Finite Group Databasebeta

← Group #13022266

Character table — Group #13022266

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222224444444444444444555588888888888888101010101010161616161616161620202020202020202020202020202020202020202020202040404040404040404040
order12222222224444444451010101010101044444410101010202020202020202044444420202020202020204444444488888888888888884488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1iiii−i−i−i−i
χ411111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1−i−i−i−iiiii
χ511111111111111-1-1-1-1111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111
χ711111111111111-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11ii−i−i−i−iii
χ811111111111111-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11−i−iiiii−i−i
χ91111111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1
χ101111111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11−i−i−i−iiiii
χ121111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11iiii−i−i−i−i
χ131111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111
χ141111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1
χ151111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-1−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-1ii−i−i−i−iii
χ171-11-111-1-1-11ii−i−ii−ii−i11-1-111-1-111-1-11-111-1-1iiii−i−i−i−i11-1-11-1i−i11-1-1i−ii−iii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1
χ181-11-111-1-1-11ii−i−ii−ii−i11-1-111-1-111-1-11-111-1-1iiii−i−i−i−i11-1-11-1i−i11-1-1i−ii−iii−i−ii−i-1-111−i−iii-1-111−i−iii1-1−ii-11−ii-11
χ191-11-111-1-1-11ii−i−ii−ii−i11-1-111-1-1-1-1111-111-1-1iiii−i−i−i−i-1-111-11i−i11-1-1i−i−ii−i−iii−iiii−i−i-1-111−i−iii11-1-1-11-11i−i1-1−ii
χ201-11-111-1-1-11ii−i−ii−ii−i11-1-111-1-1-1-1111-111-1-1iiii−i−i−i−i-1-111-11i−i11-1-1i−i−ii−i−iii−ii−i−iii11-1-1ii−i−i-1-111-111-1−ii-11i−i
χ211-11-111-1-1-11ii−i−i−ii−ii11-1-111-1-111-1-1-1111-1-1iiii−i−i−i−i11-1-11-1−ii-1-111−ii−iiii−i−i−ii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11
χ221-11-111-1-1-11ii−i−i−ii−ii11-1-111-1-111-1-1-1111-1-1iiii−i−i−i−i11-1-11-1−ii-1-111−ii−iiii−i−i−ii-1-111ii−i−i-1-111ii−i−i-11−ii1-1−ii1-1
χ231-11-111-1-1-11ii−i−i−ii−ii11-1-111-1-1-1-111-1111-1-1iiii−i−i−i−i-1-111-11−ii-1-111−iii−i−i−iiii−iii−i−i11-1-1−i−iii-1-1111-1-11−ii1-1i−i
χ241-11-111-1-1-11ii−i−i−ii−ii11-1-111-1-1-1-111-1111-1-1iiii−i−i−i−i-1-111-11−ii-1-111−iii−i−i−iiii−i−i−iii-1-111ii−i−i11-1-11-11-1i−i-11−ii
χ251-11-111-1-1-11−i−iiii−ii−i11-1-111-1-111-1-1-1111-1-1−i−i−i−iiiii11-1-11-1i−i-1-111i−ii−i−i−iiii−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11
χ261-11-111-1-1-11−i−iiii−ii−i11-1-111-1-111-1-1-1111-1-1−i−i−i−iiiii11-1-11-1i−i-1-111i−ii−i−i−iiii−i-1-111−i−iii-1-111−i−iii-11i−i1-1i−i1-1
χ271-11-111-1-1-11−i−iiii−ii−i11-1-111-1-1-1-111-1111-1-1−i−i−i−iiiii-1-111-11i−i-1-111i−i−iiii−i−i−iiii−i−i-1-111−i−iii11-1-11-11-1−ii-11i−i
χ281-11-111-1-1-11−i−iiii−ii−i11-1-111-1-1-1-111-1111-1-1−i−i−i−iiiii-1-111-11i−i-1-111i−i−iiii−i−i−ii−i−iii11-1-1ii−i−i-1-1111-1-11i−i1-1−ii
χ291-11-111-1-1-11−i−iii−ii−ii11-1-111-1-111-1-11-111-1-1−i−i−i−iiiii11-1-11-1−ii11-1-1−ii−ii−i−iii−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1
χ301-11-111-1-1-11−i−iii−ii−ii11-1-111-1-111-1-11-111-1-1−i−i−i−iiiii11-1-11-1−ii11-1-1−ii−ii−i−iii−ii-1-111ii−i−i-1-111ii−i−i1-1i−i-11i−i-11
χ311-11-111-1-1-11−i−iii−ii−ii11-1-111-1-1-1-1111-111-1-1−i−i−i−iiiii-1-111-11−ii11-1-1−iii−iii−i−ii−iii−i−i11-1-1−i−iii-1-111-111-1i−i-11−ii
χ321-11-111-1-1-11−i−iii−ii−ii11-1-111-1-1-1-1111-111-1-1−i−i−i−iiiii-1-111-11−ii11-1-1−iii−iii−i−ii−i−i−iii-1-111ii−i−i11-1-1-11-11−ii1-1i−i
χ3322222-22-2-2-20000000022-2-2-2-2222222002-22-2000000002-2-2-2-2200000000000000002-22-200002-22-200000000000000
