Finite Group Databasebeta

← Group #13022383

Character table — Group #13022383

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222224444444444444444555588888888888888101010101010161616161616161620202020202020202020202020202020202020202020202040404040404040404040
order12222244444444444451010101010101044442220202020202020202020202022224410101010202020204444444488888888888888884444444444
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
χ511111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11−i−i−i−iiiii
χ811111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11iiii−i−i−i−i
χ91111111111-1-1-1-11111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-11111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111
χ111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11ii−i−i−i−iii
χ121111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11−i−iiiii−i−i
χ131111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111
χ141111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1
χ151111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-1−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-1ii−i−i−i−iii
χ171-1-111-111-1-1ii−i−iii−i−i111-11-1-1-111-1-11-111-1-1iiii−i−i−i−i1-11-11-111-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1
χ181-1-111-111-1-1ii−i−iii−i−i111-11-1-1-111-1-11-111-1-1iiii−i−i−i−i1-11-11-111-1-1ii−i−iii−i−iii−i−i-1-111−i−iii-1-111−i−iii1-1−ii-11−ii-11
χ191-1-111-111-1-1ii−i−iii−i−i111-11-1-1-1-1-1111-111-1-1iiii−i−i−i−i-11-11-1111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-111−i−iii11-1-1-11-11i−i1-1−ii
χ201-1-111-111-1-1ii−i−iii−i−i111-11-1-1-1-1-1111-111-1-1iiii−i−i−i−i-11-11-1111-1-1ii−i−i−i−iii−i−iii−i−iii11-1-1ii−i−i-1-111-111-1−ii-11i−i
χ211-1-111-111-1-1ii−i−i−i−iii111-11-1-1-111-1-1-1111-1-1−i−i−i−iiiii1-11-11-1-1-111ii−i−iii−i−i−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11
χ221-1-111-111-1-1ii−i−i−i−iii111-11-1-1-111-1-1-1111-1-1−i−i−i−iiiii1-11-11-1-1-111ii−i−iii−i−i−i−iii-1-111−i−iii-1-111−i−iii-11i−i1-1i−i1-1
χ231-1-111-111-1-1ii−i−i−i−iii111-11-1-1-1-1-111-1111-1-1−i−i−i−iiiii-11-11-11-1-111ii−i−i−i−iiiii−i−iii−i−i-1-111−i−iii11-1-11-11-1−ii-11i−i
χ241-1-111-111-1-1ii−i−i−i−iii111-11-1-1-1-1-111-1111-1-1−i−i−i−iiiii-11-11-11-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-1ii−i−i-1-1111-1-11i−i1-1−ii
χ251-1-111-111-1-1−i−iiiii−i−i111-11-1-1-111-1-1-1111-1-1iiii−i−i−i−i1-11-11-1-1-111−i−iii−i−iiiii−i−i11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11
χ261-1-111-111-1-1−i−iiiii−i−i111-11-1-1-111-1-1-1111-1-1iiii−i−i−i−i1-11-11-1-1-111−i−iii−i−iiiii−i−i-1-111ii−i−i-1-111ii−i−i-11−ii1-1−ii1-1
χ271-1-111-111-1-1−i−iiiii−i−i111-11-1-1-1-1-111-1111-1-1iiii−i−i−i−i-11-11-11-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1−i−iii-1-1111-1-11−ii1-1i−i
χ281-1-111-111-1-1−i−iiiii−i−i111-11-1-1-1-1-111-1111-1-1iiii−i−i−i−i-11-11-11-1-111−i−iiiii−i−i−i−iii−i−iii-1-111ii−i−i11-1-11-11-1i−i-11−ii
χ291-1-111-111-1-1−i−iii−i−iii111-11-1-1-111-1-11-111-1-1−i−i−i−iiiii1-11-11-111-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1
χ301-1-111-111-1-1−i−iii−i−iii111-11-1-1-111-1-11-111-1-1−i−i−i−iiiii1-11-11-111-1-1−i−iii−i−iii−i−iii-1-111ii−i−i-1-111ii−i−i1-1i−i-11i−i-11
χ311-1-111-111-1-1−i−iii−i−iii111-11-1-1-1-1-1111-111-1-1−i−i−i−iiiii-11-11-1111-1-1−i−iiiii−i−iii−i−iii−i−i11-1-1−i−iii-1-111-111-1i−i-11−ii
χ321-1-111-111-1-1−i−iii−i−iii111-11-1-1-1-1-1111-111-1-1−i−i−i−iiiii-11-11-1111-1-1−i−iiiii−i−iii−i−i−i−iii-1-111ii−i−i11-1-1-11-11−ii1-1i−i
χ33222222-2-2-2-22-22-2000022222222222200-2-2-2-200000000-2-2-2-22200002-22-22-22-2000000000000000000000000000000
