111111111-111-1-1-1-1111111-1-111-1-1-1
χ6111111111-111-1-1-1-11111-1-111-1-111-1111111111-111-1-1-1-11111-1-111-1-111-1111111111-111-1-1-1-11111-1-111-1-111-1111111111-111-1-1-1-11111-1-111-1-111-1
χ7111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1
χ8111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1
χ92222-222220-2-2000022-2-20000000002222-222220-2-2000022-2-20000000002222-222220-2-2000022-2-20000000002222-222220-2-2000022-2-2000000000
χ102222-222220-2-20000-2-2220000000002222-222220-2-20000-2-2220000000002222-222220-2-20000-2-2220000000002222-222220-2-20000-2-222000000000
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χ122-22-2022-2-20000000002i−2i−1−i1+i00−1+i1−i0002-22-2022-2-20000000002i−2i−1−i1+i00−1+i1−i0002-22-2022-2-20000000002i−2i−1−i1+i00−1+i1−i0002-22-2022-2-20000000002i−2i−1−i1+i00−1+i1−i000
χ132-22-2022-2-2000000000−2i2i1−i−1+i001+i−1−i0002-22-2022-2-2000000000−2i2i1−i−1+i001+i−1−i0002-22-2022-2-2000000000−2i2i1−i−1+i001+i−1−i0002-22-2022-2-2000000000−2i2i1−i−1+i001+i−1−i000
χ142-22-2022-2-2000000000−2i2i−1+i1−i00−1−i1+i0002-22-2022-2-2000000000−2i2i−1+i1−i00−1−i1+i0002-22-2022-2-2000000000−2i2i−1+i1−i00−1−i1+i0002-22-2022-2-2000000000−2i2i−1+i1−i00−1−i1+i000
χ152-2-2202-22-200000002i−2i00001−i−1+i001+i−1−i02-2-2202-22-200000002i−2i00001−i−1+i001+i−1−i02-2-2202-22-200000002i−2i00001−i−1+i001+i−1−i02-2-2202-22-200000002i−2i00001−i−1+i001+i−1−i0
χ162-2-2202-22-200000002i−2i0000−1+i1−i00−1−i1+i02-2-2202-22-200000002i−2i0000−1+i1−i00−1−i1+i02-2-2202-22-200000002i−2i0000−1+i1−i00−1−i1+i02-2-2202-22-200000002i−2i0000−1+i1−i00−1−i1+i0
χ172-2-2202-22-20000000−2i2i00001+i−1−i001−i−1+i02-2-2202-22-20000000−2i2i00001+i−1−i001−i−1+i02-2-2202-22-20000000−2i2i00001+i−1−i001−i−1+i02-2-2202-22-20000000−2i2i00001+i−1−i001−i−1+i0
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χ2044444-1-1-1-1-4-1-11111000000000000044444-1-1-1-1-4-1-11111000000000000044444-1-1-1-1-4-1-11111000000000000044444-1-1-1-1-4-1-111110000000000000
χ214444-4-1-1-1-101155−5−500000000000004444-4-1-1-1-101155−5−500000000000004444-4-1-1-1-101155−5−500000000000004444-4-1-1-1-101155−5−50000000000000
χ224444-4-1-1-1-1011−5−55500000000000004444-4-1-1-1-1011−5−55500000000000004444-4-1-1-1-1011−5−55500000000000004444-4-1-1-1-1011−5−5550000000000000
χ2344-4-404-4-440000000000000000000044-4-404-4-440000000000000000000044-4-404-4-440000000000000000000044-4-404-4-4400000000000000000000
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χ2644-4-40-111-10−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18000000000000044-4-40-111-10−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18000000000000044-4-40-111-10−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18000000000000044-4-40-111-10−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000
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χ288-88-80-2-222000000000000000000008-88-80-2-222000000000000000000008-88-80-2-222000000000000000000008-88-80-2-22200000000000000000000
χ298-8-880-22-22000000000000000000008-8-880-22-22000000000000000000008-8-880-22-22000000000000000000008-8-880-22-2200000000000000000000
χ3011111111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiiiiiiii-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−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ3111111111111111111111-1-1-1-1-1-1-1-11iiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i
χ321111111111111111-1-1-1-1iiii−i−i−i−i-1iiiiiiiiiiiiiiii−i−i−i−i-1-1-1-11111−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii1111-1-1-1-1i
