Finite Group Databasebeta

← Group #11752367

Character table — Group #11752367

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222224444444444444444444455558888888888888888881010101010102020202020202020303030303030303060606060
order1222344666445101010121212121212151530303030303044442020202020206060606060606060606060602212121212446612121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ51111111111-1-11111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-11111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−iii
χ81111111111-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiii−i−i
χ911111-1-11111-1111111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-111-1-111-1-111-1-11-11-1
χ1011111-1-11111-1111111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-111-1-1-1-111-1-111-11-11
χ1111111-1-11111-1111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1111-1-111ii−i−i−i−iiii−i−ii
χ1211111-1-11111-1111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1111-1-111−i−iiiii−i−i−iii−i
χ1311111-1-1111-111111-1-111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-11111-1-111-1-1-11-11
χ1411111-1-1111-111111-1-111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-111-1-111-1-1111-11-1
χ1511111-1-1111-111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1ii−i−i−i−iii−iii−i
χ1611111-1-1111-111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1−i−iiiii−i−ii−i−ii
χ172222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1000000000000
χ182222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111111000000000000
χ192222-122-1-1-1-2-222221111-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-11111111122-1-1-1-1-2-2-1-11111000000000000
χ202222-122-1-1-1-2-222221111-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-2-211112211-1-1-1-1000000000000
χ212222-1-2-2-1-1-12-22222-1-11111-1-1-1-1-1-1-1-12222-2-222-2-21111-1-1-1-11111-2-2-1-1-1-12-211-1-111000000000000
χ222222-1-2-2-1-1-12-22222-1-11111-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-11111221111-22-1-111-1-1000000000000
χ232222-1-2-2-1-1-1-22222211-1-111-1-1-1-1-1-1-1-12222-2-2-2-22211111111-1-1-1-1-2-2-1-1-1-1-221111-1-1000000000000
χ242222-1-2-2-1-1-1-22222211-1-111-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211111111-1-1-1-12211112-2-1-1-1-111000000000000
χ2522-2-22002-2-2002-2-2200000022-2-2-2-2222i−2i2i−2i000000000000000000002i2i−2i−2i0000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000
χ2622-2-22002-2-2002-2-2200000022-2-2-2-2222i−2i2i−2i000000000000000000002i2i−2i−2i00000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1190000
χ2722-2-22002-2-2002-2-2200000022-2-2-2-222−2i2i−2i2i00000000000000000000−2i−2i2i2i00000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000
χ2822-2-22002-2-2002-2-2200000022-2-2-2-222−2i2i−2i2i00000000000000000000−2i−2i2i2i0000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000
χ292-22-222-2-22-2002-22-200002-222-2-222-2-222-2-22-2000022-2-2000000002-22-22-2002-20000000000000000
χ302-22-222-2-22-2002-22-200002-222-2-222-2-2-2-2222-2000022-2-200000000-22-22-2200-220000000000000000
χ312-22-22-22-22-2002-22-20000-2222-2-222-2-222-2-2-220000-2-22200000000-222-22-200-220000000000000000
χ322-22-22-22-22-2002-22-20000-2222-2-222-2-2-2-222-220000-2-222000000002-2-22-22002-20000000000000000
χ332-22-2-12-21-11002-22-23−33−3-11-1-111-1-11122-2-22-20000-1-11133−3−333−3−32-2-11-1100-113−33−3000000000000
χ342-22-2-12-21-11002-22-23−33−3-11-1-111-1-111-2-2222-20000-1-11133−3−333−3−3-221-11-1001-1−33−33000000000000
χ352-22-2-12-21-11002-22-2−33−33-11-1-111-1-11122-2-22-20000-1-111−3−333−3−3332-2-11-1100-11−33−33000000000000
χ362-22-2-12-21-11002-22-2−33−33-11-1-111-1-111-2-2222-20000-1-111−3−333−3−333-221-11-1001-13−33−3000000000000
χ372-22-2-1-221-11002-22-23−3−331-1-1-111-1-11122-2-2-22000011-1-133−3−3−3−333-22-11-11001-13−3−33000000000000
χ382-22-2-1-221-11002-22-23−3−331-1-1-111-1-111-2-222-22000011-1-133−3−3−3−3332-21-11-100-11−333−3000000000000
χ392-22-2-1-221-11002-22-2−333−31-1-1-111-1-11122-2-2-22000011-1-1−3−33333−3−3-22-11-11001-1−333−3000000000000
χ402-22-2-1-221-11002-22-2−333−31-1-1-111-1-111-2-222-22000011-1-1−3−33333−3−32-21-11-100-113−3−33000000000000
χ412-2-22200-2-220022-2-20000002222-2-2-2-22i−2i−2i2i000000000000000000002i−2i−2i2i00000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000
χ422-2-22200-2-220022-2-20000002222-2-2-2-22i−2i−2i2i000000000000000000002i−2i−2i2i000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119000000
χ432-2-22200-2-220022-2-20000002222-2-2-2-2−2i2i2i−2i00000000000000000000−2i2i2i−2i000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109000000
χ442-2-22200-2-220022-2-20000002222-2-2-2-2−2i2i2i−2i00000000000000000000−2i2i2i−2i00000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000000
χ45444444444444-1-1-1-1444444-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-4-4-1-1-1-1-4-4-4-444-1-1-1-1-1-1-1-10000-1-11111-1-1-1-11111111100000000000000000000000000
