Finite Group Databasebeta

← Group #13020839

Character table — Group #13020839

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444444444555588888888888888881010101010101616161616161616202020204040404040404040404040404040404040404040
order12222244445888810101020202020444488881010202040404040404040404444444040404040404040888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−iii−i−i
χ61111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii−i−iii
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−i
χ911111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1
χ1011111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111
χ1111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111
χ1211111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1
χ1311111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2-2-220000222-2-2-2-22222000022-2-20000000022-2-2-2-200000000000000000000000000002i−2i2i−2i
χ18222222-2-2-2-220000222-2-2-2-22222000022-2-20000000022-2-2-2-20000000000000000000000000000−2i2i−2i2i
χ19222222-2-2-2-220000222-2-2-2-2-2-2-2-2000022-2-200000000-2-2222200000000000000000000000000002-2-22
χ20222222-2-2-2-220000222-2-2-2-2-2-2-2-2000022-2-200000000-2-222220000000000000000000000000000-222-2
χ212222-2-222-2-2222-2-2222-2-2-2-222220000-2-2222222-2-2-2-2-2-2-2-2220000000022-2-200000000000000000000
χ222222-2-222-2-2222-2-2222-2-2-2-2-2-2-2-20000-2-2222222-2-2-2-22222-2-200000000-2-22200000000000000000000
χ232222-2-222-2-22-2-222222-2-2-2-222220000-2-222-2-2-2-22222-2-2-2-22200000000-2-22200000000000000000000
χ242222-2-222-2-22-2-222222-2-2-2-2-2-2-2-20000-2-222-2-2-2-222222222-2-20000000022-2-200000000000000000000
χ252222-2-2-2-22220000222222222220000-2-2-2-200000000-2-222-2-20000000000000000000000002-22-20000
χ262222-2-2-2-22220000222222222220000-2-2-2-200000000-2-222-2-2000000000000000000000000-22-220000
χ272222-2-2-2-222200002222222-2-2-2-20000-2-2-2-20000000022-2-2220000000000000000000000002i−2i−2i2i0000
χ282222-2-2-2-222200002222222-2-2-2-20000-2-2-2-20000000022-2-222000000000000000000000000−2i2i2i−2i0000
χ2922-2-22-22-22-220000-2-2222-2-22i2i−2i−2i00002-2-22000000002i−2i2i−2i2i−2i000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ3022-2-22-22-22-220000-2-2222-2-22i2i−2i−2i00002-2-22000000002i−2i2i−2i2i−2i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ3122-2-22-22-22-220000-2-2222-2-2−2i−2i2i2i00002-2-2200000000−2i2i−2i2i−2i2i000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ3222-2-22-22-22-220000-2-2222-2-2−2i−2i2i2i00002-2-2200000000−2i2i−2i2i−2i2i0000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ3322-2-22-2-22-2220000-2-22-2-2222i2i−2i−2i2i−2i002-22-2000000002i−2i−2i2i−2i2i2i2i−2i−2i000000002-2000000000000000000
χ3422-2-22-2-22-2220000-2-22-2-2222i2i−2i−2i−2i2i002-22-2000000002i−2i−2i2i−2i2i−2i−2i2i2i00000000-22000000000000000000
χ3522-2-22-2-22-2220000-2-22-2-222−2i−2i2i2i2i−2i002-22-200000000−2i2i2i−2i2i−2i2i2i−2i−2i00000000-22000000000000000000
χ3622-2-22-2-22-2220000-2-22-2-222−2i−2i2i2i−2i2i002-22-200000000−2i2i2i−2i2i−2i−2i−2i2i2i000000002-2000000000000000000
χ3722-2-2-222-2-2220000-2-22-2-2222i2i−2i−2i0000-22-2200000000−2i2i−2i2i2i−2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ3822-2-2-222-2-2220000-2-22-2-2222i2i−2i−2i0000-22-2200000000−2i2i−2i2i2i−2i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ3922-2-2-222-2-2220000-2-22-2-222−2i−2i2i2i0000-22-22000000002i−2i2i−2i−2i2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ4022-2-2-222-2-2220000-2-22-2-222−2i−2i2i2i0000-22-22000000002i−2i2i−2i−2i2i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ4122-2-2-22-222-220000-2-2222-2-22i2i−2i−2i002i−2i-222-200000000−2i2i2i−2i−2i2i00002i2i−2i−2i0000002-20000000000000000
χ4222-2-2-22-222-220000-2-2222-2-22i2i−2i−2i00−2i2i-222-200000000−2i2i2i−2i−2i2i0000−2i−2i2i2i000000-220000000000000000
χ4322-2-2-22-222-220000-2-2222-2-2−2i−2i2i2i002i−2i-222-2000000002i−2i−2i2i2i−2i00002i2i−2i−2i000000-220000000000000000
χ4422-2-2-22-222-220000-2-2222-2-2−2i−2i2i2i00−2i2i-222-2000000002i−2i−2i2i2i−2i0000−2i−2i2i2i0000002-20000000000000000
