Finite Group Databasebeta

← Group #13022893

Character table — Group #13022893

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12222222225101010101010104444441010101020202020202020202222222220202020202020204444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ14111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ15111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2-2-2222-2-22-2-200002i−2i22-2-20000000022-2-222-2-200002i2i−2i−2i00002i−2i0000000000000000
χ18222222-2-2-2-2222-2-22-2-200002i−2i22-2-200000000-2-222-2-22200002i2i−2i−2i0000−2i2i0000000000000000
χ19222222-2-2-2-2222-2-22-2-20000−2i2i22-2-20000000022-2-222-2-20000−2i−2i2i2i0000−2i2i0000000000000000
χ20222222-2-2-2-2222-2-22-2-20000−2i2i22-2-200000000-2-222-2-2220000−2i−2i2i2i00002i−2i0000000000000000
χ212222-2-222-2-2222-2-22-2-2002i−2i00-2-222000000002-22-22-22-22i2i−2i−2i0000002i−2i000000000000000000
χ222222-2-222-2-2222-2-22-2-2002i−2i00-2-22200000000-22-22-22-222i2i−2i−2i000000−2i2i000000000000000000
χ232222-2-222-2-2222-2-22-2-200−2i2i00-2-222000000002-22-22-22-2−2i−2i2i2i000000−2i2i000000000000000000
χ242222-2-222-2-2222-2-22-2-200−2i2i00-2-22200000000-22-22-22-22−2i−2i2i2i0000002i−2i000000000000000000
χ252222-2-2-2-222222222222-20000-2-2-2-22222-2-2-2-22-2-222-2-22000000002-200000000000000000000
χ262222-2-2-2-222222222222-20000-2-2-2-22222-2-2-2-2-222-2-222-200000000-2200000000000000000000
χ272222-2-2-2-22222222222-220000-2-2-2-2-2-2-2-222222-2-222-2-2200000000-2200000000000000000000
χ282222-2-2-2-22222222222-220000-2-2-2-2-2-2-2-22222-222-2-222-2000000002-200000000000000000000
χ2922-2-22-22-22-222-222-2-2-20000002-22-200000000222-2-2-2-2200000000000000002-20000002-20000
χ3022-2-22-22-22-222-222-2-2-20000002-22-200000000222-2-2-2-220000000000000000-22000000-220000
χ3122-2-22-22-22-222-222-2-2-20000002-22-200000000-2-2-22222-200000000000000002i−2i000000−2i2i0000
χ3222-2-22-22-22-222-222-2-2-20000002-22-200000000-2-2-22222-20000000000000000−2i2i0000002i−2i0000
χ3322-2-22-2-22-2222-2-2-2-2220000002-2-220000000022-22-2-22-20000000000000000002i−2i0000002i−2i00
χ3422-2-22-2-22-2222-2-2-2-2220000002-2-220000000022-22-2-22-2000000000000000000−2i2i000000−2i2i00
χ3522-2-22-2-22-2222-2-2-2-2220000002-2-2200000000-2-22-222-220000000000000000002-2000000-2200
χ3622-2-22-2-22-2222-2-2-2-2220000002-2-2200000000-2-22-222-22000000000000000000-220000002-200
χ3722-2-2-222-2-2222-2-2-2-222000000-222-2000000002-222-22-2-2000000000000000000002i−2i0000002i−2i
χ3822-2-2-222-2-2222-2-2-2-222000000-222-2000000002-222-22-2-200000000000000000000−2i2i000000−2i2i
χ3922-2-2-222-2-2222-2-2-2-222000000-222-200000000-22-2-22-222000000000000000000002-2000000-22
χ4022-2-2-222-2-2222-2-2-2-222000000-222-200000000-22-2-22-22200000000000000000000-220000002-2
χ4122-2-2-22-222-222-222-2-2-2000000-22-22000000002-2-2-2-2222000000000000002i−2i0000002i−2i000000
χ4222-2-2-22-222-222-222-2-2-2000000-22-22000000002-2-2-2-222200000000000000−2i2i000000−2i2i000000
χ4322-2-2-22-222-222-222-2-2-2000000-22-2200000000-22222-2-2-2000000000000002-2000000-22000000
χ4422-2-2-22-222-222-222-2-2-2000000-22-2200000000-22222-2-2-200000000000000-220000002-2000000
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
χ49444444-4-4-4-4-1-1-111-11100004i−4i-1-11155−5−555−5−500000000i5−i5i5−i5−i−iii0000000000000000000000
χ50444444-4-4-4-4-1-1-111-11100004i−4i-1-111−5−555−5−55500000000−i5i5−i5i5−i−iii0000000000000000000000
χ51444444-4-4-4-4-1-1-111-1110000−4i4i-1-11155−5−555−5−500000000−i5i5−i5i5ii−i−i0000000000000000000000
χ52444444-4-4-4-4-1-1-111-1110000−4i4i-1-111−5−555−5−55500000000i5−i5i5−i5ii−i−i0000000000000000000000
χ534444-4-444-4-4-1-1-111-111004i−4i0011-1-155−5−5−5−55500000000−i−iiii5−i5i5−i50000000000000000000000
χ544444-4-444-4-4-1-1-111-111004i−4i0011-1-1−5−55555−5−500000000−i−iii−i5i5−i5i50000000000000000000000
χ554444-4-444-4-4-1-1-111-11100−4i4i0011-1-155−5−5−5−55500000000ii−i−i−i5i5−i5i50000000000000000000000
χ564444-4-444-4-4-1-1-111-11100−4i4i0011-1-1−5−55555−5−500000000ii−i−ii5−i5i5−i50000000000000000000000
χ574444-4-4-4-444-1-1-1-1-1-1-1-14-400001111-1-1-1-11111000000005−5−555−5−550000000000000000000000
χ584444-4-4-4-444-1-1-1-1-1-1-1-14-400001111-1-1-1-1111100000000−555−5−555−50000000000000000000000
χ594444-4-4-4-444-1-1-1-1-1-1-1-1-44000011111111-1-1-1-1000000005−5−55−555−50000000000000000000000
χ604444-4-4-4-444-1-1-1-1-1-1-1-1-44000011111111-1-1-1-100000000−555−55−5−550000000000000000000000
χ6188-8-88-88-88-8-2-22-2-2222000000-22-220000000000000000000000000000000000000000000000
χ6288-8-88-8-88-88-2-22222-2-2000000-222-20000000000000000000000000000000000000000000000
χ6388-8-8-888-8-88-2-22222-2-20000002-2-220000000000000000000000000000000000000000000000
χ6488-8-8-88-888-8-2-22-2-22220000002-22-20000000000000000000000000000000000000000000000
χ658-88-80000008-8-80080000000000000000000000000000000000000000000000000000000000
χ668-88-8000000-22225−25-225−2500000000000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ1800000000000000000000000000000000000000
χ678-88-8000000-22225−25-225−25000000000000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ1800000000000000000000000000000000000000
χ688-88-8000000-222−2525-2−252500000000000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ1800000000000000000000000000000000000000
χ698-88-8000000-222−2525-2−2525000000000000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ1800000000000000000000000000000000000000
χ708-8-880000008-8800-80000000000000000000000000000000000000000000000000000000000
χ718-8-88000000-22-225−252−25250000000000−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ19000000000000000000000000000000000000000000
χ728-8-88000000-22-225−252−252500000000002ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19000000000000000000000000000000000000000000
χ738-8-88000000-22-2−2525225−2500000000002ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ19000000000000000000000000000000000000000000
χ748-8-88000000-22-2−2525225−250000000000−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ19000000000000000000000000000000000000000000

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