χ3422222-22-2-2-20000000022-2-2-2-2222222002-22-2000000002-2-2-2-220000000000000000-22-220000-22-2200000000000000
χ3522222-22-2-2-20000000022-2-2-2-222-2-2-2-2002-22-200000000-22222-200000000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000
χ3622222-22-2-2-20000000022-2-2-2-222-2-2-2-2002-22-200000000-22222-20000000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000
χ372222-22-22-2-20000000022-2-2-2-222222200-22-2200000000-2-22-22-2000000000000000000002-22-200002-22-20000000000
χ382222-22-22-2-20000000022-2-2-2-222222200-22-2200000000-2-22-22-200000000000000000000-22-220000-22-220000000000
χ392222-22-22-2-20000000022-2-2-2-222-2-2-2-200-22-220000000022-22-22000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000000000
χ402222-22-22-2-20000000022-2-2-2-222-2-2-2-200-22-220000000022-22-2200000000000000000000−2i2i−2i2i00002i−2i2i−2i0000000000
χ412222-2-2-2-222000022-2-222222222222200-2-2-2-200000000-22-22-2-2-2-2000022-2-200002200000000000000000000000000
χ422222-2-2-2-222000022-2-222222222-2-2-2-200-2-2-2-2000000002-22-222-2-2000022220000-2-200000000000000000000000000
χ432222-2-2-2-2220000-2-22222222222222200-2-2-2-200000000-22-22-2-2220000-2-2220000-2-200000000000000000000000000
χ442222-2-2-2-2220000-2-22222222222-2-2-2-200-2-2-2-2000000002-22-222220000-2-2-2-200002200000000000000000000000000
χ452-22-22-2-222-2000000002222-2-2-2-222-2-2002-2-22000000002-222-2-200000000000000002-2-2200002-2-2200000000000000
χ462-22-22-2-222-2000000002222-2-2-2-222-2-2002-2-22000000002-222-2-20000000000000000-222-20000-222-200000000000000
χ472-22-22-2-222-2000000002222-2-2-2-2-2-222002-2-2200000000-22-2-22200000000000000002i−2i−2i2i0000−2i2i2i−2i00000000000000
χ482-22-22-2-222-2000000002222-2-2-2-2-2-222002-2-2200000000-22-2-2220000000000000000−2i2i2i−2i00002i−2i−2i2i00000000000000
χ492-22-2-222-22-2000000002222-2-2-2-222-2-200-222-200000000-2-2-2222000000000000000000002i−2i−2i2i00002i−2i−2i2i0000000000
χ502-22-2-222-22-2000000002222-2-2-2-222-2-200-222-200000000-2-2-222200000000000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000
χ512-22-2-222-22-2000000002222-2-2-2-2-2-22200-222-200000000222-2-2-2000000000000000000002-2-220000-222-20000000000
χ522-22-2-222-22-2000000002222-2-2-2-2-2-22200-222-200000000222-2-2-200000000000000000000-222-200002-2-220000000000
χ532-22-2-2-222-2200002i−2i−2i2i22-2-222-2-222-2-200-2-22200000000-222-2-22−2i2i00002i−2i−2i2i00002i−2i00000000000000000000000000
χ542-22-2-2-222-2200002i−2i−2i2i22-2-222-2-2-2-22200-2-222000000002-2-222-2−2i2i00002i−2i2i−2i0000−2i2i00000000000000000000000000
χ552-22-2-2-222-220000−2i2i2i−2i22-2-222-2-222-2-200-2-22200000000-222-2-222i−2i0000−2i2i2i−2i0000−2i2i00000000000000000000000000
χ562-22-2-2-222-220000−2i2i2i−2i22-2-222-2-2-2-22200-2-222000000002-2-222-22i−2i0000−2i2i−2i2i00002i−2i00000000000000000000000000
χ57444444444444444444-1-1-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ5844444444444444-4-4-4-4-1-1-1-1-1-1-1-10000-4-4-1-1-1-1-1-1-1-1-1-1-1-1000000111111110000000000000000000000000000000000
χ594444444444-4-4-4-44444-1-1-1-1-1-1-1-10000-4-4-1-1-1-111111111000000-1-11111-1-10000000000000000000000000000000000
χ604444444444-4-4-4-4-4-4-4-4-1-1-1-1-1-1-1-1000044-1-1-1-11111111100000011-1-1-1-1110000000000000000000000000000000000
χ614444-4-4-4-444000044-4-4-1-1-1-1-1-1-1-1000000111155−5−555−5−5000000115−55−5-1-10000000000000000000000000000000000
χ624444-4-4-4-444000044-4-4-1-1-1-1-1-1-1-10000001111−5−555−5−55500000011−55−55-1-10000000000000000000000000000000000
χ634444-4-4-4-4440000-4-444-1-1-1-1-1-1-1-1000000111155−5−555−5−5000000-1-1−55−55110000000000000000000000000000000000
