Finite Group Databasebeta

← Group #13019213

Character table — Group #13019213

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444444444555588888888888888881010101010101616161616161616202020204040404040404040404040404040404040404040
order12222222222222510101010101010444444441010101010101010101010104444442020202020202020444424448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−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−iii−i−iii−i−iii−i−iii
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−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−iiiii−i−i−i−iiiii−i−i
χ91111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ101111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ121111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ131111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii
χ141111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i
χ151111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2-2-2000022-2-222-2-22222000022-2-200000000-2-222-2-2000000000000000000002-22-200000000
χ18222222-2-2-2-2000022-2-222-2-22222000022-2-200000000-2-222-2-200000000000000000000-22-2200000000
χ19222222-2-2-2-2000022-2-222-2-2-2-2-2-2000022-2-20000000022-2-222000000000000000000002i−2i−2i2i00000000
χ20222222-2-2-2-2000022-2-222-2-2-2-2-2-2000022-2-20000000022-2-22200000000000000000000−2i2i2i−2i00000000
χ212222-2-222-2-2000022-2-222-2-222220000-2-22200000000-2-2-2-22200000000000000002-22-2000000000000
χ222222-2-222-2-2000022-2-222-2-222220000-2-22200000000-2-2-2-2220000000000000000-22-22000000000000
χ232222-2-222-2-2000022-2-222-2-2-2-2-2-20000-2-222000000002222-2-200000000000000002i−2i−2i2i000000000000
χ242222-2-222-2-2000022-2-222-2-2-2-2-2-20000-2-222000000002222-2-20000000000000000−2i2i2i−2i000000000000
χ252222-2-2-2-22200002222222222222-200-2-2-2-20000000022-2-2-2-222-2-200000000-22000000000000000000
χ262222-2-2-2-2220000222222222222-2200-2-2-2-20000000022-2-2-2-2-2-222000000002-2000000000000000000
χ272222-2-2-2-222000022222222-2-2-2-22-200-2-2-2-200000000-2-2222222-2-2000000002-2000000000000000000
χ282222-2-2-2-222000022222222-2-2-2-2-2200-2-2-2-200000000-2-22222-2-22200000000-22000000000000000000
χ292-22-22-22-22-2000022-2-2-2-2222i2i−2i−2i00002-22-2000000002i−2i2i−2i2i−2i0000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ302-22-22-22-22-2000022-2-2-2-2222i2i−2i−2i00002-22-2000000002i−2i2i−2i2i−2i00000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ312-22-22-22-22-2000022-2-2-2-222−2i−2i2i2i00002-22-200000000−2i2i−2i2i−2i2i0000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ322-22-22-22-22-2000022-2-2-2-222−2i−2i2i2i00002-22-200000000−2i2i−2i2i−2i2i00000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ332-22-22-2-22-2222-2-22222-2-2-2-22i2i−2i−2i00002-2-222222-2-2-2-2−2i2i2i−2i−2i2i000000002i2i−2i−2i00000000000000000000
χ342-22-22-2-22-2222-2-22222-2-2-2-2−2i−2i2i2i00002-2-222222-2-2-2-22i−2i−2i2i2i−2i00000000−2i−2i2i2i00000000000000000000
χ352-22-22-2-22-22-2-2222222-2-2-2-22i2i−2i−2i00002-2-22-2-2-2-22222−2i2i2i−2i−2i2i00000000−2i−2i2i2i00000000000000000000
χ362-22-22-2-22-22-2-2222222-2-2-2-2−2i−2i2i2i00002-2-22-2-2-2-222222i−2i−2i2i2i−2i000000002i2i−2i−2i00000000000000000000
χ372-22-2-222-2-2200002222-2-2-2-22i2i−2i−2i002i−2i-222-200000000−2i2i−2i2i2i−2i00002i2i−2i−2i0000002-20000000000000000
χ382-22-2-222-2-2200002222-2-2-2-22i2i−2i−2i00−2i2i-222-200000000−2i2i−2i2i2i−2i0000−2i−2i2i2i000000-220000000000000000
χ392-22-2-222-2-2200002222-2-2-2-2−2i−2i2i2i002i−2i-222-2000000002i−2i2i−2i−2i2i00002i2i−2i−2i000000-220000000000000000
χ402-22-2-222-2-2200002222-2-2-2-2−2i−2i2i2i00−2i2i-222-2000000002i−2i2i−2i−2i2i0000−2i−2i2i2i0000002-20000000000000000
χ412-22-2-22-222-2000022-2-2-2-2222i2i−2i−2i0000-22-22000000002i−2i−2i2i−2i2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ422-22-2-22-222-2000022-2-2-2-2222i2i−2i−2i0000-22-22000000002i−2i−2i2i−2i2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ432-22-2-22-222-2000022-2-2-2-222−2i−2i2i2i0000-22-2200000000−2i2i2i−2i2i−2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ442-22-2-22-222-2000022-2-2-2-222−2i−2i2i2i0000-22-2200000000−2i2i2i−2i2i−2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ4544444444444444-1-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1000000000000000000000000
