Finite Group Databasebeta

← Group #13022603

Character table — Group #13022603

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12442224445101010202020202444881010202020202020202020202222444410102020404040402444444488888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i-1-1ii−i−iiiii−i−i−i−i
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii-1-1−i−iii−i−i−i−iiiii
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111ii−i−i11−i−iiiii−i−i−i−iii
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−i−iii11ii−i−i−i−iiiii−i−i
χ9111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111
χ10111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1
χ11111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i11−i−iii−i−iiiii−i−i
χ12111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii11ii−i−iii−i−i−i−iii
χ13111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ14111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111
χ15111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i-1-1ii−i−i−i−i−i−iiiii
χ16111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii-1-1−i−iiiiiii−i−i−i−i
χ1722222-2-22-2-22-2-2222-2-2002i−2i002-22-22i2i2i2i−2i−2i−2i−2i22-2-22-2-2200000000002i−2i000000000000000000
χ1822222-2-22-2-22-2-2222-2-2002i−2i002-22-22i2i2i2i−2i−2i−2i−2i-2-222-222-20000000000−2i2i000000000000000000
χ1922222-2-22-2-22-2-2222-2-200−2i2i002-22-2−2i−2i−2i−2i2i2i2i2i22-2-22-2-220000000000−2i2i000000000000000000
χ2022222-2-22-2-22-2-2222-2-200−2i2i002-22-2−2i−2i−2i−2i2i2i2i2i-2-222-222-200000000002i−2i000000000000000000
χ212222-22-2-2-2222222222000000-2-2-2-2000000002-22-2-2-2220000000000000000000000002-2002-2
χ222222-22-2-2-2222222222000000-2-2-2-2000000002-22-2-2-222000000000000000000000000-2200-22
χ232222-22-2-2-2222222222000000-2-2-2-200000000-22-2222-2-20000000000000000000000002i−2i00−2i2i
χ242222-22-2-2-2222222222000000-2-2-2-200000000-22-2222-2-2000000000000000000000000−2i2i002i−2i
χ252222-2-22-22-22-2-2222-2-2000000-22-22000000002-2-22-22-220000000000002-22-200000000000000
χ262222-2-22-22-22-2-2222-2-2000000-22-22000000002-2-22-22-22000000000000-22-2200000000000000
χ272222-2-22-22-22-2-2222-2-2000000-22-2200000000-222-22-22-20000000000002i−2i−2i2i00000000000000
χ282222-2-22-22-22-2-2222-2-2000000-22-2200000000-222-22-22-2000000000000−2i2i2i−2i00000000000000
χ2922-2-2222-2-2-22222-2-2-2-200000022-2-2000000002222-2-2-2-20000000000000000002i−2i2i−2i00000000
χ3022-2-2222-2-2-22222-2-2-2-200000022-2-2000000002222-2-2-2-2000000000000000000−2i2i−2i2i00000000
χ3122-2-2222-2-2-22222-2-2-2-200000022-2-200000000-2-2-2-222220000000000000000002-2-2200000000
χ3222-2-2222-2-2-22222-2-2-2-200000022-2-200000000-2-2-2-22222000000000000000000-222-200000000
χ3322-2-22-2-2-2222-2-22-2-2220000002-2-220000000022-2-2-222-200000000000000000000002i−2i002i−2i00
