Finite Group Databasebeta

← Group #11752435

Character table — Group #11752435

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222224444444444444444444455558888888888888888881010101010102020202020202020303030303030303060606060
order122234466622566661010101212151530303030303044441010101020203030303030303030606060602212121212446612121212888888888888
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
χ51111111111-1-11-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-11-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−iii
χ81111111111-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111−i−i−i−iiiiiii−i−i
χ911111-1-11111-1111-1-1111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-111-1-111-1-11-11-1
χ1011111-1-11111-1111-1-1111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-111-1-111-11-11
χ1111111-1-11111-1111-1-1111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111ii−i−i−i−iiii−i−ii
χ1211111-1-11111-1111-1-1111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111−i−iiiii−i−i−iii−i
χ1311111-1-1111-111-1-111111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-1-1-11111-1-111-1-1-11-11
χ1411111-1-1111-111-1-111111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-1-1-111-1-111-1-1111-11-1
χ1511111-1-1111-111-1-111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-11111-1-1ii−i−i−i−iii−iii−i
χ1611111-1-1111-111-1-111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-11111-1-1−i−iiiii−i−ii−i−ii
χ172222-122-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1000000000000
χ182222-122-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111111000000000000
χ192222-122-1-1-1-2-221111222-1-1-1-1-1-1-1-1-1-12222-2-2-2-22211111111-1-1-1-122-1-1-1-1-2-2-1-11111000000000000
χ202222-122-1-1-1-2-221111222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211111111-1-1-1-1-2-211112211-1-1-1-1000000000000
χ212222-1-2-2-1-1-12-22-1-11122211-1-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-111111111-2-2-1-1-1-12-211-1-111000000000000
χ222222-1-2-2-1-1-12-22-1-11122211-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111221111-22-1-111-1-1000000000000
χ232222-1-2-2-1-1-1-22211-1-122211-1-1-1-1-1-1-1-12222-2-222-2-21111-1-1-1-11111-2-2-1-1-1-1-221111-1-1000000000000
χ242222-1-2-2-1-1-1-22211-1-122211-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-111112211112-2-1-1-1-111000000000000
χ2522-2-22002-2-200200002-2-2002222-2-2-2-22i2i−2i−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
χ2622-2-22002-2-200200002-2-2002222-2-2-2-22i2i−2i−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
χ2722-2-22002-2-200200002-2-2002222-2-2-2-2−2i−2i2i2i00000000000000000000−2i−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
χ2822-2-22002-2-200200002-2-2002222-2-2-2-2−2i−2i2i2i00000000000000000000−2i−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
χ292-22-2200-22-20020000-22-20022-2-222-2-22i−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
χ302-22-2200-22-20020000-22-20022-2-222-2-22i−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
χ312-22-2200-22-20020000-22-20022-2-222-2-2−2i2i−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
χ322-22-2200-22-20020000-22-20022-2-222-2-2−2i2i−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
χ332-2-2222-2-2-220020000-2-222-222-2-2-2-2222-2-2200002-20000000022-2-22-22-2-22002-20000000000000000
χ342-2-2222-2-2-220020000-2-222-222-2-2-2-222-222-200002-20000000022-2-2-22-222-200-220000000000000000
χ352-2-222-22-2-220020000-2-22-2222-2-2-2-2222-2-220000-2200000000-2-222-222-2-2200-220000000000000000
χ362-2-222-22-2-220020000-2-22-2222-2-2-2-222-222-20000-2200000000-2-2222-2-222-2002-20000000000000000
χ372-2-22-12-211-1002−i3i3−i3i3-2-22-11-1-11111-1-12-2-2200002-2−i3−i3i3i3−i3−i3i3i3-1-1112-2-111-100-11−i3i3−i3i3000000000000
χ382-2-22-12-211-1002−i3i3−i3i3-2-22-11-1-11111-1-1-222-200002-2−i3−i3i3i3−i3−i3i3i3-1-111-221-1-11001-1i3−i3i3−i3000000000000
χ392-2-22-12-211-1002i3−i3i3−i3-2-22-11-1-11111-1-12-2-2200002-2i3i3−i3−i3i3i3−i3−i3-1-1112-2-111-100-11i3−i3i3−i3000000000000
