Finite Group Databasebeta

← Group #13019201

Character table — Group #13019201

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
χ91111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ101111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ121111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ131111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ141111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ151111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111ii−i−iii−i−i−i−iii−i−iii
χ161111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111−i−iii−i−iiiii−i−iii−i−i
χ17222222-2-2-2-20000222222222222002-2-2-2-2-20000000022-2-2-2-2000022-2-200002-2000000000000000000
χ18222222-2-2-2-2000022222222222200-22-2-2-2-20000000022-2-2-2-20000-2-2220000-22000000000000000000
χ19222222-2-2-2-2000022222222-2-2-2-2002-2-2-2-2-200000000-2-22222000022-2-20000-22000000000000000000
χ20222222-2-2-2-2000022222222-2-2-2-200-22-2-2-2-200000000-2-222220000-2-22200002-2000000000000000000
χ212222-2-222-2-2000022-2-22-2-222222000022-2-200000000-2-222-2-2000000000000000000002-22-200000000
χ222222-2-222-2-2000022-2-22-2-222222000022-2-200000000-2-222-2-200000000000000000000-22-2200000000
χ232222-2-222-2-2000022-2-22-2-22-2-2-2-2000022-2-20000000022-2-222000000000000000000002i−2i−2i2i00000000
χ242222-2-222-2-2000022-2-22-2-22-2-2-2-2000022-2-20000000022-2-22200000000000000000000−2i2i2i−2i00000000
χ252222-2-2-2-222000022-2-22-2-2222220000-2-22200000000-2-2-2-22200000000000000002-22-2000000000000
χ262222-2-2-2-222000022-2-22-2-2222220000-2-22200000000-2-2-2-2220000000000000000-22-22000000000000
χ272222-2-2-2-222000022-2-22-2-22-2-2-2-20000-2-222000000002222-2-200000000000000002i−2i−2i2i000000000000
χ282222-2-2-2-222000022-2-22-2-22-2-2-2-20000-2-222000000002222-2-20000000000000000−2i2i2i−2i000000000000
χ292-22-22-22-22-200002-2-2-2222-22i2i−2i−2i00002-22-2000000002i−2i2i−2i2i−2i0000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ302-22-22-22-22-200002-2-2-2222-22i2i−2i−2i00002-22-2000000002i−2i2i−2i2i−2i00000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ312-22-22-22-22-200002-2-2-2222-2−2i−2i2i2i00002-22-200000000−2i2i−2i2i−2i2i0000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ322-22-22-22-22-200002-2-2-2222-2−2i−2i2i2i00002-22-200000000−2i2i−2i2i−2i2i00000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ332-22-22-2-22-2200002-2-2-2222-22i2i−2i−2i0000-22-22000000002i−2i−2i2i−2i2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ342-22-22-2-22-2200002-2-2-2222-22i2i−2i−2i0000-22-22000000002i−2i−2i2i−2i2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ352-22-22-2-22-2200002-2-2-2222-2−2i−2i2i2i0000-22-2200000000−2i2i2i−2i2i−2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ362-22-22-2-22-2200002-2-2-2222-2−2i−2i2i2i0000-22-2200000000−2i2i2i−2i2i−2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ372-22-2-222-2-222i2i−2i−2i2-2222-2-2-22i2i−2i−2i00002-2-222i2i2i2i−2i−2i−2i−2i−2i2i2i−2i−2i2i0000000022-2-200000000000000000000
χ382-22-2-222-2-222i2i−2i−2i2-2222-2-2-2−2i−2i2i2i00002-2-222i2i2i2i−2i−2i−2i−2i2i−2i−2i2i2i−2i00000000-2-22200000000000000000000
χ392-22-2-222-2-22−2i−2i2i2i2-2222-2-2-22i2i−2i−2i00002-2-22−2i−2i−2i−2i2i2i2i2i−2i2i2i−2i−2i2i00000000-2-22200000000000000000000
χ402-22-2-222-2-22−2i−2i2i2i2-2222-2-2-2−2i−2i2i2i00002-2-22−2i−2i−2i−2i2i2i2i2i2i−2i−2i2i2i−2i0000000022-2-200000000000000000000
χ412-22-2-22-222-200002-2222-2-2-22i2i−2i−2i2-200-222-200000000−2i2i−2i2i2i−2i22-2-200000000002i−2i0000000000000000
χ422-22-2-22-222-200002-2222-2-2-22i2i−2i−2i-2200-222-200000000−2i2i−2i2i2i−2i-2-2220000000000−2i2i0000000000000000
χ432-22-2-22-222-200002-2222-2-2-2−2i−2i2i2i2-200-222-2000000002i−2i2i−2i−2i2i22-2-20000000000−2i2i0000000000000000
