Finite Group Databasebeta

← Group #13026424

Character table — Group #13026424

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444488888888888888888816161616161616162020202020202020404040408080808080808080
order12442424510101020202020248888101010101010202020202020404040404040404022448888448844448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-11-11-11-1
χ6111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-11-11-11
χ7111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111i−i−iii−i−ii
χ8111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−iii−i−iii−i
χ91111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-11-1-11-11
χ101111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-111-11-1
χ111111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1i−i−ii−iii−i
χ121111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1−iii−ii−i−ii
χ131111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ141111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ151111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ161111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ17222222-2-22222222200002-2-2-20000-2-20000000022-2-22-2-2222-2-2000000000000
χ18222222-2-22222222200002-2-2-20000-2-20000000022-2-2-222-2-2-222000000000000
χ19222222-2-2222222220000-22-2-20000-2-200000000-2-2222-2-22-2-222000000000000
χ20222222-2-2222222220000-22-2-20000-2-200000000-2-222-222-222-2-2000000000000
χ2122-2-22-22-22222-2-2-2-22-20000222222-2-2-2-2-2-2000000002-22-200002-20000000000
χ2222-2-22-22-22222-2-2-2-22-20000222222-2-2-2-2-2-200000000-22-220000-220000000000
χ2322-2-22-22-22222-2-2-2-2-22000022-2-2-2-2-2-22222000000002-22-20000-220000000000
χ2422-2-22-22-22222-2-2-2-2-22000022-2-2-2-2-2-2222200000000-22-2200002-20000000000
χ2522-2-22-2-222222-2-2-2-2002i−2i00-2-200002200002i2i−2i−2i000022-2-20000002i−2i00000000
χ2622-2-22-2-222222-2-2-2-2002i−2i00-2-200002200002i2i−2i−2i0000-2-222000000−2i2i00000000
χ2722-2-22-2-222222-2-2-2-200−2i2i00-2-20000220000−2i−2i2i2i000022-2-2000000−2i2i00000000
χ2822-2-22-2-222222-2-2-2-200−2i2i00-2-20000220000−2i−2i2i2i0000-2-2220000002i−2i00000000
χ2944444444-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ3044444444-1-1-1-1-1-1-1-144-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-444-4-4-1-11111-1-11111-1-1-1-1111100000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-444-1-11111-1-111111111-1-1-1-100000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-100004-41155−5−51155−5−55−55−5-1-11100000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-100004-411−5−55511−5−555−55−55-1-11100000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-10000-441155−5−51155−5−5−55−5511-1-100000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-10000-4411−5−55511−5−5555−55−511-1-100000000000000000000
χ374444-4-4004-4-4444-4-4000000000000000000000000000000004i−4i000000000000
χ384444-4-4004-4-4444-4-400000000000000000000000000000000−4i4i000000000000
χ3944-4-44-44-4-1-1-1-111114-40000-1-1-1-1-1-1111111i5−i5−i5i5i5−i5i5−i500000000000000000000
χ4044-4-44-44-4-1-1-1-111114-40000-1-1-1-1-1-1111111−i5i5i5−i5−i5i5−i5i500000000000000000000
χ4144-4-44-44-4-1-1-1-11111-440000-1-1111111-1-1-1-1i5−i5−i5i5−i5i5−i5i500000000000000000000
χ4244-4-44-44-4-1-1-1-11111-440000-1-1111111-1-1-1-1−i5i5i5−i5i5−i5i5−i500000000000000000000
χ4344-4-44-4-44-1-1-1-11111004i−4i001155−5−5-1-1−5−555−i−iiii5−i5−i5i500000000000000000000
χ4444-4-44-4-44-1-1-1-11111004i−4i0011−5−555-1-155−5−5−i−iii−i5i5i5−i500000000000000000000
χ4544-4-44-4-44-1-1-1-1111100−4i4i001155−5−5-1-1−5−555ii−i−i−i5i5i5−i500000000000000000000
χ4644-4-44-4-44-1-1-1-1111100−4i4i0011−5−555-1-155−5−5ii−i−ii5−i5−i5i500000000000000000000
χ4744-4-4-44004-4-44-4-4440000000000000000000000000000004-400000000000000
χ4844-4-4-44004-4-44-4-444000000000000000000000000000000-4400000000000000
χ498888-8-800-222-2-2-22200000025−25000025−2500000000000000000000000000000000
χ508888-8-800-222-2-2-222000000−25250000−252500000000000000000000000000000000
χ5188-8-8-8800-222-222-2-200000025−250000−252500000000000000000000000000000000
χ5288-8-8-8800-222-222-2-2000000−2525000025−2500000000000000000000000000000000
χ538-88i−8i0000800-88i−8i000000000000000000000000000000000000000000000000
χ548-88i−8i0000-225−252−2i2i2i5−2i5000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000
χ558-88i−8i0000-225−252−2i2i2i5−2i500000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000
χ568-88i−8i0000-2−25252−2i2i−2i52i500000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000
χ578-88i−8i0000-2−25252−2i2i−2i52i5000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000
χ588-8−8i8i0000800-8−8i8i000000000000000000000000000000000000000000000000
χ598-8−8i8i0000-225−2522i−2i−2i52i5000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000
χ608-8−8i8i0000-225−2522i−2i−2i52i500000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000
χ618-8−8i8i0000-2−252522i−2i2i5−2i500000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000
χ628-8−8i8i0000-2−252522i−2i2i5−2i5000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000

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