Finite Group Databasebeta

← Group #13022451

Character table — Group #13022451

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12442224445101010202020202244441010101010102020202020202222444410102020202020202244444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ51111111111111111111-11-1-1-111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111-11-1-1-111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111-11-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111-11-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111111111-11-11-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-111-11-11-1-111-1-111-1-111-1-111-1-1
χ10111111111111111111-11-11-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-111-11-11-1-1-1-111-1-111-1-111-1-111
χ11111111111111111111-11-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-11-111ii−i−i−i−iiiii−i−i−i−iii
χ12111111111111111111-11-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-11-111−i−iiiii−i−i−i−iiiii−i−i
χ13111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222-2-22-2-22-2-2222-2-20000002-200002-2000022-2-22-22-200000000000000002i−2i002i−2i00000000
χ1822222-2-22-2-22-2-2222-2-20000002-200002-2000022-2-22-22-20000000000000000−2i2i00−2i2i00000000
χ1922222-2-22-2-22-2-2222-2-20000002-200002-20000-2-222-22-2200000000000000002-200-2200000000
χ2022222-2-22-2-22-2-2222-2-20000002-200002-20000-2-222-22-220000000000000000-22002-200000000
χ212222-22-2-22-22-2-2222-2-2000000-220000-2200002-22-222-2-200000000000000000000002i−2i002i−2i00
χ222222-22-2-22-22-2-2222-2-2000000-220000-2200002-22-222-2-20000000000000000000000−2i2i00−2i2i00
χ232222-22-2-22-22-2-2222-2-2000000-220000-220000-22-22-2-22200000000000000000000002-200-2200
χ242222-22-2-22-22-2-2222-2-2000000-220000-220000-22-22-2-2220000000000000000000000-22002-200
χ252222-2-22-2-222222222200002-2-2-20000-2-200002-2-222-2-220022-2-20000002-20000000000000000
χ262222-2-22-2-222222222200002-2-2-20000-2-20000-222-2-222-20022-2-2000000-220000000000000000
χ272222-2-22-2-22222222220000-22-2-20000-2-200002-2-222-2-2200-2-222000000-220000000000000000
χ282222-2-22-2-22222222220000-22-2-20000-2-20000-222-2-222-200-2-2220000002-20000000000000000
χ2922-2-2222-2-2-22222-2-2-2-220-2000222222-2-2-2-2-2-22222-2-2-2-200000000-2020000000000000000000
χ3022-2-2222-2-2-22222-2-2-2-220-2000222222-2-2-2-2-2-2-2-2-2-222220000000020-20000000000000000000
χ3122-2-2222-2-2-22222-2-2-2-2-20200022-2-2-2-2-2-222222222-2-2-2-20000000020-20000000000000000000
χ3222-2-2222-2-2-22222-2-2-2-2-20200022-2-2-2-2-2-22222-2-2-2-2222200000000-2020000000000000000000
χ3322-2-22-2-2-2222-2-22-2-2220000002-20000-22000022-2-2-22-22000000000000002i−2i002i−2i0000000000
χ3422-2-22-2-2-2222-2-22-2-2220000002-20000-22000022-2-2-22-2200000000000000−2i2i00−2i2i0000000000
χ3522-2-22-2-2-2222-2-22-2-2220000002-20000-220000-2-2222-22-2000000000000002-200-220000000000
χ3622-2-22-2-2-2222-2-22-2-2220000002-20000-220000-2-2222-22-200000000000000-22002-20000000000
χ3722-2-2-22-22-222-2-22-2-222000000-2200002-200002-22-2-2-2220000000000000000000000002-2002-2
χ3822-2-2-22-22-222-2-22-2-222000000-2200002-200002-22-2-2-222000000000000000000000000-2200-22
χ3922-2-2-22-22-222-2-22-2-222000000-2200002-20000-22-2222-2-20000000000000000000000002i−2i00−2i2i
χ4022-2-2-22-22-222-2-22-2-222000000-2200002-20000-22-2222-2-2000000000000000000000000−2i2i002i−2i