χ3422-2-22-2-2-2222-2-22-2-2220000002-2-220000000022-2-2-222-20000000000000000000000−2i2i00−2i2i00
χ3522-2-22-2-2-2222-2-22-2-2220000002-2-2200000000-2-2222-2-2200000000000000000000002-200-2200
χ3622-2-22-2-2-2222-2-22-2-2220000002-2-2200000000-2-2222-2-220000000000000000000000-22002-200
χ3722-2-2-22-222-22222-2-2-2-22-20000-2-222000000002-22-222-2-222-2-20000-2200000000000000000000
χ3822-2-2-22-222-22222-2-2-2-22-20000-2-22200000000-22-22-2-22222-2-200002-200000000000000000000
χ3922-2-2-22-222-22222-2-2-2-2-220000-2-222000000002-22-222-2-2-2-22200002-200000000000000000000
χ4022-2-2-22-222-22222-2-2-2-2-220000-2-22200000000-22-22-2-222-2-2220000-2200000000000000000000
χ4122-2-2-2-222-222-2-22-2-22200002-2-222-2000000002-2-222-22-2000022-2-2000000002-2000000000000
χ4222-2-2-2-222-222-2-22-2-22200002-2-222-200000000-222-2-22-22000022-2-200000000-22000000000000
χ4322-2-2-2-222-222-2-22-2-2220000-22-222-2000000002-2-222-22-20000-2-22200000000-22000000000000
χ4422-2-2-2-222-222-2-22-2-2220000-22-222-200000000-222-2-22-220000-2-222000000002-2000000000000
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
χ464444444444-1-1-1-1-1-1-1-144-4-4-4-4-1-1-1-11111111100000000-1-1-1-111110000000000000000000000
χ474444444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-100000000111111110000000000000000000000
χ484444444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-111111111000000001111-1-1-1-10000000000000000000000
χ4944444-4-44-4-4-111-1-1-111004i−4i00-11-11−i−i−i−iiiii000000005−55−5i5−i5i5−i50000000000000000000000
χ5044444-4-44-4-4-111-1-1-111004i−4i00-11-11−i−i−i−iiiii00000000−55−55−i5i5−i5i50000000000000000000000
χ5144444-4-44-4-4-111-1-1-11100−4i4i00-11-11iiii−i−i−i−i000000005−55−5−i5i5−i5i50000000000000000000000
χ5244444-4-44-4-4-111-1-1-11100−4i4i00-11-11iiii−i−i−i−i00000000−55−55i5−i5i5−i50000000000000000000000
χ5344-4-4-44-444-4-1-1-1-111114-4000011-1-1i5i5−i5−i5i5i5−i5−i500000000-1-111i5−i5−i5i50000000000000000000000
χ5444-4-4-44-444-4-1-1-1-111114-4000011-1-1−i5−i5i5i5−i5−i5i5i500000000-1-111−i5i5i5−i50000000000000000000000
χ5544-4-4-44-444-4-1-1-1-11111-44000011-1-1i5i5−i5−i5i5i5−i5−i50000000011-1-1−i5i5i5−i50000000000000000000000
χ5644-4-4-44-444-4-1-1-1-11111-44000011-1-1−i5−i5i5i5−i5−i5i5i50000000011-1-1i5−i5−i5i50000000000000000000000
χ5744-4-4-4-444-44-111-111-1-100004-41-1-1155−5−5−5−555000000005−5−55-1-1110000000000000000000000
χ5844-4-4-4-444-44-111-111-1-100004-41-1-11−5−55555−5−500000000−555−5-1-1110000000000000000000000
χ5944-4-4-4-444-44-111-111-1-10000-441-1-1155−5−5−5−55500000000−555−511-1-10000000000000000000000
χ6044-4-4-4-444-44-111-111-1-10000-441-1-11−5−55555−5−5000000005−5−5511-1-10000000000000000000000
χ618888-88-8-8-88-2-2-2-2-2-2-2-200000022220000000000000000000000000000000000000000000000
χ628888-8-88-88-8-222-2-2-2220000002-22-20000000000000000000000000000000000000000000000