χ331111111111111111-1-1-1-1−i−i−i−iiiii-1iiiiiiiiiiiiiiii−i−i−i−i1111-1-1-1-1−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111i
χ34111111111-111-1-1-1-1111111-1-111-1-1-1iiiiiiiii−iii−i−i−i−iiiiiii−i−iii−i−i−i-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-111-1-1111−i−i−i−i−i−i−i−i−ii−i−iiiii−i−i−i−i−i−iii−i−iiii
χ35111111111-111-1-1-1-11111-1-111-1-111-1iiiiiiiii−iii−i−i−i−iiiii−i−iii−i−iii−i-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-111-1-11−i−i−i−i−i−i−i−i−ii−i−iiiii−i−i−i−iii−i−iii−i−ii
χ36111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1iiiiiiiii−iii−i−i−i−i−i−i−i−i-1-11111-1-1i-1-1-1-1-1-1-1-1-11-1-111111111−i−iiiii−i−i-1−i−i−i−i−i−i−i−i−ii−i−iiiiiiiii11-1-1-1-111−i
χ37111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1iiiiiiiii−iii−i−i−i−i−i−i−i−i11-1-1-1-111i-1-1-1-1-1-1-1-1-11-1-111111111ii−i−i−i−iii-1−i−i−i−i−i−i−i−i−ii−i−iiiiiiiii-1-11111-1-1−i
χ382222-222220-2-2000022-2-20000000002i2i2i2i−2i2i2i2i2i0−2i−2i00002i2i−2i−2i000000000-2-2-2-22-2-2-2-20220000-2-222000000000−2i−2i−2i−2i2i−2i−2i−2i−2i02i2i0000−2i−2i2i2i000000000
χ392222-222220-2-20000-2-2220000000002i2i2i2i−2i2i2i2i2i0−2i−2i0000−2i−2i2i2i000000000-2-2-2-22-2-2-2-2022000022-2-2000000000−2i−2i−2i−2i2i−2i−2i−2i−2i02i2i00002i2i−2i−2i000000000
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χ6011111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1
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χ94111111111-111-1-1-1-1-1-1-1-1ii−i−i−i−iii1−i−i−i−i−i−i−i−i−ii−i−iiiiiiiii11-1-1-1-111−i-1-1-1-1-1-1-1-1-11-1-111111111−i−iiiii−i−i-1iiiiiiiii−iii−i−i−i−i−i−i−i−i-1-11111-1-1i
χ95111111111-111-1-1-1-1-1-1-1-1−i−iiiii−i−i1−i−i−i−i−i−i−i−i−ii−i−iiiiiiiii-1-11111-1-1−i-1-1-1-1-1-1-1-1-11-1-111111111ii−i−i−i−iii-1iiiiiiiii−iii−i−i−i−i−i−i−i−i11-1-1-1-111i
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χ11144-4-40-111-105−5−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000−4i−4i4i4i0i−i−ii0−i5i5−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ190000000000000-4-44401-1-110−55ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ1800000000000004i4i−4i−4i0−iii−i0i5−i5ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ190000000000000
χ11244-4-40-111-105−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000−4i−4i4i4i0i−i−ii0−i5i5ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ190000000000000-4-44401-1-110−55−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ1800000000000004i4i−4i−4i0−iii−i0i5−i5−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ190000000000000
χ11344-4-40-111-10−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000−4i−4i4i4i0i−i−ii0i5−i5−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ190000000000000-4-44401-1-1105−5ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ1800000000000004i4i−4i−4i0−iii−i0−i5i5ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ190000000000000
χ11444-4-40-111-10−55ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000−4i−4i4i4i0i−i−ii0i5−i5ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ190000000000000-4-44401-1-1105−5−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ1800000000000004i4i−4i−4i0−iii−i0−i5i5−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ190000000000000
χ1158-88-80-2-22200000000000000000000−8i8i−8i8i02i2i−2i−2i00000000000000000000-88-88022-2-2000000000000000000008i−8i8i−8i0−2i−2i2i2i00000000000000000000
χ1168-8-880-22-2200000000000000000000−8i8i8i−8i02i−2i2i−2i00000000000000000000-888-802-22-2000000000000000000008i−8i−8i8i0−2i2i−2i2i00000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.