χ4644444444444444-1-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000011111111000000000000000000000000
χ474444444444-4-4-4-4-1-1-1-1-1-1-1-1000044-4-4-1-1-1-111111111000000-1-1-1-11111000000000000000000000000
χ484444444444-4-4-4-4-1-1-1-1-1-1-1-10000-4-444-1-1-1-1111111110000001111-1-1-1-1000000000000000000000000
χ494444-4-4-4-4440000-1-1-1-1-1-1-1-100004-400111155−5−555−5−5000000-1-1115−55−5000000000000000000000000
χ504444-4-4-4-4440000-1-1-1-1-1-1-1-100004-4001111−5−555−5−555000000-1-111−55−55000000000000000000000000
χ514444-4-4-4-4440000-1-1-1-1-1-1-1-10000-4400111155−5−555−5−500000011-1-1−55−55000000000000000000000000
χ524444-4-4-4-4440000-1-1-1-1-1-1-1-10000-44001111−5−555−5−55500000011-1-15−55−5000000000000000000000000
χ5344-4-40000002-22-24-4004-4004i−4i4i−4i000000002-22-22-22-2000000000000002i−2i2i−2i00000000000000000000
χ5444-4-40000002-22-24-4004-400−4i4i−4i4i000000002-22-22-22-200000000000000−2i2i−2i2i00000000000000000000
χ5544-4-4000000-22-224-4004-4004i−4i4i−4i00000000-22-22-22-2200000000000000−2i2i−2i2i00000000000000000000
χ5644-4-4000000-22-224-4004-400−4i4i−4i4i00000000-22-22-22-22000000000000002i−2i2i−2i00000000000000000000
χ574-44-44-4-44-4444-4-4-1-1-1-1111100000000-111-1-1-1-1-11111000000i5−i5i5−i5i5−i5−i5i5000000000000000000000000
χ584-44-44-4-44-4444-4-4-1-1-1-1111100000000-111-1-1-1-1-11111000000−i5i5−i5i5−i5i5i5−i5000000000000000000000000
χ594-44-44-4-44-44-4-444-1-1-1-1111100000000-111-11111-1-1-1-1000000i5−i5i5−i5−i5i5i5−i5000000000000000000000000
χ604-44-44-4-44-44-4-444-1-1-1-1111100000000-111-11111-1-1-1-1000000−i5i5−i5i5i5−i5−i5i5000000000000000000000000
χ614-44-4-444-4-440000-1-1-1-111110000004i−4i1-1-1155−5−5−5−555000000i5−i5−i5i5−i−iii000000000000000000000000
χ624-44-4-444-4-440000-1-1-1-111110000004i−4i1-1-11−5−55555−5−5000000−i5i5i5−i5−i−iii000000000000000000000000
χ634-44-4-444-4-440000-1-1-1-11111000000−4i4i1-1-1155−5−5−5−555000000−i5i5i5−i5ii−i−i000000000000000000000000
χ644-44-4-444-4-440000-1-1-1-11111000000−4i4i1-1-11−5−55555−5−5000000i5−i5−i5i5ii−i−i000000000000000000000000
χ654-4-440000002-2-224-400-44004-4-44000000002-22-2-22-22000000000000002-2-2200000000000000000000
χ664-4-440000002-2-224-400-4400-444-4000000002-22-2-22-2200000000000000-222-200000000000000000000
χ674-4-44000000-222-24-400-44004-4-4400000000-22-222-22-200000000000000-222-200000000000000000000
χ684-4-44000000-222-24-400-4400-444-400000000-22-222-22-2000000000000002-2-2200000000000000000000
χ69888888-8-8-8-80000-2-222-2-22200000000-2-2220000000000000000000000000000000000000000000000
χ708888-8-888-8-80000-2-222-2-2220000000022-2-20000000000000000000000000000000000000000000000
χ7188-8-80000004-44-4-2225−25-2225−25000000000000−1+51−5−1−51+5−1+51−5−1−51+500000000000000000000000000000000000000
χ7288-8-80000004-44-4-22−2525-22−2525000000000000−1−51+5−1+51−5−1−51+5−1+51−500000000000000000000000000000000000000
χ7388-8-8000000-44-44-2225−25-2225−250000000000001−5−1+51+5−1−51−5−1+51+5−1−500000000000000000000000000000000000000
χ7488-8-8000000-44-44-22−2525-22−25250000000000001+5−1−51−5−1+51+5−1−51−5−1+500000000000000000000000000000000000000
χ758-88-88-88-88-80000-2-22222-2-200000000-22-220000000000000000000000000000000000000000000000
χ768-88-8-88-888-80000-2-22222-2-2000000002-22-20000000000000000000000000000000000000000000000
χ778-8-880000004-4-44-2225−252-2−2525000000000000−1+51−5−1−51+51−5−1+51+5−1−500000000000000000000000000000000000000
χ788-8-880000004-4-44-22−25252-225−25000000000000−1−51+5−1+51−51+5−1−51−5−1+500000000000000000000000000000000000000
χ798-8-88000000-444-4-2225−252-2−25250000000000001−5−1+51+5−1−5−1+51−5−1−51+500000000000000000000000000000000000000
χ808-8-88000000-444-4-22−25252-225−250000000000001+5−1−51−5−1+5−1−51+5−1+51−500000000000000000000000000000000000000

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