Finite Group Databasebeta

← Group #13023900

Character table — Group #13023900

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122224444444448888888888888810101010101010101010161620202032323232404040404040404040404040404040408080
order1222224445888810101010102020202040404040404040404444448888444882020202088888888161616161616161644
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111-1-111-1111-1-1111-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-11
χ101111-1-111-1111-1-1111-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-11
χ111111-1-111-1111-1-1111-1-11-1-111111-1-1-1-111-1-1111111-11-1-1-111-1-111-1-111-1-1-1-111-1-1111-1
χ121111-1-111-1111-1-1111-1-11-1-111111-1-1-1-111-1-1111111-11-1-1-111-1-1-1-111-1-11111-1-111-1-11-1
χ131111-1-111-1111-1-1111-1-11-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-1-111ii−i−i−i−iiiii−i−i−i−iii1-1
χ141111-1-111-1111-1-1111-1-11-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-1-111−i−iiiii−i−i−i−iiiii−i−i1-1
χ151111-1-111-1111-1-1111-1-11-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i-11
χ161111-1-111-1111-1-1111-1-11-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii-11
χ172222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2222222-2-2-2-2002-2-20000000000000000000000
χ182222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200-2220000000000000000000000
χ19222222-2-2-22000022222-2-2-2-20000000022-2-2-2-2000000200000000000000i2−i2i2−i2i2−i2i2−i200
χ20222222-2-2-22000022222-2-2-2-20000000022-2-2-2-2000000200000000000000−i2i2−i2i2−i2i2−i2i200
χ21222222-2-2-22000022222-2-2-2-200000000-2-22222000000-2000000000000002−22−2−22−2200
χ22222222-2-2-22000022222-2-2-2-200000000-2-22222000000-200000000000000−22−222−22−200
χ232222-2-222-22-2-222222-2-22-2-22-2-2-2-2222222-2-222-2-2-2-200-2220000000000000000000000
χ242222-2-222-22-2-222222-2-22-2-22-2-2-2-22222-2-222-2-22222002-2-20000000000000000000000
χ252222-2-2-2-2220000222-2-2-222-2000000002222-2-2000000-200000000000000i2−i2−i2i2i2−i2−i2i200
χ262222-2-2-2-2220000222-2-2-222-2000000002222-2-2000000-200000000000000−i2i2i2−i2−i2i2i2−i200
χ272222-2-2-2-2220000222-2-2-222-200000000-2-2-2-2220000002000000000000002−2−22−222−200
χ282222-2-2-2-2220000222-2-2-222-200000000-2-2-2-222000000200000000000000−222−22−2−2200
χ292-22-2002-2022-200-2-2200-200222-2-200002i−2i002i−2i2i2i−2i−2i00000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ302-22-2002-2022-200-2-2200-200222-2-200002i−2i002i−2i2i2i−2i−2i000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ312-22-2002-2022-200-2-2200-200222-2-20000−2i2i00−2i2i−2i−2i2i2i00000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ322-22-2002-2022-200-2-2200-200222-2-20000−2i2i00−2i2i−2i−2i2i2i000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ332-22-2002-202-2200-2-2200-2002-2-22200002i−2i002i−2i−2i−2i2i2i000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ342-22-2002-202-2200-2-2200-2002-2-22200002i−2i002i−2i−2i−2i2i2i0000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ352-22-2002-202-2200-2-2200-2002-2-2220000−2i2i00−2i2i2i2i−2i−2i000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ362-22-2002-202-2200-2-2200-2002-2-2220000−2i2i00−2i2i2i2i−2i−2i0000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ37444444444-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000044000-1-1-1-1000000000000000000
χ38444444444-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000-4-40001111000000000000000000
χ39444444444-1-4-4-4-4-1-1-1-1-1-1-1-1-1111111110000000000000005−55−5000000000000000000
χ40444444444-1-4-4-4-4-1-1-1-1-1-1-1-1-111111111000000000000000−55−55000000000000000000
χ414444-4-444-4-144-4-4-1-1-111-111-1-1-1-1-1111100000000004-400011-1-1000000000000000000
χ424444-4-444-4-144-4-4-1-1-111-111-1-1-1-1-111110000000000-44000-1-111000000000000000000
χ434444-4-444-4-1-4-444-1-1-111-111-11111-1-1-1-10000000000000005−5−55000000000000000000
χ444444-4-444-4-1-4-444-1-1-111-111-11111-1-1-1-1000000000000000−555−5000000000000000000
χ4544-4-44-4000400004-4-44-400000000000000000022−2222−2200022−220000000000000000000000
χ4644-4-44-4000400004-4-44-4000000000000000000−2222−2222000−22220000000000000000000000
χ4744-4-4-44000400004-4-4-4400000000000000000022−2222−22000−22220000000000000000000000
χ4844-4-4-44000400004-4-4-44000000000000000000−2222−222200022−220000000000000000000000
χ494-44-400-44040000-4-4400400-4000000004i−4i00−4i4i0000000000000000000000000000000
χ504-44-400-44040000-4-4400400-400000000−4i4i004i−4i0000000000000000000000000000000
χ514-4-44000004002i2−2i2-44-400000000002i22i2−2i2−2i2004-4002i2−2i2−2i22i2000000000000000000000000000
χ524-4-44000004002i2−2i2-44-400000000002i22i2−2i2−2i200-4400−2i22i22i2−2i2000000000000000000000000000
χ534-4-4400000400−2i22i2-44-40000000000−2i2−2i22i22i2004-400−2i22i22i2−2i2000000000000000000000000000
χ544-4-4400000400−2i22i2-44-40000000000−2i2−2i22i22i200-44002i2−2i2−2i22i2000000000000000000000000000
χ55888888-8-8-8-20000-2-2-2-2-22222000000000000000000000000000000000000000000000
χ568888-8-8-8-88-20000-2-2-2222-2-22000000000000000000000000000000000000000000000
χ5788-8-88-8000-20000-222-22000010−1010−1010−1010−100000000000000000000000000000000000000
χ5888-8-88-8000-20000-222-220000−1010−1010−1010−10100000000000000000000000000000000000000
χ5988-8-8-88000-20000-2222-2000010−1010−10−1010−10100000000000000000000000000000000000000
χ6088-8-8-88000-20000-2222-20000−1010−101010−1010−100000000000000000000000000000000000000
χ618-88-8008-80-28-80022-200200-2-2-22200000000000000000000000000000000000000000
χ628-88-8008-80-2-880022-200200-222-2-200000000000000000000000000000000000000000
χ638-88-800-880-2000022-200-200200002i5−2i5−2i52i50000000000000000000000000000000000000
χ648-88-800-880-2000022-200-20020000−2i52i52i5−2i50000000000000000000000000000000000000
χ658-8-8800000-2004i2−4i22-220002i5−2i5010−10−1010−i2−i2i2i20000000000000000000000000000000000000
χ668-8-8800000-2004i2−4i22-22000−2i52i50−101010−10−i2−i2i2i20000000000000000000000000000000000000
χ678-8-8800000-200−4i24i22-220002i5−2i50−101010−10i2i2−i2−i20000000000000000000000000000000000000
χ688-8-8800000-200−4i24i22-22000−2i52i5010−10−1010i2i2−i2−i20000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.