Finite Group Databasebeta

← Group #13023902

Character table — Group #13023902

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122224444444448888888888888810101010101010101010161620202032323232404040404040404040404040404040408080
order1222444445888810101020202020202040404040404040402244448888444882020202088888888161616161616161644
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
χ91111-1-111-1111-1-1111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-111111-1-1ii−i−iii−i−iii−i−iii−i−i1-1
χ101111-1-111-1111-1-1111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-111111-1-1−i−iii−i−iii−i−iii−i−iii1-1
χ111111-1-111-1111-1-1111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii-11
χ121111-1-111-1111-1-1111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i-11
χ131111-1-111-1111-1-1111-1-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-11
χ141111-1-111-1111-1-1111-1-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-11
χ151111-1-111-1111-1-1111-1-1-1-1111111-1-1-1-1-1-111111111-11-1-1-1-1-11111-1-1-1-111-1-11111-1-11-1
χ161111-1-111-1111-1-1111-1-1-1-1111111-1-1-1-1-1-111111111-11-1-1-1-1-111-1-11111-1-111-1-1-1-1111-1
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
χ19222222-2-2-220000222-2-222-2-20000000022-2-222000000-2000000000000002−22−22−22−200
χ20222222-2-2-220000222-2-222-2-20000000022-2-222000000-200000000000000−22−22−22−2200
χ21222222-2-2-220000222-2-222-2-200000000-2-222-2-2000000200000000000000i2−i2i2−i2−i2i2−i2i200
χ22222222-2-2-220000222-2-222-2-200000000-2-222-2-2000000200000000000000−i2i2−i2i2i2−i2i2−i200
χ232222-2-222-22-2-222222-2-2-2-222-2-2-2-2222222-2-2-2-22222002-2-20000000000000000000000
χ242222-2-222-22-2-222222-2-2-2-222-2-2-2-22222-2-22222-2-2-2-200-2220000000000000000000000
χ252222-2-2-2-222000022222-2-2-2-2000000002222-2-2000000-200000000000000i2−i2−i2i2i2−i2−i2i200
χ262222-2-2-2-222000022222-2-2-2-2000000002222-2-2000000-200000000000000−i2i2i2−i2−i2i2i2−i200
χ272222-2-2-2-222000022222-2-2-2-200000000-2-2-2-2220000002000000000000002−2−22−222−200
χ282222-2-2-2-222000022222-2-2-2-200000000-2-2-2-222000000200000000000000−222−22−2−2200
χ292-2-22002-2022-2002-2-200002-222-2-20000002i−2i2i−2i2i2i−2i−2i00000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ302-2-22002-2022-2002-2-200002-222-2-20000002i−2i2i−2i2i2i−2i−2i000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ312-2-22002-2022-2002-2-200002-222-2-2000000−2i2i−2i2i−2i−2i2i2i00000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ322-2-22002-2022-2002-2-200002-222-2-2000000−2i2i−2i2i−2i−2i2i2i000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ332-2-22002-202-22002-2-200002-2-2-2220000002i−2i2i−2i−2i−2i2i2i000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ342-2-22002-202-22002-2-200002-2-2-2220000002i−2i2i−2i−2i−2i2i2i0000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ352-2-22002-202-22002-2-200002-2-2-222000000−2i2i−2i2i2i2i−2i−2i000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ362-2-22002-202-22002-2-200002-2-2-222000000−2i2i−2i2i2i2i−2i−2i0000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
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
χ414444-4-444-4-144-4-4-1-1-11111-1-1-1-1-1-1111100000000004-4000-1-111000000000000000000
χ424444-4-444-4-144-4-4-1-1-11111-1-1-1-1-1-111110000000000-4400011-1-1000000000000000000
χ434444-4-444-4-1-4-444-1-1-11111-1-11111-1-1-1-10000000000000005−5−55000000000000000000
χ444444-4-444-4-1-4-444-1-1-11111-1-11111-1-1-1-1000000000000000−555−5000000000000000000
χ4544-4-40000040022−22-44-400000000002222−22−224-4000022−2222−22000000000000000000000000000
χ4644-4-40000040022−22-44-400000000002222−22−22-440000−2222−2222000000000000000000000000000
χ4744-4-400000400−2222-44-40000000000−22−2222224-40000−2222−2222000000000000000000000000000
χ4844-4-400000400−2222-44-40000000000−22−222222-44000022−2222−22000000000000000000000000000
χ494-44-44-400040000-4-44004-400000000000000002i2−2i2−2i22i20002i2−2i20000000000000000000000
χ504-44-44-400040000-4-44004-40000000000000000−2i22i22i2−2i2000−2i22i20000000000000000000000
χ514-44-4-4400040000-4-4400-4400000000000000002i2−2i2−2i22i2000−2i22i20000000000000000000000
χ524-44-4-4400040000-4-4400-440000000000000000−2i22i22i2−2i20002i2−2i20000000000000000000000
χ534-4-4400-440400004-4-40000-4400000000004i−4i−4i4i0000000000000000000000000000000
χ544-4-4400-440400004-4-40000-440000000000−4i4i4i−4i0000000000000000000000000000000
χ55888888-8-8-8-20000-2-2-222-2-222000000000000000000000000000000000000000000000
χ568888-8-8-8-88-20000-2-2-2-2-22222000000000000000000000000000000000000000000000
χ5788-8-800000-20042−422-2225−25000010−1010−10−2−2220000000000000000000000000000000000000
χ5888-8-800000-20042−422-22−25250000−1010−1010−2−2220000000000000000000000000000000000000
χ5988-8-800000-200−42422-2225−250000−1010−101022−2−20000000000000000000000000000000000000
χ6088-8-800000-200−42422-22−2525000010−1010−1022−2−20000000000000000000000000000000000000
χ618-88-88-8000-2000022-200-220010−10−101010−1010−100000000000000000000000000000000000000
χ628-88-88-8000-2000022-200-2200−101010−10−1010−10100000000000000000000000000000000000000
χ638-88-8-88000-2000022-2002-20010−10−1010−1010−10100000000000000000000000000000000000000
χ648-88-8-88000-2000022-2002-200−101010−1010−1010−100000000000000000000000000000000000000
χ658-8-88008-80-28-800-2220000-22-2-22200000000000000000000000000000000000000000
χ668-8-88008-80-2-8800-2220000-2222-2-200000000000000000000000000000000000000000
χ678-8-8800-880-20000-22200002-2000025−25−25250000000000000000000000000000000000000
χ688-8-8800-880-20000-22200002-20000−252525−250000000000000000000000000000000000000

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