χ442-22-2-22-222-200002-2222-2-2-2−2i−2i2i2i-2200-222-2000000002i−2i2i−2i−2i2i-2-22200000000002i−2i0000000000000000
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
χ49444444-4-4-4-40000-1-1-1-1-1-1-1-10000004-4111155−5−555−5−50000005−55−5-1-111000000000000000000000000
χ50444444-4-4-4-40000-1-1-1-1-1-1-1-10000004-41111−5−555−5−555000000−55−55-1-111000000000000000000000000
χ51444444-4-4-4-40000-1-1-1-1-1-1-1-1000000-44111155−5−555−5−5000000−55−5511-1-1000000000000000000000000
χ52444444-4-4-4-40000-1-1-1-1-1-1-1-1000000-441111−5−555−5−5550000005−55−511-1-1000000000000000000000000
χ5344-4-40000002-22-24-400-40044i−4i4i−4i000000002-22-22-22-2000000000000002i−2i2i−2i00000000000000000000
χ5444-4-40000002-22-24-400-4004−4i4i−4i4i000000002-22-22-22-200000000000000−2i2i−2i2i00000000000000000000
χ5544-4-4000000-22-224-400-40044i−4i4i−4i00000000-22-22-22-2200000000000000−2i2i−2i2i00000000000000000000
χ5644-4-4000000-22-224-400-4004−4i4i−4i4i00000000-22-22-22-22000000000000002i−2i2i−2i00000000000000000000
χ574-44-4-444-4-444i4i−4i−4i-11-1-1-111100000000-111-1−i−i−i−iiiii0000005−5−55i5−i5i5−i5000000000000000000000000
χ584-44-4-444-4-444i4i−4i−4i-11-1-1-111100000000-111-1−i−i−i−iiiii000000−555−5−i5i5−i5i5000000000000000000000000
χ594-44-4-444-4-44−4i−4i4i4i-11-1-1-111100000000-111-1iiii−i−i−i−i0000005−5−55−i5i5−i5i5000000000000000000000000
χ604-44-4-444-4-44−4i−4i4i4i-11-1-1-111100000000-111-1iiii−i−i−i−i000000−555−5i5−i5i5−i5000000000000000000000000
χ614-44-4-44-444-40000-11-1-1-111100004-4001-1-11i5i5−i5−i5−i5−i5i5i5000000-1-111i5−i5−i5i5000000000000000000000000
χ624-44-4-44-444-40000-11-1-1-111100004-4001-1-11−i5−i5i5i5i5i5−i5−i5000000-1-111−i5i5i5−i5000000000000000000000000
χ634-44-4-44-444-40000-11-1-1-11110000-44001-1-11i5i5−i5−i5−i5−i5i5i500000011-1-1−i5i5i5−i5000000000000000000000000
χ644-44-4-44-444-40000-11-1-1-11110000-44001-1-11−i5−i5i5i5i5i5−i5−i500000011-1-1i5−i5−i5i5000000000000000000000000
χ654-4-440000002i−2i−2i2i4400-400-44-4-44000000002i−2i2i−2i−2i2i−2i2i00000000000000−2i2i2i−2i00000000000000000000
χ664-4-440000002i−2i−2i2i4400-400-4-444-4000000002i−2i2i−2i−2i2i−2i2i000000000000002i−2i−2i2i00000000000000000000
χ674-4-44000000−2i2i2i−2i4400-400-44-4-4400000000−2i2i−2i2i2i−2i2i−2i000000000000002i−2i−2i2i00000000000000000000
χ684-4-44000000−2i2i2i−2i4400-400-4-444-400000000−2i2i−2i2i2i−2i2i−2i00000000000000−2i2i2i−2i00000000000000000000
χ698888-8-888-8-80000-2-222-222-200000000-2-2220000000000000000000000000000000000000000000000
χ708888-8-8-8-8880000-2-222-222-20000000022-2-20000000000000000000000000000000000000000000000
χ7188-8-80000004-44-4-2225−25225−25-2000000000000−1+51−5−1−51+5−1+51−5−1−51+500000000000000000000000000000000000000
χ7288-8-80000004-44-4-22−25252−2525-2000000000000−1−51+5−1+51−5−1−51+5−1+51−500000000000000000000000000000000000000
χ7388-8-8000000-44-44-2225−25225−25-20000000000001−5−1+51+5−1−51−5−1+51+5−1−500000000000000000000000000000000000000
χ7488-8-8000000-44-44-22−25252−2525-20000000000001+5−1−51−5−1+51+5−1−51−5−1+500000000000000000000000000000000000000
χ758-88-88-88-88-80000-2222-2-2-2200000000-22-220000000000000000000000000000000000000000000000
χ768-88-88-8-88-880000-2222-2-2-22000000002-22-20000000000000000000000000000000000000000000000
χ778-8-880000004i−4i−4i4i-2-225−252−25252000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ142ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000000000000000
χ788-8-880000004i−4i−4i4i-2-2−2525225−252000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ382ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000000000000000
χ798-8-88000000−4i4i4i−4i-2-225−252−252520000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000000000000000
χ808-8-88000000−4i4i4i−4i-2-2−2525225−2520000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000000000000000

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