Finite Group Databasebeta

← Group #13019200

Character table — Group #13019200

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444444444555588888888888888881010101010101616161616161616202020204040404040404040404040404040404040404040
order12222244444444510101010101010444422442020202020202020202020204444441010101020202020444444448888888888888888
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
χ91111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ101111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1
χ111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ121111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ131111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ141111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111−i−iiiii−i−iii−i−i−i−iii
χ151111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1ii−i−iii−i−i−i−iii−i−iii
χ161111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1−i−iii−i−iiiii−i−iii−i−i
χ17222222-2-2-2-20000222222222222002-200000000-2-2-2-222-2-2-2-2000022-2-20000002-20000000000000000
χ18222222-2-2-2-2000022222222222200-2200000000-2-2-2-222-2-2-2-20000-2-222000000-220000000000000000
χ19222222-2-2-2-2000022222222-2-2-2-2002-200000000-2-2-2-2-2-22222000022-2-2000000-220000000000000000
χ20222222-2-2-2-2000022222222-2-2-2-200-2200000000-2-2-2-2-2-222220000-2-2220000002-20000000000000000
χ212222-2-222-2-20000222-2-2-2-22222200000000000022-2-2-2-222-2-2000000000000000000002-22-200000000
χ222222-2-222-2-20000222-2-2-2-22222200000000000022-2-2-2-222-2-200000000000000000000-22-2200000000
χ232222-2-222-2-20000222-2-2-2-22-2-2-2-200000000000022-2-222-2-222000000000000000000002i−2i−2i2i00000000
χ242222-2-222-2-20000222-2-2-2-22-2-2-2-200000000000022-2-222-2-22200000000000000000000−2i2i2i−2i00000000
χ252222-2-2-2-2220000222-2-2-2-222222000000000000-2-222-2-2-2-22200000000000000002-22-2000000000000
χ262222-2-2-2-2220000222-2-2-2-222222000000000000-2-222-2-2-2-2220000000000000000-22-22000000000000
χ272222-2-2-2-2220000222-2-2-2-22-2-2-2-2000000000000-2-2222222-2-200000000000000002i−2i−2i2i000000000000
χ282222-2-2-2-2220000222-2-2-2-22-2-2-2-2000000000000-2-2222222-2-20000000000000000−2i2i2i−2i000000000000
χ2922-2-22-22-22-200002-2-2-2-22222i2i−2i−2i2-200000000002-22-22i−2i2i−2i2i−2i22-2-2000000002i−2i000000000000000000
χ3022-2-22-22-22-200002-2-2-2-22222i2i−2i−2i-2200000000002-22-22i−2i2i−2i2i−2i-2-22200000000−2i2i000000000000000000
χ3122-2-22-22-22-200002-2-2-2-2222−2i−2i2i2i2-200000000002-22-2−2i2i−2i2i−2i2i22-2-200000000−2i2i000000000000000000
χ3222-2-22-22-22-200002-2-2-2-2222−2i−2i2i2i-2200000000002-22-2−2i2i−2i2i−2i2i-2-222000000002i−2i000000000000000000
χ3322-2-22-2-22-2222-2-22-2-2-2-22222i2i−2i−2i00002222-2-2-2-2-22-222i−2i−2i2i−2i2i000000002i2i−2i−2i00000000000000000000
χ3422-2-22-2-22-2222-2-22-2-2-2-2222−2i−2i2i2i00002222-2-2-2-2-22-22−2i2i2i−2i2i−2i00000000−2i−2i2i2i00000000000000000000
χ3522-2-22-2-22-22-2-2222-2-2-2-22222i2i−2i−2i0000-2-2-2-22222-22-222i−2i−2i2i−2i2i00000000−2i−2i2i2i00000000000000000000
χ3622-2-22-2-22-22-2-2222-2-2-2-2222−2i−2i2i2i0000-2-2-2-22222-22-22−2i2i2i−2i2i−2i000000002i2i−2i−2i00000000000000000000
χ3722-2-2-222-2-2200002-2-222-2-222i2i−2i−2i0000000000002-2-22−2i2i2i−2i−2i2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ3822-2-2-222-2-2200002-2-222-2-222i2i−2i−2i0000000000002-2-22−2i2i2i−2i−2i2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ3922-2-2-222-2-2200002-2-222-2-22−2i−2i2i2i0000000000002-2-222i−2i−2i2i2i−2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ4022-2-2-222-2-2200002-2-222-2-22−2i−2i2i2i0000000000002-2-222i−2i−2i2i2i−2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ4122-2-2-22-222-200002-2-222-2-222i2i−2i−2i000000000000-222-2−2i2i−2i2i2i−2i0000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ4222-2-2-22-222-200002-2-222-2-222i2i−2i−2i000000000000-222-2−2i2i−2i2i2i−2i00000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ4322-2-2-22-222-200002-2-222-2-22−2i−2i2i2i000000000000-222-22i−2i2i−2i−2i2i0000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ4422-2-2-22-222-200002-2-222-2-22−2i−2i2i2i000000000000-222-22i−2i2i−2i−2i2i00000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