χ34222222-2-2-2-22-22-2000022222222-2-2-2-200-2-2-2-2000000002222-2-200002-22-2-22-22000000000000000000000000000000
χ35222222-2-2-2-2-22-22000022222222222200-2-2-2-200000000-2-2-2-2220000-22-22-22-22000000000000000000000000000000
χ36222222-2-2-2-2-22-22000022222222-2-2-2-200-2-2-2-2000000002222-2-20000-22-222-22-2000000000000000000000000000000
χ372222-2-22-22-2000000002-2-222-2-222222002-22-2000000002-2-22-2-2000000000000000000002-22-200002-22-20000000000
χ382222-2-22-22-2000000002-2-222-2-222222002-22-2000000002-2-22-2-200000000000000000000-22-220000-22-220000000000
χ392222-2-22-22-2000000002-2-222-2-22-2-2-2-2002-22-200000000-222-222000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000000000
χ402222-2-22-22-2000000002-2-222-2-22-2-2-2-2002-22-200000000-222-22200000000000000000000−2i2i−2i2i00002i−2i2i−2i0000000000
χ412222-2-2-22-22000000002-2-222-2-22222200-22-2200000000-222-2-2-200000000000000002-22-200002-22-200000000000000
χ422222-2-2-22-22000000002-2-222-2-22222200-22-2200000000-222-2-2-20000000000000000-22-220000-22-2200000000000000
χ432222-2-2-22-22000000002-2-222-2-22-2-2-2-200-22-22000000002-2-222200000000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000
χ442222-2-2-22-22000000002-2-222-2-22-2-2-2-200-22-22000000002-2-22220000000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000
χ452-2-222-2-2-2222i−2i−2i2i0000222-22-2-2-222-2-200-2-22200000000-22-222-200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ462-2-222-2-2-2222i−2i−2i2i0000222-22-2-2-2-2-22200-2-222000000002-22-2-2200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ472-2-222-2-2-222−2i2i2i−2i0000222-22-2-2-222-2-200-2-22200000000-22-222-20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ482-2-222-2-2-222−2i2i2i−2i0000222-22-2-2-2-2-22200-2-222000000002-22-2-220000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ492-2-22-222-2-22000000002-2-2-2222-222-2-2002-2-220000000022-2-2-22000000000000000000002i−2i−2i2i00002i−2i−2i2i0000000000
χ502-2-22-222-2-22000000002-2-2-2222-222-2-2002-2-220000000022-2-2-2200000000000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000
χ512-2-22-222-2-22000000002-2-2-2222-2-2-222002-2-2200000000-2-2222-2000000000000000000002-2-220000-222-20000000000
χ522-2-22-222-2-22000000002-2-2-2222-2-2-222002-2-2200000000-2-2222-200000000000000000000-222-200002-2-220000000000
χ532-2-22-22-222-2000000002-2-2-2222-222-2-200-222-200000000-2-222-2200000000000000002-2-2200002-2-2200000000000000
χ542-2-22-22-222-2000000002-2-2-2222-222-2-200-222-200000000-2-222-220000000000000000-222-20000-222-200000000000000
χ552-2-22-22-222-2000000002-2-2-2222-2-2-22200-222-20000000022-2-22-200000000000000002i−2i−2i2i0000−2i2i2i−2i00000000000000
χ562-2-22-22-222-2000000002-2-2-2222-2-2-22200-222-20000000022-2-22-20000000000000000−2i2i2i−2i00002i−2i−2i2i00000000000000
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
χ5844444444444444-4-4-4-4-1-1-1-1-1-1-1-10000-4-4-1-1-1-1111111110000001111-1-1-1-10000000000000000000000000000000000
χ594444444444-4-4-4-44444-1-1-1-1-1-1-1-10000-4-4-1-1-1-1-1-1-1-1-1-1-1-1000000111111110000000000000000000000000000000000
χ604444444444-4-4-4-4-4-4-4-4-1-1-1-1-1-1-1-1000044-1-1-1-111111111000000-1-1-1-111110000000000000000000000000000000000
χ61444444-4-4-4-44-44-40000-1-1-1-1-1-1-1-1000000111155−5−555−5−50000005−55−5-11-110000000000000000000000000000000000
χ62444444-4-4-4-44-44-40000-1-1-1-1-1-1-1-10000001111−5−555−5−555000000−55−55-11-110000000000000000000000000000000000
χ63444444-4-4-4-4-44-440000-1-1-1-1-1-1-1-1000000111155−5−555−5−5000000−55−551-11-10000000000000000000000000000000000