χ454444444444-14444-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1000000000000000000000000
χ464444444444-14444-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000011111111000000000000000000000000
χ474444444444-1-4-4-4-4-1-1-1-1-1-1-1000044-4-4-1-1-1-111111111000000-1-1-1-11111000000000000000000000000
χ484444444444-1-4-4-4-4-1-1-1-1-1-1-10000-4-444-1-1-1-1111111110000001111-1-1-1-1000000000000000000000000
χ494444-4-444-4-4-144-4-4-1-1-111110000000011-1-1-1-1-1-11111000000i5−i5i5−i5i5−i5i5−i5000000000000000000000000
χ504444-4-444-4-4-144-4-4-1-1-111110000000011-1-1-1-1-1-11111000000−i5i5−i5i5−i5i5−i5i5000000000000000000000000
χ514444-4-444-4-4-1-4-444-1-1-111110000000011-1-11111-1-1-1-1000000i5−i5i5−i5−i5i5−i5i5000000000000000000000000
χ524444-4-444-4-4-1-4-444-1-1-111110000000011-1-11111-1-1-1-1000000−i5i5−i5i5i5−i5i5−i5000000000000000000000000
χ5344-4-44-4-44-44-1000011-111-1-100004i−4i00-11-11i5i5−i5−i5i5i5−i5−i5000000−i−iii5−5−55000000000000000000000000
χ5444-4-44-4-44-44-1000011-111-1-100004i−4i00-11-11−i5−i5i5i5−i5−i5i5i5000000−i−iii−555−5000000000000000000000000
χ5544-4-44-4-44-44-1000011-111-1-10000−4i4i00-11-11i5i5−i5−i5i5i5−i5−i5000000ii−i−i−555−5000000000000000000000000
χ5644-4-44-4-44-44-1000011-111-1-10000−4i4i00-11-11−i5−i5i5i5−i5−i5i5i5000000ii−i−i5−5−55000000000000000000000000
χ5744-4-4-44-444-4-1000011-1-1-1110000004i−4i1-1-11i5i5−i5−i5−i5−i5i5i5000000−555−5−i−iii000000000000000000000000
χ5844-4-4-44-444-4-1000011-1-1-1110000004i−4i1-1-11−i5−i5i5i5i5i5−i5−i50000005−5−55−i−iii000000000000000000000000
χ5944-4-4-44-444-4-1000011-1-1-111000000−4i4i1-1-11i5i5−i5−i5−i5−i5i5i50000005−5−55ii−i−i000000000000000000000000
χ6044-4-4-44-444-4-1000011-1-1-111000000−4i4i1-1-11−i5−i5i5i5i5i5−i5−i5000000−555−5ii−i−i000000000000000000000000
χ614-44-40000004002i2−2i24-4-400004-44-40000000000002i2−2i22i2−2i200000000000000002i2−2i200000000000000000000
χ624-44-40000004002i2−2i24-4-40000-44-440000000000002i2−2i22i2−2i20000000000000000−2i22i200000000000000000000
χ634-44-4000000400−2i22i24-4-400004-44-4000000000000−2i22i2−2i22i20000000000000000−2i22i200000000000000000000
χ644-44-4000000400−2i22i24-4-40000-44-44000000000000−2i22i2−2i22i200000000000000002i2−2i200000000000000000000
χ654-4-4400000042i2−2i200-44-400004i−4i−4i4i000000002i2−2i22i2−2i200000000000000000022−220000000000000000000000
χ664-4-4400000042i2−2i200-44-40000−4i4i4i−4i000000002i2−2i22i2−2i2000000000000000000−22220000000000000000000000
χ674-4-440000004−2i22i200-44-400004i−4i−4i4i00000000−2i22i2−2i22i2000000000000000000−22220000000000000000000000
χ684-4-440000004−2i22i200-44-40000−4i4i4i−4i00000000−2i22i2−2i22i200000000000000000022−220000000000000000000000
χ69888888-8-8-8-8-20000-2-2-2222200000000-2-2220000000000000000000000000000000000000000000000
χ708888-8-8-8-888-20000-2-2-2-2-2-2-20000000022220000000000000000000000000000000000000000000000
χ7188-8-88-88-88-8-2000022-2-2-22200000000-222-20000000000000000000000000000000000000000000000
χ7288-8-8-888-8-88-2000022-222-2-2000000002-22-20000000000000000000000000000000000000000000000
χ738-88-8000000-2004i2−4i2-2222i5−2i52i5−2i500000000000010−10−1010−i2i2−i2i200000000000000000000000000000000000000
χ748-88-8000000-2004i2−4i2-222−2i52i5−2i52i5000000000000−101010−10−i2i2−i2i200000000000000000000000000000000000000
χ758-88-8000000-200−4i24i2-2222i5−2i52i5−2i5000000000000−101010−10i2−i2i2−i200000000000000000000000000000000000000
χ768-88-8000000-200−4i24i2-222−2i52i5−2i52i500000000000010−10−1010i2−i2i2−i200000000000000000000000000000000000000
χ778-8-88000000-24i2−4i2002-222i5−2i5−2i52i5000000000000−i2i2−i2i210−10−101000000000000000000000000000000000000000
χ788-8-88000000-24i2−4i2002-22−2i52i52i5−2i5000000000000−i2i2−i2i2−101010−1000000000000000000000000000000000000000
χ798-8-88000000-2−4i24i2002-222i5−2i5−2i52i5000000000000i2−i2i2−i2−101010−1000000000000000000000000000000000000000
χ808-8-88000000-2−4i24i2002-22−2i52i52i5−2i5000000000000i2−i2i2−i210−10−101000000000000000000000000000000000000000

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