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
χ474444444444-4-4-4-4-1-1-1-1-1-1-1-1000044-4-411111111-1-1-1-1000000-1-1-1-11111000000000000000000000000
χ484444444444-4-4-4-4-1-1-1-1-1-1-1-10000-4-44411111111-1-1-1-10000001111-1-1-1-1000000000000000000000000
χ49444444-4-4-4-40000-1-1-1-1-1-1-1-10000004-455−5−555−5−511110000005−55−5-1-111000000000000000000000000
χ50444444-4-4-4-40000-1-1-1-1-1-1-1-10000004-4−5−555−5−5551111000000−55−55-1-111000000000000000000000000
χ51444444-4-4-4-40000-1-1-1-1-1-1-1-1000000-4455−5−555−5−51111000000−55−5511-1-1000000000000000000000000
χ52444444-4-4-4-40000-1-1-1-1-1-1-1-1000000-44−5−555−5−55511110000005−55−511-1-1000000000000000000000000
χ5344-4-44-44-44-40000-11111-1-1-100004-40055−5−5−5−555-11-11000000-1-1115−55−5000000000000000000000000
χ5444-4-44-44-44-40000-11111-1-1-100004-400−5−55555−5−5-11-11000000-1-111−55−55000000000000000000000000
χ5544-4-44-44-44-40000-11111-1-1-10000-440055−5−5−5−555-11-1100000011-1-1−55−55000000000000000000000000
χ5644-4-44-44-44-40000-11111-1-1-10000-4400−5−55555−5−5-11-1100000011-1-15−55−5000000000000000000000000
χ5744-4-44-4-44-4444-4-4-11111-1-1-100000000-1-1-1-111111-11-10000005−5−555−5−55000000000000000000000000
χ5844-4-44-4-44-4444-4-4-11111-1-1-100000000-1-1-1-111111-11-1000000−555−5−555−5000000000000000000000000
χ5944-4-44-4-44-44-4-444-11111-1-1-1000000001111-1-1-1-11-11-10000005−5−55−555−5000000000000000000000000
χ6044-4-44-4-44-44-4-444-11111-1-1-1000000001111-1-1-1-11-11-1000000−555−55−5−55000000000000000000000000
χ614-44-40000002i−2i2i−2i44-40000-44-44-400002i−2i2i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i00000000000000000000
χ624-44-40000002i−2i2i−2i44-40000-4-44-4400002i−2i2i−2i2i−2i2i−2i000000000000000000−2i2i−2i2i00000000000000000000
χ634-44-4000000−2i2i−2i2i44-40000-44-44-40000−2i2i−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i00000000000000000000
χ644-44-4000000−2i2i−2i2i44-40000-4-44-440000−2i2i−2i2i−2i2i−2i2i0000000000000000002i−2i2i−2i00000000000000000000
χ654-4-440000002i−2i−2i2i4-440000-44i−4i−4i4i00002i−2i2i−2i−2i2i−2i2i000000000000000000-222-200000000000000000000
χ664-4-440000002i−2i−2i2i4-440000-4−4i4i4i−4i00002i−2i2i−2i−2i2i−2i2i0000000000000000002-2-2200000000000000000000
χ674-4-44000000−2i2i2i−2i4-440000-44i−4i−4i4i0000−2i2i−2i2i2i−2i2i−2i0000000000000000002-2-2200000000000000000000
χ684-4-44000000−2i2i2i−2i4-440000-4−4i4i4i−4i0000−2i2i−2i2i2i−2i2i−2i000000000000000000-222-200000000000000000000
χ698888-8-888-8-80000-2-2-22222-20000000000000000-2-22200000000000000000000000000000000000000
χ708888-8-8-8-8880000-2-2-22222-2000000000000000022-2-200000000000000000000000000000000000000
χ7188-8-8-888-8-880000-222-2-222-20000000000000000-222-200000000000000000000000000000000000000
χ7288-8-8-88-888-80000-222-2-222-200000000000000002-2-2200000000000000000000000000000000000000
χ738-88-80000004i−4i4i−4i-2-2225−2525−25200000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38000000000000000000000000000000000000000000
χ748-88-80000004i−4i4i−4i-2-22−2525−2525200000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000000000000000000000000000000000000000
χ758-88-8000000−4i4i−4i4i-2-2225−2525−252000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38000000000000000000000000000000000000000000
χ768-88-8000000−4i4i−4i4i-2-22−2525−25252000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000000000000000000000000000000000000000
χ778-8-880000004i−4i−4i4i-22-225−25−2525200000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ142ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000000000000000000000000000000000000000
χ788-8-880000004i−4i−4i4i-22-2−252525−25200000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ382ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38000000000000000000000000000000000000000000
χ798-8-88000000−4i4i4i−4i-22-225−25−25252000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000000000000000000000000000000000000000
χ808-8-88000000−4i4i4i−4i-22-2−252525−252000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38000000000000000000000000000000000000000000

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