χ64444444-4-4-4-4-44-440000-1-1-1-1-1-1-1-10000001111−5−555−5−5550000005−55−51-11-10000000000000000000000000000000000
χ6544-4-400000000002-22-2400-4-40044i−4i4i−4i0000002-22-22-22-20000000000000000002i−2i2i−2i00000000000000000000000000
χ6644-4-400000000002-22-2400-4-4004−4i4i−4i4i0000002-22-22-22-2000000000000000000−2i2i−2i2i00000000000000000000000000
χ6744-4-40000000000-22-22400-4-40044i−4i4i−4i000000-22-22-22-22000000000000000000−2i2i−2i2i00000000000000000000000000
χ6844-4-40000000000-22-22400-4-4004−4i4i−4i4i000000-22-22-22-220000000000000000002i−2i2i−2i00000000000000000000000000
χ694-44-400000000002i−2i−2i2i4004-400-44i−4i−4i4i0000002i−2i2i−2i−2i2i−2i2i000000000000000000-222-200000000000000000000000000
χ704-44-400000000002i−2i−2i2i4004-400-4−4i4i4i−4i0000002i−2i2i−2i−2i2i−2i2i0000000000000000002-2-2200000000000000000000000000
χ714-44-40000000000−2i2i2i−2i4004-400-44i−4i−4i4i000000−2i2i−2i2i2i−2i2i−2i0000000000000000002-2-2200000000000000000000000000
χ724-44-40000000000−2i2i2i−2i4004-400-4−4i4i4i−4i000000−2i2i−2i2i2i−2i2i−2i000000000000000000-222-200000000000000000000000000
χ734-4-444-444-4-44i4i−4i−4i4i4i−4i−4i-1-1-11-111100004-4-1-111−i−i−i−iiiii000000-1-111−i−iii0000000000000000000000000000000000
χ744-4-444-444-4-44i4i−4i−4i−4i−4i4i4i-1-1-11-11110000-44-1-111iiii−i−i−i−i00000011-1-1−i−iii0000000000000000000000000000000000
χ754-4-444-444-4-4−4i−4i4i4i4i4i−4i−4i-1-1-11-11110000-44-1-111−i−i−i−iiiii00000011-1-1ii−i−i0000000000000000000000000000000000
χ764-4-444-444-4-4−4i−4i4i4i−4i−4i4i4i-1-1-11-111100004-4-1-111iiii−i−i−i−i000000-1-111ii−i−i0000000000000000000000000000000000
χ774-4-444-4-4-4444i−4i−4i4i0000-1-1-11-111100000011-1-1i5i5−i5−i5−i5−i5i5i50000005−5−55−iii−i0000000000000000000000000000000000
χ784-4-444-4-4-4444i−4i−4i4i0000-1-1-11-111100000011-1-1−i5−i5i5i5i5i5−i5−i5000000−555−5−iii−i0000000000000000000000000000000000
χ794-4-444-4-4-444−4i4i4i−4i0000-1-1-11-111100000011-1-1i5i5−i5−i5−i5−i5i5i5000000−555−5i−i−ii0000000000000000000000000000000000
χ804-4-444-4-4-444−4i4i4i−4i0000-1-1-11-111100000011-1-1−i5−i5i5i5i5i5−i5−i50000005−5−55i−i−ii0000000000000000000000000000000000
χ818888-8-88-88-800000000-222-2-222-2000000-22-2200000000000000000000000000000000000000000000000000000000
χ828888-8-8-88-8800000000-222-2-222-20000002-22-200000000000000000000000000000000000000000000000000000000
χ8388-8-800000000004-44-4-225−252225−25-20000000000−1+51−5−1−51+5−1+51−5−1−51+5000000000000000000000000000000000000000000000000
χ8488-8-800000000004-44-4-2−252522−2525-20000000000−1−51+5−1+51−5−1−51+5−1+51−5000000000000000000000000000000000000000000000000
χ8588-8-80000000000-44-44-225−252225−25-200000000001−5−1+51+5−1−51−5−1+51+5−1−5000000000000000000000000000000000000000000000000
χ8688-8-80000000000-44-44-2−252522−2525-200000000001+5−1−51−5−1+51+5−1−51−5−1+5000000000000000000000000000000000000000000000000
χ878-88-800000000004i−4i−4i4i-225−25-22−252520000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000000000000000000000000000
χ888-88-800000000004i−4i−4i4i-2−2525-2225−2520000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000000000000000000000000
χ898-88-80000000000−4i4i4i−4i-225−25-22−2525200000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000000000000000000000000000
χ908-88-80000000000−4i4i4i−4i-2−2525-2225−25200000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000000000000000000000000
χ918-8-88-888-8-8800000000-2222-2-2-22000000-222-200000000000000000000000000000000000000000000000000000000
χ928-8-88-88-888-800000000-2222-2-2-220000002-2-2200000000000000000000000000000000000000000000000000000000

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