Finite Group Databasebeta

← Group #13022772

Character table — Group #13022772

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12442224445101010202020204488881010202020202020202020202222444440404040404040404444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-111
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii1111ii−i−i−i−iii
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i1111−i−iiiii−i−i
χ9111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ10111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ11111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i-1-111−i−i−i−iiiii
χ12111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiii-1-111iiii−i−i−i−i
χ13111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-111-1-111-1-111
χ14111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ16111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222-2-22-2-222-2-222-2-20000002-22-2000000002-22-222-2-20000000000002-2002-2000000000000
χ1822222-2-22-2-222-2-222-2-20000002-22-2000000002-22-222-2-2000000000000-2200-22000000000000
χ1922222-2-22-2-222-2-222-2-20000002-22-200000000-22-22-2-2220000000000002i−2i00−2i2i000000000000
χ2022222-2-22-2-222-2-222-2-20000002-22-200000000-22-22-2-222000000000000−2i2i002i−2i000000000000
χ212222-22-2-22-222-2-222-2-2000000-22-22000000002-2-222-22-200000000002-2002-200000000000000
χ222222-22-2-22-222-2-222-2-2000000-22-22000000002-2-222-22-20000000000-2200-2200000000000000
χ232222-22-2-22-222-2-222-2-2000000-22-2200000000-222-2-22-2200000000002i−2i00−2i2i00000000000000
χ242222-22-2-22-222-2-222-2-2000000-22-2200000000-222-2-22-220000000000−2i2i002i−2i00000000000000
χ252222-2-22-2-2222222222002-200-2-2-2-20000000022-2-22-2-2222-2-2000000000000002-20000000000
χ262222-2-22-2-2222222222002-200-2-2-2-200000000-2-222-222-222-2-200000000000000-220000000000
χ272222-2-22-2-222222222200-2200-2-2-2-20000000022-2-22-2-22-2-22200000000000000-220000000000
χ282222-2-22-2-222222222200-2200-2-2-2-200000000-2-222-222-2-2-222000000000000002-20000000000
χ2922-2-2222-2-2-22222-2-2-2-200002i−2i22-2-2000000002222-2-2-2-200002i2i−2i−2i0000000000002i−2i00000000
χ3022-2-2222-2-2-22222-2-2-2-200002i−2i22-2-200000000-2-2-2-2222200002i2i−2i−2i000000000000−2i2i00000000
χ3122-2-2222-2-2-22222-2-2-2-20000−2i2i22-2-2000000002222-2-2-2-20000−2i−2i2i2i000000000000−2i2i00000000
χ3222-2-2222-2-2-22222-2-2-2-20000−2i2i22-2-200000000-2-2-2-222220000−2i−2i2i2i0000000000002i−2i00000000
χ3322-2-22-2-2-22222-2-2-2-2220000002-2-22000000002-22-2-2-22200000000000000000000002-2002-200
χ3422-2-22-2-2-22222-2-2-2-2220000002-2-22000000002-22-2-2-2220000000000000000000000-2200-2200
χ3522-2-22-2-2-22222-2-2-2-2220000002-2-2200000000-22-2222-2-200000000000000000000002i−2i00−2i2i00
χ3622-2-22-2-2-22222-2-2-2-2220000002-2-2200000000-22-2222-2-20000000000000000000000−2i2i002i−2i00
χ3722-2-2-22-22-2222-2-2-2-222000000-222-2000000002-2-22-22-220000000000000000000000002-2002-2
χ3822-2-2-22-22-2222-2-2-2-222000000-222-2000000002-2-22-22-22000000000000000000000000-2200-22
χ3922-2-2-22-22-2222-2-2-2-222000000-222-200000000-222-22-22-20000000000000000000000002i−2i00−2i2i
χ4022-2-2-22-22-2222-2-2-2-222000000-222-200000000-222-22-22-2000000000000000000000000−2i2i002i−2i
χ4122-2-2-2-2222-22222-2-2-2-22-20000-2-2222222-2-2-2-222-2-2-222-2000000002-200000000000000000000