χ644444-4-4-4-4440000-4-444-1-1-1-1-1-1-1-10000001111−5−555−5−555000000-1-15−55−5110000000000000000000000000000000000
χ6544-4-40000002-22-200004-40000-444i−4i4i−4i0000002-22-22-22-200000000000000002i−2i2i−2i0000000000000000000000000000
χ6644-4-40000002-22-200004-40000-44−4i4i−4i4i0000002-22-22-22-20000000000000000−2i2i−2i2i0000000000000000000000000000
χ6744-4-4000000-22-2200004-40000-444i−4i4i−4i000000-22-22-22-220000000000000000−2i2i−2i2i0000000000000000000000000000
χ6844-4-4000000-22-2200004-40000-44−4i4i−4i4i000000-22-22-22-2200000000000000002i−2i2i−2i0000000000000000000000000000
χ694-44-444-4-4-444i4i−4i−4i4i−4i4i−4i-1-111-1-11100004-4-1-111−i−i−i−iiiii000000−ii-1-111−ii0000000000000000000000000000000000
χ704-44-444-4-4-444i4i−4i−4i−4i4i−4i4i-1-111-1-1110000-44-1-111−i−i−i−iiiii000000i−i11-1-1i−i0000000000000000000000000000000000
χ714-44-444-4-4-44−4i−4i4i4i4i−4i4i−4i-1-111-1-1110000-44-1-111iiii−i−i−i−i000000−ii11-1-1−ii0000000000000000000000000000000000
χ724-44-444-4-4-44−4i−4i4i4i−4i4i−4i4i-1-111-1-11100004-4-1-111iiii−i−i−i−i000000i−i-1-111i−i0000000000000000000000000000000000
χ734-44-4-4-444-4400004i−4i−4i4i-1-111-1-11100000011-1-1i5i5−i5−i5−i5−i5i5i5000000i−i5−5−55−ii0000000000000000000000000000000000
χ744-44-4-4-444-4400004i−4i−4i4i-1-111-1-11100000011-1-1−i5−i5i5i5i5i5−i5−i5000000i−i−555−5−ii0000000000000000000000000000000000
χ754-44-4-4-444-440000−4i4i4i−4i-1-111-1-11100000011-1-1i5i5−i5−i5−i5−i5i5i5000000−ii−555−5i−i0000000000000000000000000000000000
χ764-44-4-4-444-440000−4i4i4i−4i-1-111-1-11100000011-1-1−i5−i5i5i5i5i5−i5−i5000000−ii5−5−55i−i0000000000000000000000000000000000
χ774-4-440000002i−2i−2i2i00004-400004-44i−4i−4i4i0000002i−2i2i−2i−2i2i−2i2i0000000000000000-222-20000000000000000000000000000
χ784-4-440000002i−2i−2i2i00004-400004-4−4i4i4i−4i0000002i−2i2i−2i−2i2i−2i2i00000000000000002-2-220000000000000000000000000000
χ794-4-44000000−2i2i2i−2i00004-400004-44i−4i−4i4i000000−2i2i−2i2i2i−2i2i−2i00000000000000002-2-220000000000000000000000000000
χ804-4-44000000−2i2i2i−2i00004-400004-4−4i4i4i−4i000000−2i2i−2i2i2i−2i2i−2i0000000000000000-222-20000000000000000000000000000
χ8188888-88-8-8-800000000-2-22222-2-2000000-22-2200000000000000000000000000000000000000000000000000000000
χ828888-88-88-8-800000000-2-22222-2-20000002-22-200000000000000000000000000000000000000000000000000000000
χ8388-8-80000004-44-40000-2225−2525−252-20000000000−1+51−5−1−51+5−1+51−5−1−51+5000000000000000000000000000000000000000000000000
χ8488-8-80000004-44-40000-22−2525−25252-20000000000−1−51+5−1+51−5−1−51+5−1+51−5000000000000000000000000000000000000000000000000
χ8588-8-8000000-44-440000-2225−2525−252-200000000001−5−1+51+5−1−51−5−1+51+5−1−5000000000000000000000000000000000000000000000000
χ8688-8-8000000-44-440000-22−2525−25252-200000000001+5−1−51−5−1+51+5−1−51−5−1+5000000000000000000000000000000000000000000000000
χ878-88-88-8-888-800000000-2-2-2-22222000000-222-200000000000000000000000000000000000000000000000000000000
χ888-88-8-888-88-800000000-2-2-2-222220000002-2-2200000000000000000000000000000000000000000000000000000000
χ898-8-880000004i−4i−4i4i0000-2225−25−2525-220000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000000000000000000000000
χ908-8-880000004i−4i−4i4i0000-22−252525−25-220000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000000000000000000000000000
χ918-8-88000000−4i4i4i−4i0000-2225−25−2525-2200000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000000000000000000000000
χ928-8-88000000−4i4i4i−4i0000-22−252525−25-2200000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000000000000000000000000000

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