χ6388-8-8888-8-8-8-2-2-2-22222000000-2-2220000000000000000000000000000000000000000000000
χ6488-8-88-8-8-888-222-222-2-2000000-222-20000000000000000000000000000000000000000000000
χ658-88i−8i000000800-88i−8i0000000000000000000000000000000000000000000000000000000000
χ668-88i−8i000000-225−252−2i2i2i5−2i50000000000−ζ2−ζ3−ζ6+ζ7−ζ11+ζ14+ζ18+ζ19ζ2+ζ3+ζ6−ζ7+ζ11−ζ14−ζ18−ζ19−ζ2+ζ3+ζ6−ζ7−ζ11−ζ14+ζ18+ζ19ζ2−ζ3−ζ6+ζ7+ζ11+ζ14−ζ18−ζ19−ζ2−ζ3+ζ6+ζ7+ζ11−ζ14+ζ18−ζ19ζ2+ζ3−ζ6−ζ7−ζ11+ζ14−ζ18+ζ19−ζ2+ζ3−ζ6−ζ7+ζ11+ζ14+ζ18−ζ19ζ2−ζ3+ζ6+ζ7−ζ11−ζ14−ζ18+ζ1900000000000000000000000000000000000000
χ678-88i−8i000000-225−252−2i2i2i5−2i50000000000ζ2+ζ3+ζ6−ζ7+ζ11−ζ14−ζ18−ζ19−ζ2−ζ3−ζ6+ζ7−ζ11+ζ14+ζ18+ζ19ζ2−ζ3−ζ6+ζ7+ζ11+ζ14−ζ18−ζ19−ζ2+ζ3+ζ6−ζ7−ζ11−ζ14+ζ18+ζ19ζ2+ζ3−ζ6−ζ7−ζ11+ζ14−ζ18+ζ19−ζ2−ζ3+ζ6+ζ7+ζ11−ζ14+ζ18−ζ19ζ2−ζ3+ζ6+ζ7−ζ11−ζ14−ζ18+ζ19−ζ2+ζ3−ζ6−ζ7+ζ11+ζ14+ζ18−ζ1900000000000000000000000000000000000000
χ688-88i−8i000000-2−25252−2i2i−2i52i50000000000−ζ2+ζ3+ζ6−ζ7−ζ11−ζ14+ζ18+ζ19ζ2−ζ3−ζ6+ζ7+ζ11+ζ14−ζ18−ζ19ζ2+ζ3+ζ6−ζ7+ζ11−ζ14−ζ18−ζ19−ζ2−ζ3−ζ6+ζ7−ζ11+ζ14+ζ18+ζ19ζ2−ζ3+ζ6+ζ7−ζ11−ζ14−ζ18+ζ19−ζ2+ζ3−ζ6−ζ7+ζ11+ζ14+ζ18−ζ19−ζ2−ζ3+ζ6+ζ7+ζ11−ζ14+ζ18−ζ19ζ2+ζ3−ζ6−ζ7−ζ11+ζ14−ζ18+ζ1900000000000000000000000000000000000000
χ698-88i−8i000000-2−25252−2i2i−2i52i50000000000ζ2−ζ3−ζ6+ζ7+ζ11+ζ14−ζ18−ζ19−ζ2+ζ3+ζ6−ζ7−ζ11−ζ14+ζ18+ζ19−ζ2−ζ3−ζ6+ζ7−ζ11+ζ14+ζ18+ζ19ζ2+ζ3+ζ6−ζ7+ζ11−ζ14−ζ18−ζ19−ζ2+ζ3−ζ6−ζ7+ζ11+ζ14+ζ18−ζ19ζ2−ζ3+ζ6+ζ7−ζ11−ζ14−ζ18+ζ19ζ2+ζ3−ζ6−ζ7−ζ11+ζ14−ζ18+ζ19−ζ2−ζ3+ζ6+ζ7+ζ11−ζ14+ζ18−ζ1900000000000000000000000000000000000000
χ708-8−8i8i000000800-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000000-225−2522i−2i−2i52i50000000000−ζ2+ζ3−ζ6−ζ7+ζ11+ζ14+ζ18−ζ19ζ2−ζ3+ζ6+ζ7−ζ11−ζ14−ζ18+ζ19−ζ2−ζ3+ζ6+ζ7+ζ11−ζ14+ζ18−ζ19ζ2+ζ3−ζ6−ζ7−ζ11+ζ14−ζ18+ζ19−ζ2+ζ3+ζ6−ζ7−ζ11−ζ14+ζ18+ζ19ζ2−ζ3−ζ6+ζ7+ζ11+ζ14−ζ18−ζ19−ζ2−ζ3−ζ6+ζ7−ζ11+ζ14+ζ18+ζ19ζ2+ζ3+ζ6−ζ7+ζ11−ζ14−ζ18−ζ1900000000000000000000000000000000000000
χ728-8−8i8i000000-225−2522i−2i−2i52i50000000000ζ2−ζ3+ζ6+ζ7−ζ11−ζ14−ζ18+ζ19−ζ2+ζ3−ζ6−ζ7+ζ11+ζ14+ζ18−ζ19ζ2+ζ3−ζ6−ζ7−ζ11+ζ14−ζ18+ζ19−ζ2−ζ3+ζ6+ζ7+ζ11−ζ14+ζ18−ζ19ζ2−ζ3−ζ6+ζ7+ζ11+ζ14−ζ18−ζ19−ζ2+ζ3+ζ6−ζ7−ζ11−ζ14+ζ18+ζ19ζ2+ζ3+ζ6−ζ7+ζ11−ζ14−ζ18−ζ19−ζ2−ζ3−ζ6+ζ7−ζ11+ζ14+ζ18+ζ1900000000000000000000000000000000000000
χ738-8−8i8i000000-2−252522i−2i2i5−2i50000000000−ζ2−ζ3+ζ6+ζ7+ζ11−ζ14+ζ18−ζ19ζ2+ζ3−ζ6−ζ7−ζ11+ζ14−ζ18+ζ19ζ2−ζ3+ζ6+ζ7−ζ11−ζ14−ζ18+ζ19−ζ2+ζ3−ζ6−ζ7+ζ11+ζ14+ζ18−ζ19ζ2+ζ3+ζ6−ζ7+ζ11−ζ14−ζ18−ζ19−ζ2−ζ3−ζ6+ζ7−ζ11+ζ14+ζ18+ζ19−ζ2+ζ3+ζ6−ζ7−ζ11−ζ14+ζ18+ζ19ζ2−ζ3−ζ6+ζ7+ζ11+ζ14−ζ18−ζ1900000000000000000000000000000000000000
χ748-8−8i8i000000-2−252522i−2i2i5−2i50000000000ζ2+ζ3−ζ6−ζ7−ζ11+ζ14−ζ18+ζ19−ζ2−ζ3+ζ6+ζ7+ζ11−ζ14+ζ18−ζ19−ζ2+ζ3−ζ6−ζ7+ζ11+ζ14+ζ18−ζ19ζ2−ζ3+ζ6+ζ7−ζ11−ζ14−ζ18+ζ19−ζ2−ζ3−ζ6+ζ7−ζ11+ζ14+ζ18+ζ19ζ2+ζ3+ζ6−ζ7+ζ11−ζ14−ζ18−ζ19ζ2−ζ3−ζ6+ζ7+ζ11+ζ14−ζ18−ζ19−ζ2+ζ3+ζ6−ζ7−ζ11−ζ14+ζ18+ζ1900000000000000000000000000000000000000

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