χ4122-2-2-2-2222-22222-2-2-2-2020-200-2-200002200002-2-22-222-2220000-2-20-202000000000000000000
χ4222-2-2-2-2222-22222-2-2-2-2020-200-2-20000220000-222-22-2-22220000-2-2020-2000000000000000000
χ4322-2-2-2-2222-22222-2-2-2-20-20200-2-200002200002-2-22-222-2-2-2000022020-2000000000000000000
χ4422-2-2-2-2222-22222-2-2-2-20-20200-2-20000220000-222-22-2-22-2-20000220-202000000000000000000
χ454444444444-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444-1-1-1-1-1-1-1-14-44-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000000111111110000000000000000000000
χ474444444444-1-1-1-1-1-1-1-1-44-44-4-4-1-11111-1-1111100000000-1-11111-1-10000000000000000000000
χ484444444444-1-1-1-1-1-1-1-1-4-4-4-444-1-11111-1-111110000000011-1-1-1-1110000000000000000000000
χ494444-4-44-4-44-1-1-1-1-1-1-1-100004-41155−5−51155−5−5000000005−5-1-1115−50000000000000000000000
χ504444-4-44-4-44-1-1-1-1-1-1-1-100004-411−5−55511−5−55500000000−55-1-111−550000000000000000000000
χ514444-4-44-4-44-1-1-1-1-1-1-1-10000-441155−5−51155−5−500000000−5511-1-1−550000000000000000000000
χ524444-4-44-4-44-1-1-1-1-1-1-1-10000-4411−5−55511−5−555000000005−511-1-15−50000000000000000000000
χ5344-4-4444-4-4-4-1-1-1-1111140-4000-1-1-1-1-1-1111111000000005−55−55−5−550000000000000000000000
χ5444-4-4444-4-4-4-1-1-1-1111140-4000-1-1-1-1-1-111111100000000−55−55−555−50000000000000000000000
χ5544-4-4444-4-4-4-1-1-1-11111-404000-1-1111111-1-1-1-1000000005−5−55−55−550000000000000000000000
χ5644-4-4444-4-4-4-1-1-1-11111-404000-1-1111111-1-1-1-100000000−555−55−55−50000000000000000000000
χ5744-4-4-4-4444-4-1-1-1-11111040-4001155−5−5-1-1−5−55500000000-1-15−5−55110000000000000000000000
χ5844-4-4-4-4444-4-1-1-1-11111040-40011−5−555-1-155−5−500000000-1-1−555−5110000000000000000000000
χ5944-4-4-4-4444-4-1-1-1-111110-404001155−5−5-1-1−5−5550000000011−555−5-1-10000000000000000000000
χ6044-4-4-4-4444-4-1-1-1-111110-4040011−5−555-1-155−5−500000000115−5−55-1-10000000000000000000000
χ6188888-8-88-8-8-222-2-2-222000000-220000-22000000000000000000000000000000000000000000
χ628888-88-8-88-8-222-2-2-2220000002-200002-2000000000000000000000000000000000000000000
χ6388-8-88-8-8-888-222-222-2-2000000-2200002-2000000000000000000000000000000000000000000
χ6488-8-8-88-88-88-222-222-2-20000002-20000-22000000000000000000000000000000000000000000
χ658-88i−8i000000800-88i−8i0000000000000000000000000000000000000000000000000000000000
χ668-88i−8i000000-225−252−2i2i2i5−2i5000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000000000000000
χ678-88i−8i000000-225−252−2i2i2i5−2i500000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000000000000000
χ688-88i−8i000000-2−25252−2i2i−2i52i500000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000000000000000
χ698-88i−8i000000-2−25252−2i2i−2i52i5000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000000000000000
χ708-8−8i8i000000800-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000000-225−2522i−2i−2i52i5000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000000000000000
χ728-8−8i8i000000-225−2522i−2i−2i52i500000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000000000000000
χ738-8−8i8i000000-2−252522i−2i2i5−2i500000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000000000000000
χ748-8−8i8i000000-2−252522i−2i2i5−2i5000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000000000000000

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