Finite Group Databasebeta

← Group #13018332

Character table — Group #13018332

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444444488888888888888881010101010101010161616161616161620202020404040408080808080808080
order12224424588881010102020202024881010202040404040404040402244888810102020404040402488448844448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ9111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-11-11-1
χ10111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-11-11-11-11
χ11111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111i−i−iii−i−ii
χ12111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111−iii−i−iii−i
χ13111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-11-1-11-11
χ14111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-11-111-11-1
χ15111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1i−i−ii−iii−i
χ16111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1−iii−ii−i−ii
χ17222222-2-2222-2-222222220000-2-2-2-22222-2-2-2-222-2-2222200000000-22-2-2000000000000
χ18222222-2-2222-2-222222220000-2-2-2-22222-2-2-2-2-2-222-2-2-2-2000000002-222000000000000
χ19222222-2-22-2-22222222220000-2-2-2-2-2-2-2-2222222-2-2-2-2-2-200000000-2222000000000000
χ20222222-2-22-2-22222222220000-2-2-2-2-2-2-2-22222-2-2222222000000002-2-2-2000000000000
χ212222-2-22-220000222-2-2-2-2002i−2i22-2-20000000022-2-2000000002i2i−2i−2i2-200002i−2i00000000
χ222222-2-22-220000222-2-2-2-2002i−2i22-2-200000000-2-222000000002i2i−2i−2i-220000−2i2i00000000
χ232222-2-22-220000222-2-2-2-200−2i2i22-2-20000000022-2-200000000−2i−2i2i2i2-20000−2i2i00000000
χ242222-2-22-220000222-2-2-2-200−2i2i22-2-200000000-2-22200000000−2i−2i2i2i-2200002i−2i00000000
χ252222-2-2-2220000222-2-2-2-22-200-2-222000000002222000022-2-20000-2-2002-20000000000
χ262222-2-2-2220000222-2-2-2-22-200-2-22200000000-2-2-2-2000022-2-200002200-220000000000
χ272222-2-2-2220000222-2-2-2-2-2200-2-2220000000022220000-2-2220000-2-200-220000000000
χ282222-2-2-2220000222-2-2-2-2-2200-2-22200000000-2-2-2-20000-2-222000022002-20000000000
χ2944444444-14444-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000000000000000
χ3044444444-14444-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000000111111110000000000000000
χ3144444444-1-4-4-4-4-1-1-1-1-1-1-144-4-4-1-1-1-11111111100000000-1-1-1-111110000000000000000
χ3244444444-1-4-4-4-4-1-1-1-1-1-1-1-4-444-1-1-1-111111111000000001111-1-1-1-10000000000000000
χ33444444-4-4-144-4-4-1-1-1-1-1-1-100001111-1-1-1-11111000000005−55−55−55−50000000000000000
χ34444444-4-4-144-4-4-1-1-1-1-1-1-100001111-1-1-1-1111100000000−55−55−55−550000000000000000
χ35444444-4-4-1-4-444-1-1-1-1-1-1-1000011111111-1-1-1-1000000005−55−5−55−550000000000000000
χ36444444-4-4-1-4-444-1-1-1-1-1-1-1000011111111-1-1-1-100000000−55−555−55−50000000000000000
χ374444-4-44-4-10000-1-1-11111004i−4i-1-111i5i5−i5−i5i5i5−i5−i5000000005−5−55−i−iii0000000000000000
χ384444-4-44-4-10000-1-1-11111004i−4i-1-111−i5−i5i5i5−i5−i5i5i500000000−555−5−i−iii0000000000000000
χ394444-4-44-4-10000-1-1-1111100−4i4i-1-111i5i5−i5−i5i5i5−i5−i500000000−555−5ii−i−i0000000000000000
χ404444-4-44-4-10000-1-1-1111100−4i4i-1-111−i5−i5i5i5−i5−i5i5i5000000005−5−55ii−i−i0000000000000000
χ414444-4-4-44-10000-1-1-111114-40011-1-1i5i5−i5−i5−i5−i5i5i500000000-1-111i5−i5−i5i50000000000000000
χ424444-4-4-44-10000-1-1-111114-40011-1-1−i5−i5i5i5i5i5−i5−i500000000-1-111−i5i5i5−i50000000000000000
χ434444-4-4-44-10000-1-1-11111-440011-1-1i5i5−i5−i5−i5−i5i5i50000000011-1-1−i5i5i5−i50000000000000000
χ444444-4-4-44-10000-1-1-11111-440011-1-1−i5−i5i5i5i5i5−i5−i50000000011-1-1i5−i5−i5i50000000000000000
χ4544-4-400004002i2−2i24-4-400000000000000002i2−2i22i2−2i2004i−4i2222−22−22000000000000000000000000
χ4644-4-400004002i2−2i24-4-400000000000000002i2−2i22i2−2i200−4i4i−22−222222000000000000000000000000
χ4744-4-40000400−2i22i24-4-40000000000000000−2i22i2−2i22i2004i−4i−22−222222000000000000000000000000
χ4844-4-40000400−2i22i24-4-40000000000000000−2i22i2−2i22i200−4i4i2222−22−22000000000000000000000000
χ494-44-40000422−2200-44-400000000000022−2222−2200004-40022−2222−22000000000000000000000000
χ504-44-40000422−2200-44-400000000000022−2222−220000-4400−2222−2222000000000000000000000000
χ514-44-400004−222200-44-4000000000000−2222−222200004-400−2222−2222000000000000000000000000
χ524-44-400004−222200-44-4000000000000−2222−22220000-440022−2222−22000000000000000000000000
χ534-4-444-40040000-4-4444-4-400000000000000000000000000000000004i−4i000000000000
χ544-4-444-40040000-4-4444-4-40000000000000000000000000000000000−4i4i000000000000
χ554-4-44-440040000-4-44-4-444000000000000000000004-4-44000000000000000000000000
χ564-4-44-440040000-4-44-4-44400000000000000000000-444-4000000000000000000000000
χ5788-8-80000-2004i2−4i2-2222i5−2i52i5−2i50000000000002ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ3900000000000000000000000000000000
χ5888-8-80000-2004i2−4i2-222−2i52i5−2i52i50000000000002ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ2900000000000000000000000000000000
χ5988-8-80000-200−4i24i2-2222i5−2i52i5−2i5000000000000−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ3900000000000000000000000000000000
χ6088-8-80000-200−4i24i2-222−2i52i5−2i52i5000000000000−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ2900000000000000000000000000000000
χ618-88-80000-242−42002-222i5−2i5−2i52i5000000002ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ39−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ29000000000000000000000000000000000000
χ628-88-80000-242−42002-22−2i52i52i5−2i500000000−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ292ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ39000000000000000000000000000000000000
χ638-88-80000-2−4242002-222i5−2i5−2i52i500000000−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ392ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ29000000000000000000000000000000000000
χ648-88-80000-2−4242002-22−2i52i52i5−2i5000000002ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ29−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ39000000000000000000000000000000000000
χ658-8-888-800-2000022-2-2-222000025−2525−250000000000000000000000000000000000000000
χ668-8-888-800-2000022-2-2-2220000−2525−25250000000000000000000000000000000000000000
χ678-8-88-8800-2000022-222-2-2000025−25−25250000000000000000000000000000000000000000
χ688-8-88-8800-2000022-222-2-20000−252525−250000000000000000000000000000000000000000

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