Finite Group Databasebeta

← Group #13026385

Character table — Group #13026385

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444488888888888888888816161616161616162020202020202020404040408080808080808080
order12222222510101010101010444444101010102020202020202020202020202020202022444444444444448888
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
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ91111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111-11-11-11-1
χ101111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11-11-11-11
χ111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1i−i−iii−i−ii
χ121111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1−iii−i−iii−i
χ131111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11-11-1-11-11
χ141111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-11-111-11-1
χ151111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111i−i−ii−iii−i
χ161111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111−iii−ii−i−ii
χ17222222-2-2222222222-20000-2-2-2-200000000220000-2-22222-2-2-2-2000000000000
χ18222222-2-2222222222-20000-2-2-2-200000000220000-2-2-2-2-2-22222000000000000
χ19222222-2-222222222-220000-2-2-2-200000000-2-200002222-2-222-2-2000000000000
χ20222222-2-222222222-220000-2-2-2-200000000-2-2000022-2-222-2-222000000000000
χ212-2-222-22-222-2-222-2-200002-222-2-2000000000022-2-2002-200002-22-20000000000
χ222-2-222-22-222-2-222-2-200002-222-2-2000000000022-2-200-220000-22-220000000000
χ232-2-222-22-222-2-222-2-20000-2222-2-20000000000-2-222002-200002-2-220000000000
χ242-2-222-22-222-2-222-2-20000-2222-2-20000000000-2-22200-220000-222-20000000000
χ252-2-222-2-2222-2-222-2-2002i−2i00-2-2222i2i2i2i−2i−2i−2i−2i000000002-20000-22002i−2i00000000
χ262-2-222-2-2222-2-222-2-2002i−2i00-2-2222i2i2i2i−2i−2i−2i−2i00000000-2200002-200−2i2i00000000
χ272-2-222-2-2222-2-222-2-200−2i2i00-2-222−2i−2i−2i−2i2i2i2i2i000000002-20000-2200−2i2i00000000
χ282-2-222-2-2222-2-222-2-200−2i2i00-2-222−2i−2i−2i−2i2i2i2i2i00000000-2200002-2002i−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
χ3044444444-1-1-1-1-1-1-1-144-4-4-4-4-1-1-1-111111111-1-11111-1-100000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-11111111111-1-1-1-11100000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-14-40000111155−5−555−5−5-1-15−55−51100000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-400001111−5−555−5−555-1-1−55−551100000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-440000111155−5−555−5−511−55−55-1-100000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-4400001111−5−555−5−555115−55−5-1-100000000000000000000
χ374444-4-40044-4-4-4-4440000000000000000000000000000004-400000000000000
χ384444-4-40044-4-4-4-444000000000000000000000000000000-4400000000000000
χ394-4-444-44-4-1-111-1-11100004-4-1-111i5i5−i5−i5−i5−i5i5i5i5−i5-1-111i5−i500000000000000000000
χ404-4-444-44-4-1-111-1-11100004-4-1-111−i5−i5i5i5i5i5−i5−i5−i5i5-1-111−i5i500000000000000000000
χ414-4-444-44-4-1-111-1-1110000-44-1-111i5i5−i5−i5−i5−i5i5i5−i5i511-1-1−i5i500000000000000000000
χ424-4-444-44-4-1-111-1-1110000-44-1-111−i5−i5i5i5i5i5−i5−i5i5−i511-1-1i5−i500000000000000000000
χ434-4-444-4-44-1-111-1-111004i−4i0011-1-1−i−i−i−iiiiii5−i55−5−55−i5i500000000000000000000
χ444-4-444-4-44-1-111-1-111004i−4i0011-1-1−i−i−i−iiiii−i5i5−555−5i5−i500000000000000000000
χ454-4-444-4-44-1-111-1-11100−4i4i0011-1-1iiii−i−i−i−ii5−i5−555−5−i5i500000000000000000000
χ464-4-444-4-44-1-111-1-11100−4i4i0011-1-1iiii−i−i−i−i−i5i55−5−55i5−i500000000000000000000
χ474-4-44-44004444-4-4-4-400000000000000000000000000004i−4i0000000000000000
χ484-4-44-44004444-4-4-4-40000000000000000000000000000−4i4i0000000000000000
χ498888-8-800-2-22222-2-200000025−2525−25000000000000000000000000000000000000
χ508888-8-800-2-22222-2-2000000−2525−2525000000000000000000000000000000000000
χ5188-8-800008-800008-80000000000000000000000000000000000000000000000
χ5288-8-80000-2225−2525−25-2200000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000
χ5388-8-80000-2225−2525−25-220000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000
χ5488-8-80000-22−2525−2525-220000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000
χ5588-8-80000-22−2525−2525-2200000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000
χ568-88-800008-80000-880000000000000000000000000000000000000000000000
χ578-88-80000-2225−25−25252-200000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000
χ588-88-80000-2225−25−25252-20000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000
χ598-88-80000-22−252525−252-20000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000
χ608-88-80000-22−252525−252-200000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000
χ618-8-88-8800-2-2-2-2222200000025−25−2525000000000000000000000000000000000000
χ628-8-88-8800-2-2-2-22222000000−252525−25000000000000000000000000000000000000

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