χ4744444-4-44444-4-1-1-1-144-4-4-4-4-1-1-1-1-1-1-1-1000011-1-1111111-1-1-1-1111100000000000000000000000000
χ4844444-4-4444-44-1-1-1-1-4-444-4-4-1-1-1-1-1-1-1-100001111-1-111111111-1-1-1-100000000000000000000000000
χ494444-244-2-2-244-1-1-1-1-2-2-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1520000-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200000000000000000000000000
χ504444-244-2-2-244-1-1-1-1-2-2-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1520000-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200000000000000000000000000
χ514444-244-2-2-2-4-4-1-1-1-12222-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1520000-1-111111−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000000
χ524444-244-2-2-2-4-4-1-1-1-12222-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1520000-1-111111+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000000
χ534444-2-4-4-2-2-24-4-1-1-1-1-2-222221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152000011-1-111−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000000
χ544444-2-4-4-2-2-24-4-1-1-1-1-2-222221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152000011-1-111−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000000
χ554444-2-4-4-2-2-2-44-1-1-1-122-2-2221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200001111-1-1−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i15200000000000000000000000000
χ564444-2-4-4-2-2-2-44-1-1-1-122-2-2221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200001111-1-1−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i15200000000000000000000000000
χ5744-4-4-200-222004-4-44000000-2-22222-2-24i−4i4i−4i00000000000000000000−2i−2i2i2i00000000000000000000
χ5844-4-4-200-222004-4-44000000-2-22222-2-2−4i4i−4i4i000000000000000000002i2i−2i−2i00000000000000000000
χ594-44-444-4-44-400-11-1100004-4-1-111-1-1110000-11−i5i5−i5i5-1-111−i5i5i5−i5−i5i5i5−i500000000000000000000000000
χ604-44-444-4-44-400-11-1100004-4-1-111-1-1110000-11i5−i5i5−i5-1-111i5−i5−i5i5i5−i5−i5i500000000000000000000000000
χ614-44-44-44-44-400-11-110000-44-1-111-1-11100001-1−i5i5i5−i511-1-1−i5i5i5−i5i5−i5−i5i500000000000000000000000000
χ624-44-44-44-44-400-11-110000-44-1-111-1-11100001-1i5−i5−i5i511-1-1i5−i5−i5i5−i5i5i5−i500000000000000000000000000
χ634-44-4-24-42-2200-11-1123−2323−23-221−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i1520000-11i5−i5i5−i51−i1521+i152−1+i152−1−i152ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ9400000000000000000000000000
χ644-44-4-24-42-2200-11-1123−2323−23-221+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i1520000-11−i5i5−i5i51+i1521−i152−1−i152−1+i152ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ11800000000000000000000000000
χ654-44-4-24-42-2200-11-11−2323−2323-221−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i1520000-11−i5i5−i5i51−i1521+i152−1+i152−1−i152−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ9400000000000000000000000000
χ664-44-4-24-42-2200-11-11−2323−2323-221+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i1520000-11i5−i5i5−i51+i1521−i152−1−i152−1+i152−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ11800000000000000000000000000
χ674-44-4-2-442-2200-11-1123−23−23232-21−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i15200001-1i5−i5−i5i5−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ9400000000000000000000000000
χ684-44-4-2-442-2200-11-1123−23−23232-21+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i15200001-1−i5i5i5−i5−1−i152−1+i1521+i1521−i152ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ11800000000000000000000000000
χ694-44-4-2-442-2200-11-11−232323−232-21−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i15200001-1−i5i5i5−i5−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ9400000000000000000000000000
χ704-44-4-2-442-2200-11-11−232323−232-21+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i15200001-1i5−i5−i5i5−1−i152−1+i1521+i1521−i152−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ11800000000000000000000000000
χ714-4-44-20022-20044-4-4000000-2-2-2-222224i−4i−4i4i00000000000000000000−2i2i2i−2i00000000000000000000
χ724-4-44-20022-20044-4-4000000-2-2-2-22222−4i4i4i−4i000000000000000000002i−2i−2i2i00000000000000000000
χ7388-8-88008-8-800-222-2000000-2-22222-2-2000000000000000000000000000000000000000000000000
χ7488-8-8-400-44400-222-20000001−i151+i15−1+i15−1−i15−1+i15−1−i151−i151+i15000000000000000000000000000000000000000000000000
χ7588-8-8-400-44400-222-20000001+i151−i15−1−i15−1+i15−1−i15−1+i151+i151−i15000000000000000000000000000000000000000000000000
χ768-8-88800-8-8800-2-222000000-2-2-2-22222000000000000000000000000000000000000000000000000
χ778-8-88-40044-400-2-2220000001−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i15000000000000000000000000000000000000000000000000
χ788-8-88-40044-400-2-2220000001+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i15000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.