χ4222-2-2-2-2222-22222-2-2-2-22-20000-2-2222222-2-2-2-2-2-2222-2-2200000000-2200000000000000000000
χ4322-2-2-2-2222-22222-2-2-2-2-220000-2-222-2-2-2-2222222-2-2-222-200000000-2200000000000000000000
χ4422-2-2-2-2222-22222-2-2-2-2-220000-2-222-2-2-2-22222-2-2222-2-22000000002-200000000000000000000
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
χ464444444444-1-1-1-1-1-1-1-144-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000000111111110000000000000000000000
χ474444444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-11111111100000000-1-1-1-111110000000000000000000000
χ484444444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-111111111000000001111-1-1-1-10000000000000000000000
χ494444-4-44-4-44-1-1-1-1-1-1-1-1004-400111155−5−555−5−500000000-1-1115−55−50000000000000000000000
χ504444-4-44-4-44-1-1-1-1-1-1-1-1004-4001111−5−555−5−55500000000-1-111−55−550000000000000000000000
χ514444-4-44-4-44-1-1-1-1-1-1-1-100-4400111155−5−555−5−50000000011-1-1−55−550000000000000000000000
χ524444-4-44-4-44-1-1-1-1-1-1-1-100-44001111−5−555−5−5550000000011-1-15−55−50000000000000000000000
χ5344-4-4444-4-4-4-1-1-1-1111100004i−4i-1-11155−5−5−5−55500000000i5−i5i5−i5−i−iii0000000000000000000000
χ5444-4-4444-4-4-4-1-1-1-1111100004i−4i-1-111−5−55555−5−500000000−i5i5−i5i5−i−iii0000000000000000000000
χ5544-4-4444-4-4-4-1-1-1-111110000−4i4i-1-11155−5−5−5−55500000000−i5i5−i5i5ii−i−i0000000000000000000000
χ5644-4-4444-4-4-4-1-1-1-111110000−4i4i-1-111−5−55555−5−500000000i5−i5i5−i5ii−i−i0000000000000000000000
χ5744-4-4-4-4444-4-1-1-1-111114-4000011-1-1-1-1-1-1111100000000i5−i5−i5i5i5−i5−i5i50000000000000000000000
χ5844-4-4-4-4444-4-1-1-1-111114-4000011-1-1-1-1-1-1111100000000−i5i5i5−i5−i5i5i5−i50000000000000000000000
χ5944-4-4-4-4444-4-1-1-1-11111-44000011-1-11111-1-1-1-100000000i5−i5−i5i5−i5i5i5−i50000000000000000000000
χ6044-4-4-4-4444-4-1-1-1-11111-44000011-1-11111-1-1-1-100000000−i5i5i5−i5i5−i5−i5i50000000000000000000000
χ6188888-8-88-8-8-2-222-2-222000000-22-220000000000000000000000000000000000000000000000
χ628888-88-8-88-8-2-222-2-2220000002-22-20000000000000000000000000000000000000000000000
χ6388-8-88-8-8-888-2-22222-2-2000000-222-20000000000000000000000000000000000000000000000
χ6488-8-8-88-88-88-2-22222-2-20000002-2-220000000000000000000000000000000000000000000000
χ658-88i−8i0000008-8008i−8i0000000000000000000000000000000000000000000000000000000000
χ668-88i−8i000000-2225−25−2i2i2i5−2i500000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000
χ678-88i−8i000000-2225−25−2i2i2i5−2i50000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000
χ688-88i−8i000000-22−2525−2i2i−2i52i50000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000000000
χ698-88i−8i000000-22−2525−2i2i−2i52i500000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000000000
χ708-8−8i8i0000008-800−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000000-2225−252i−2i−2i52i500000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000
χ728-8−8i8i000000-2225−252i−2i−2i52i50000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000
χ738-8−8i8i000000-22−25252i−2i2i5−2i50000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000000000
χ748-8−8i8i000000-22−25252i−2i2i5−2i500000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000000000

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