Finite Group Databasebeta

← Group #11752434

Character table — Group #11752434

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222224444444444444444444455558888888888888888881010101010102020202020202020303030303030303060606060
order122222366624566661010101212151530303030303044441010101020203030303030303030606060604412121212246612121212888888888888
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
χ51111111111-1-1111-1-1111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1
χ61111111111-1-1111-1-1111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-1111-1-1111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−iii
χ81111111111-1-1111-1-1111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiii−i−i
χ91111-1-111111-11-1-111111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-1-1-11111-1-111-1-11-11-1
χ101111-1-111111-11-1-111111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-1-1-111-1-111-1-111-11-11
χ111111-1-111111-11-1-111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-11111-1-1ii−i−i−i−iiii−i−ii
χ121111-1-111111-11-1-111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-11111-1-1−i−iiiii−i−i−iii−i
χ131111-1-11111-111-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-111-1-111-1-1-11-11
χ141111-1-11111-111-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-111-1-1111-11-1
χ151111-1-11111-111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111ii−i−i−i−iii−iii−i
χ161111-1-11111-111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111−i−iiiii−i−ii−i−ii
χ17222222-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1000000000000
χ18222222-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111111000000000000
χ19222222-1-1-1-1-2-22-1-11122211-1-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-11111111122-1-1-1-1-2-211-1-111000000000000
χ20222222-1-1-1-1-2-22-1-11122211-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-2-2111122-1-111-1-1000000000000
χ212222-2-2-1-1-1-12-2211-1-122211-1-1-1-1-1-1-1-12222-2-222-2-21111-1-1-1-11111-2-2-1-1-1-1-221111-1-1000000000000
χ222222-2-2-1-1-1-12-2211-1-122211-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-111112211112-2-1-1-1-111000000000000
χ232222-2-2-1-1-1-1-2221111222-1-1-1-1-1-1-1-1-1-12222-2-2-2-22211111111-1-1-1-1-2-2-1-1-1-12-2-1-11111000000000000
χ242222-2-2-1-1-1-1-2221111222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211111111-1-1-1-1221111-2211-1-1-1-1000000000000
χ2522-2-20022-2-200200002-2-2002222-2-2-2-22i2i−2i−2i000000000000000000002i2i−2i−2i00000000002ζ7+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
χ2622-2-20022-2-200200002-2-2002222-2-2-2-22i2i−2i−2i000000000000000000002i2i−2i−2i0000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000
χ2722-2-20022-2-200200002-2-2002222-2-2-2-2−2i−2i2i2i00000000000000000000−2i−2i2i2i0000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000
χ2822-2-20022-2-200200002-2-2002222-2-2-2-2−2i−2i2i2i00000000000000000000−2i−2i2i2i00000000002ζ13+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
χ292-22-2002-22-20020000-22-20022-2-222-2-22i−2i2i−2i000000000000000000002i−2i2i−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
χ302-22-2002-22-20020000-22-20022-2-222-2-22i−2i2i−2i000000000000000000002i−2i2i−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
χ312-22-2002-22-20020000-22-20022-2-222-2-2−2i2i−2i2i00000000000000000000−2i2i−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
χ322-22-2002-22-20020000-22-20022-2-222-2-2−2i2i−2i2i00000000000000000000−2i2i−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
χ332-2-222-22-2-220022-200-2-220022-2-2-2-2222-2-222-2000022-2-2000000002-22-2-2200002-200000000000000
χ342-2-222-22-2-220022-200-2-220022-2-2-2-222-222-22-2000022-2-200000000-22-222-20000-2200000000000000
χ352-2-222-2-111-1002-11−i3i3-2-22−i3i3-1-11111-1-12-2-222-20000-1-111−i3−i3i3i3−i3−i3i3i32-2-111-100−i3i3-11−i3i3000000000000
χ362-2-222-2-111-1002-11−i3i3-2-22−i3i3-1-11111-1-1-222-22-20000-1-111−i3−i3i3i3−i3−i3i3i3-221-1-1100i3−i31-1i3−i3000000000000
χ372-2-222-2-111-1002-11i3−i3-2-22i3−i3-1-11111-1-12-2-222-20000-1-111i3i3−i3−i3i3i3−i3−i32-2-111-100i3−i3-11i3−i3000000000000
χ382-2-222-2-111-1002-11i3−i3-2-22i3−i3-1-11111-1-1-222-22-20000-1-111i3i3−i3−i3i3i3−i3−i3-221-1-1100−i3i31-1−i3i3000000000000
χ392-2-22-222-2-22002-2200-2-220022-2-2-2-2222-2-22-220000-2-22200000000-222-2-220000-2200000000000000
χ402-2-22-222-2-22002-2200-2-220022-2-2-2-222-222-2-220000-2-222000000002-2-222-200002-200000000000000
χ412-2-22-22-111-10021-1−i3i3-2-22i3−i3-1-11111-1-12-2-22-22000011-1-1−i3−i3i3i3i3i3−i3−i3-22-111-100i3−i31-1−i3i3000000000000
χ422-2-22-22-111-10021-1−i3i3-2-22i3−i3-1-11111-1-1-222-2-22000011-1-1−i3−i3i3i3i3i3−i3−i32-21-1-1100−i3i3-11i3−i3000000000000
