Finite Group Databasebeta

← Group #13026441

Character table — Group #13026441

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444488888888888888888816161616161616162020202020202020404040408080808080808080
order12442424510101020202020448888101020202020202020202020404040404040404022448888248888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ7111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iii
χ8111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i
χ91111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-11-11-1
χ101111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11-11-11
χ111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ121111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ131111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-11
χ141111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-111-1
χ151111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1i−i−ii−iii−i
χ161111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−iii−ii−i−ii
χ17222222-2-222222222002-200-2-2-2-20000000022-2-200002-22-222-2-2000000000000
χ18222222-2-222222222002-200-2-2-2-20000000022-2-20000-22-22-2-222000000000000
χ19222222-2-22222222200-2200-2-2-2-200000000-2-22200002-22-2-2-222000000000000
χ20222222-2-22222222200-2200-2-2-2-200000000-2-2220000-22-2222-2-2000000000000
χ2122-2-22-22-22222-2-2-2-200002i−2i22-2-20000000000002i2i−2i−2i2-2-220000002i−2i00000000
χ2222-2-22-22-22222-2-2-2-200002i−2i22-2-20000000000002i2i−2i−2i-222-2000000−2i2i00000000
χ2322-2-22-22-22222-2-2-2-20000−2i2i22-2-2000000000000−2i−2i2i2i2-2-22000000−2i2i00000000
χ2422-2-22-22-22222-2-2-2-20000−2i2i22-2-2000000000000−2i−2i2i2i-222-20000002i−2i00000000
χ2522-2-22-2-222222-2-2-2-22-20000-2-2222222-2-2-2-20000000022-2-200002-20000000000
χ2622-2-22-2-222222-2-2-2-22-20000-2-2222222-2-2-2-200000000-2-2220000-220000000000
χ2722-2-22-2-222222-2-2-2-2-220000-2-222-2-2-2-222220000000022-2-20000-220000000000
χ2822-2-22-2-222222-2-2-2-2-220000-2-222-2-2-2-2222200000000-2-22200002-20000000000
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
χ3144444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-111111111-1-1-1-1111100000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-1111111111111-1-1-1-100000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-1004-400111155−5−555−5−5-1-1115−55−500000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-1004-4001111−5−555−5−555-1-111−55−5500000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-100-4400111155−5−555−5−511-1-1−55−5500000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-100-44001111−5−555−5−55511-1-15−55−500000000000000000000
χ374444-4-40044-4-444-4-4000000000000000000000000000000004i−4i000000000000
χ384444-4-40044-4-444-4-400000000000000000000000000000000−4i4i000000000000
χ3944-4-44-44-4-1-1-1-1111100004i−4i-1-11155−5−5−5−555i5−i5i5−i5−i−iii00000000000000000000
χ4044-4-44-44-4-1-1-1-1111100004i−4i-1-111−5−55555−5−5−i5i5−i5i5−i−iii00000000000000000000
χ4144-4-44-44-4-1-1-1-111110000−4i4i-1-11155−5−5−5−555−i5i5−i5i5ii−i−i00000000000000000000
χ4244-4-44-44-4-1-1-1-111110000−4i4i-1-111−5−55555−5−5i5−i5i5−i5ii−i−i00000000000000000000
χ4344-4-44-4-44-1-1-1-111114-4000011-1-1-1-1-1-11111i5−i5−i5i5i5−i5−i5i500000000000000000000
χ4444-4-44-4-44-1-1-1-111114-4000011-1-1-1-1-1-11111−i5i5i5−i5−i5i5i5−i500000000000000000000
χ4544-4-44-4-44-1-1-1-11111-44000011-1-11111-1-1-1-1i5−i5−i5i5−i5i5i5−i500000000000000000000
χ4644-4-44-4-44-1-1-1-11111-44000011-1-11111-1-1-1-1−i5i5i5−i5i5−i5−i5i500000000000000000000
χ4744-4-4-440044-4-4-4-4440000000000000000000000000000004-400000000000000
χ4844-4-4-440044-4-4-4-444000000000000000000000000000000-4400000000000000
χ498888-8-800-2-222-2-22200000025−2525−25000000000000000000000000000000000000
χ508888-8-800-2-222-2-222000000−2525−2525000000000000000000000000000000000000
χ5188-8-8-8800-2-22222-2-200000025−25−2525000000000000000000000000000000000000
χ5288-8-8-8800-2-22222-2-2000000−252525−25000000000000000000000000000000000000
χ538-88i−8i00008-8008i−8i000000000000000000000000000000000000000000000000
χ548-88i−8i0000-2225−25−2i2i2i5−2i500000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000
χ558-88i−8i0000-2225−25−2i2i2i5−2i50000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000
χ568-88i−8i0000-22−2525−2i2i−2i52i50000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000
χ578-88i−8i0000-22−2525−2i2i−2i52i500000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000
χ588-8−8i8i00008-800−8i8i000000000000000000000000000000000000000000000000
χ598-8−8i8i0000-2225−252i−2i−2i52i500000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000
χ608-8−8i8i0000-2225−252i−2i−2i52i50000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000
χ618-8−8i8i0000-22−25252i−2i2i5−2i50000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000
χ628-8−8i8i0000-22−25252i−2i2i5−2i500000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000

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