Finite Group Databasebeta

← Group #13019593

Character table — Group #13019593

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12222222225101010101010104444441010101020202020202020204444444420202020202020202444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ51111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111111111-111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111111111-111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111111111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ12111111111111111111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ13111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2-2-22-2-222-2-2200000022-2-2000000002222-2-2-2-20000000000000000000000002i−2i002i−2i
χ18222222-2-2-2-22-2-222-2-2200000022-2-2000000002222-2-2-2-2000000000000000000000000−2i2i00−2i2i
χ19222222-2-2-2-22-2-222-2-2200000022-2-200000000-2-2-2-222220000000000000000000000002-200-22
χ20222222-2-2-2-22-2-222-2-2200000022-2-200000000-2-2-2-22222000000000000000000000000-22002-2
χ212222-2-222-2-22-2-222-2-22000000-2-2220000000022-2-222-2-200000000000000000000002i−2i002i−2i00
χ222222-2-222-2-22-2-222-2-22000000-2-2220000000022-2-222-2-20000000000000000000000−2i2i00−2i2i00
χ232222-2-222-2-22-2-222-2-22000000-2-22200000000-2-222-2-22200000000000000000000002-200-2200
χ242222-2-222-2-22-2-222-2-22000000-2-22200000000-2-222-2-2220000000000000000000000-22002-200
χ252222-2-2-2-22222222222200-200-2-2-2-20000000022-2-2-2-22222-2-20000-2200000000000000000000
χ262222-2-2-2-22222222222200-200-2-2-2-200000000-2-22222-2-222-2-200002-200000000000000000000
χ272222-2-2-2-22222222222-200200-2-2-2-20000000022-2-2-2-222-2-22200002-200000000000000000000
χ282222-2-2-2-22222222222-200200-2-2-2-200000000-2-22222-2-2-2-2220000-2200000000000000000000
χ292-22-22-22-22-22-2-2-2-22220000002-22-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ302-22-22-22-22-22-2-2-2-22220000002-22-2000000002i−2i2i−2i2i−2i2i−2i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ312-22-22-22-22-22-2-2-2-22220000002-22-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ322-22-22-22-22-22-2-2-2-22220000002-22-200000000−2i2i−2i2i−2i2i−2i2i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ332-22-22-2-22-22222-2-2-2-2202-20002-2-222222-2-2-2-22i−2i2i−2i−2i2i−2i2i00000000002i−2i000000000000000000
χ342-22-22-2-22-22222-2-2-2-2202-20002-2-222222-2-2-2-2−2i2i−2i2i2i−2i2i−2i0000000000−2i2i000000000000000000
χ352-22-22-2-22-22222-2-2-2-220-220002-2-22-2-2-2-222222i−2i2i−2i−2i2i−2i2i0000000000−2i2i000000000000000000
χ362-22-22-2-22-22222-2-2-2-220-220002-2-22-2-2-2-22222−2i2i−2i2i2i−2i2i−2i00000000002i−2i000000000000000000
χ372-22-2-222-2-22222-2-2-2-2200002i−2i-222-2000000002i−2i−2i2i2i−2i−2i2i00002i2i−2i−2i00002-20000000000000000
χ382-22-2-222-2-22222-2-2-2-2200002i−2i-222-200000000−2i2i2i−2i−2i2i2i−2i00002i2i−2i−2i0000-220000000000000000
χ392-22-2-222-2-22222-2-2-2-220000−2i2i-222-2000000002i−2i−2i2i2i−2i−2i2i0000−2i−2i2i2i0000-220000000000000000
χ402-22-2-222-2-22222-2-2-2-220000−2i2i-222-200000000−2i2i2i−2i−2i2i2i−2i0000−2i−2i2i2i00002-20000000000000000
χ412-22-2-22-222-22-2-2-2-2222000000-22-22000000002i−2i−2i2i−2i2i2i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ422-22-2-22-222-22-2-2-2-2222000000-22-22000000002i−2i−2i2i−2i2i2i−2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ432-22-2-22-222-22-2-2-2-2222000000-22-2200000000−2i2i2i−2i2i−2i−2i2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ442-22-2-22-222-22-2-2-2-2222000000-22-2200000000−2i2i2i−2i2i−2i−2i2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ454444444444-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444-1-1-1-1-1-1-1-14-4-44-4-4-1-1-1-11111111100000000-1-1-1-111110000000000000000000000
χ474444444444-1-1-1-1-1-1-1-1-444-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000000111111110000000000000000000000
χ484444444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-111111111000000001111-1-1-1-10000000000000000000000
χ494444-4-4-4-444-1-1-1-1-1-1-1-1400-400111155−5−555−5−500000000-1-1115−55−50000000000000000000000
χ504444-4-4-4-444-1-1-1-1-1-1-1-1400-4001111−5−555−5−55500000000-1-111−55−550000000000000000000000
χ514444-4-4-4-444-1-1-1-1-1-1-1-1-400400111155−5−555−5−50000000011-1-1−55−550000000000000000000000
χ524444-4-4-4-444-1-1-1-1-1-1-1-1-4004001111−5−555−5−5550000000011-1-15−55−50000000000000000000000
χ534-44-44-4-44-44-1-1-11111-104-4000-111-1-1-1-1-1111100000000i5−i5i5−i5i5−i5−i5i50000000000000000000000
χ544-44-44-4-44-44-1-1-11111-104-4000-111-1-1-1-1-1111100000000−i5i5−i5i5−i5i5i5−i50000000000000000000000
χ554-44-44-4-44-44-1-1-11111-10-44000-111-11111-1-1-1-100000000i5−i5i5−i5−i5i5i5−i50000000000000000000000
χ564-44-44-4-44-44-1-1-11111-10-44000-111-11111-1-1-1-100000000−i5i5−i5i5i5−i5−i5i50000000000000000000000
χ574-44-4-444-4-44-1-1-11111-100004i−4i1-1-1155−5−5−5−55500000000i5−i5−i5i5−i−iii0000000000000000000000
χ584-44-4-444-4-44-1-1-11111-100004i−4i1-1-11−5−55555−5−500000000−i5i5i5−i5−i−iii0000000000000000000000
χ594-44-4-444-4-44-1-1-11111-10000−4i4i1-1-1155−5−5−5−55500000000−i5i5i5−i5ii−i−i0000000000000000000000
χ604-44-4-444-4-44-1-1-11111-10000−4i4i1-1-11−5−55555−5−500000000i5−i5−i5i5ii−i−i0000000000000000000000
χ61888888-8-8-8-8-222-2-222-2000000-2-2220000000000000000000000000000000000000000000000
χ628888-8-888-8-8-222-2-222-200000022-2-20000000000000000000000000000000000000000000000
χ6388-8-80000008008-800-800000000000000000000000000000000000000000000000000000000
χ6488-8-8000000-225−25-2225−25200000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000000000000000000
χ6588-8-8000000-225−25-2225−2520000000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000000000000000000
χ6688-8-8000000-2−2525-22−252520000000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000
χ6788-8-8000000-2−2525-22−2525200000000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000
χ688-88-88-88-88-8-22222-2-2-2000000-22-220000000000000000000000000000000000000000000000
χ698-88-8-88-888-8-22222-2-2-20000002-22-20000000000000000000000000000000000000000000000
χ708-8-88000000800-8800-800000000000000000000000000000000000000000000000000000000
χ718-8-88000000-225−252-2−2525200000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000000000000000000
χ728-8-88000000-225−252-2−252520000000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000000000000000000
χ738-8-88000000-2−25252-225−2520000000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000
χ748-8-88000000-2−25252-225−25200000000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000

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