χ432-2-22-22-111-10021-1i3−i3-2-22−i3i3-1-11111-1-12-2-22-22000011-1-1i3i3−i3−i3−i3−i3i3i3-22-111-100−i3i31-1i3−i3000000000000
χ442-2-22-22-111-10021-1i3−i3-2-22−i3i3-1-11111-1-1-222-2-22000011-1-1i3i3−i3−i3−i3−i3i3i32-21-1-1100i3−i3-11−i3i3000000000000
χ45444444444444-14444-1-1-144-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-4-4-144-4-4-1-1-1-4-4-1-1-1-1-1-1-1-10000-1-11111-1-1-1-11111111100000000000000000000000000
χ47444444-2-2-2-244-1-2-2-2-2-1-1-1-2-21−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
χ48444444-2-2-2-244-1-2-2-2-2-1-1-1-2-21+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
χ49444444-2-2-2-2-4-4-1-2-222-1-1-1221−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
χ50444444-2-2-2-2-4-4-1-2-222-1-1-1221+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
χ514444-4-444444-4-1-4-444-1-1-1-4-4-1-1-1-1-1-1-1-1000011-1-1111111-1-1-1-1111100000000000000000000000000
χ524444-4-44444-44-1-4-4-4-4-1-1-144-1-1-1-1-1-1-1-100001111-1-111111111-1-1-1-100000000000000000000000000
χ534444-4-4-2-2-2-24-4-122-2-2-1-1-1221−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
χ544444-4-4-2-2-2-24-4-122-2-2-1-1-1221+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
χ554444-4-4-2-2-2-2-44-12222-1-1-1-2-21−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
χ564444-4-4-2-2-2-2-44-12222-1-1-1-2-21+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
χ5744-4-400-2-22200400004-4-400-2-2-2-222224i4i−4i−4i00000000000000000000−2i−2i2i2i00000000000000000000
χ5844-4-400-2-22200400004-4-400-2-2-2-22222−4i−4i4i4i000000000000000000002i2i−2i−2i00000000000000000000
χ594-44-400-22-220040000-44-400-2-222-2-2224i−4i4i−4i00000000000000000000−2i2i−2i2i00000000000000000000
χ604-44-400-22-220040000-44-400-2-222-2-222−4i4i−4i4i000000000000000000002i−2i2i−2i00000000000000000000
χ614-4-444-44-4-4400-14-40011-100-1-11111-1-10000-11−55−55-1-111−555−5−555−500000000000000000000000000
χ624-4-444-44-4-4400-14-40011-100-1-11111-1-10000-115−55−5-1-1115−5−555−5−5500000000000000000000000000
χ634-4-444-4-222-200-1-22−2i32i311-1−2i32i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1520000-115−55−51−i1521+i152−1+i152−1−i152ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ9200000000000000000000000000
χ644-4-444-4-222-200-1-22−2i32i311-1−2i32i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1520000-11−55−551+i1521−i152−1−i152−1+i152ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ11600000000000000000000000000
χ654-4-444-4-222-200-1-222i3−2i311-12i3−2i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1520000-11−55−551−i1521+i152−1+i152−1−i152−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ9200000000000000000000000000
χ664-4-444-4-222-200-1-222i3−2i311-12i3−2i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1520000-115−55−51+i1521−i152−1−i152−1+i152−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ11600000000000000000000000000
χ674-4-44-444-4-4400-1-440011-100-1-11111-1-100001-1−555−511-1-1−555−55−5−5500000000000000000000000000
χ684-4-44-444-4-4400-1-440011-100-1-11111-1-100001-15−5−5511-1-15−5−55−555−500000000000000000000000000
χ694-4-44-44-222-200-12-2−2i32i311-12i3−2i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i15200001-15−5−55−1+i152−1−i1521−i1521+i152ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ9200000000000000000000000000
χ704-4-44-44-222-200-12-2−2i32i311-12i3−2i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i15200001-1−555−5−1−i152−1+i1521+i1521−i152ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ11600000000000000000000000000
χ714-4-44-44-222-200-12-22i3−2i311-1−2i32i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i15200001-1−555−5−1+i152−1−i1521−i1521+i152−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ9200000000000000000000000000
χ724-4-44-44-222-200-12-22i3−2i311-1−2i32i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i15200001-15−5−55−1−i152−1+i1521+i1521−i152−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ11600000000000000000000000000
χ7388-8-80088-8-800-20000-22200-2-2-2-22222000000000000000000000000000000000000000000000000
χ7488-8-800-4-44400-20000-222001−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i15000000000000000000000000000000000000000000000000
χ7588-8-800-4-44400-20000-222001+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i15000000000000000000000000000000000000000000000000
χ768-88-8008-88-800-200002-2200-2-222-2-222000000000000000000000000000000000000000000000000
χ778-88-800-44-4400-200002-22001−i151+i15−1+i15−1−i151−i151+i15−1+i15−1−i15000000000000000000000000000000000000000000000000
χ788-88-800-44-4400-200002-22001+i151−i15−1−i15−1+i151+i151−i15−1−i15−1+i15000000000000000000000000000000000000000000000000

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