χ402-2-22-12-211-1002i3−i3i3−i3-2-22-11-1-11111-1-1-222-200002-2i3i3−i3−i3i3i3−i3−i3-1-111-221-1-11001-1−i3i3−i3i3000000000000
χ412-2-22-1-2211-1002−i3i3i3−i3-2-221-1-1-11111-1-12-2-220000-22−i3−i3i3i3i3i3−i3−i311-1-1-22-111-1001-1−i3i3i3−i3000000000000
χ422-2-22-1-2211-1002−i3i3i3−i3-2-221-1-1-11111-1-1-222-20000-22−i3−i3i3i3i3i3−i3−i311-1-12-21-1-1100-11i3−i3−i3i3000000000000
χ432-2-22-1-2211-1002i3−i3−i3i3-2-221-1-1-11111-1-12-2-220000-22i3i3−i3−i3−i3−i3i3i311-1-1-22-111-1001-1i3−i3−i3i3000000000000
χ442-2-22-1-2211-1002i3−i3−i3i3-2-221-1-1-11111-1-1-222-20000-22i3i3−i3−i3−i3−i3i3i311-1-12-21-1-1100-11−i3i3i3−i3000000000000
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
χ464444444444-4-4-1-4-4-4-4-1-1-144-1-1-1-1-1-1-1-100001111-1-111111111-1-1-1-100000000000000000000000000
χ4744444-4-44444-4-144-4-4-1-1-1-4-4-1-1-1-1-1-1-1-10000-1-11111-1-1-1-11111111100000000000000000000000000
χ4844444-4-4444-44-1-4-444-1-1-1-4-4-1-1-1-1-1-1-1-1000011-1-1111111-1-1-1-1111100000000000000000000000000
χ494444-244-2-2-244-1-2-2-2-2-1-1-1-2-21−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
χ504444-244-2-2-244-1-2-2-2-2-1-1-1-2-21+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
χ514444-244-2-2-2-4-4-12222-1-1-1-2-21−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
χ524444-244-2-2-2-4-4-12222-1-1-1-2-21+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
χ534444-2-4-4-2-2-24-4-1-2-222-1-1-1221−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
χ544444-2-4-4-2-2-24-4-1-2-222-1-1-1221+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
χ554444-2-4-4-2-2-2-44-122-2-2-1-1-1221−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
χ564444-2-4-4-2-2-2-44-122-2-2-1-1-1221+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
χ5744-4-4-200-22200400004-4-400-2-2-2-222224i4i−4i−4i00000000000000000000−2i−2i2i2i00000000000000000000
χ5844-4-4-200-22200400004-4-400-2-2-2-22222−4i−4i4i4i000000000000000000002i2i−2i−2i00000000000000000000
χ594-44-4-2002-220040000-44-400-2-222-2-2224i−4i4i−4i00000000000000000000−2i2i−2i2i00000000000000000000
χ604-44-4-2002-220040000-44-400-2-222-2-222−4i4i−4i4i000000000000000000002i−2i2i−2i00000000000000000000
χ614-4-4444-4-4-4400-1000011-14-4-1-11111-1-10000−55−55-11−555−5−555−5-1-11100000000000000000000000000
χ624-4-4444-4-4-4400-1000011-14-4-1-11111-1-100005−55−5-115−5−555−5−55-1-11100000000000000000000000000
χ634-4-444-44-4-4400-1000011-1-44-1-11111-1-10000−555−51-1−555−55−5−5511-1-100000000000000000000000000
χ644-4-444-44-4-4400-1000011-1-44-1-11111-1-100005−5−551-15−5−55−555−511-1-100000000000000000000000000
χ654-4-44-24-422-200-1−2i32i3−2i32i311-1-221−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i15200005−55−5-11ζ28−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+ζ921−i1521+i152−1+i152−1−i15200000000000000000000000000
χ664-4-44-24-422-200-1−2i32i3−2i32i311-1-221+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1520000−55−55-11ζ4−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+ζ1161+i1521−i152−1−i152−1+i15200000000000000000000000000
χ674-4-44-24-422-200-12i3−2i32i3−2i311-1-221−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1520000−55−55-11−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−ζ921−i1521+i152−1+i152−1−i15200000000000000000000000000
χ684-4-44-24-422-200-12i3−2i32i3−2i311-1-221+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i15200005−55−5-11−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−ζ1161+i1521−i152−1−i152−1+i15200000000000000000000000000
χ694-4-44-2-4422-200-1−2i32i32i3−2i311-12-21−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i15200005−5−551-1ζ28−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−ζ92−1+i152−1−i1521−i1521+i15200000000000000000000000000
χ704-4-44-2-4422-200-1−2i32i32i3−2i311-12-21+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1520000−555−51-1ζ4−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−ζ116−1−i152−1+i1521+i1521−i15200000000000000000000000000
χ714-4-44-2-4422-200-12i3−2i3−2i32i311-12-21−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1520000−555−51-1−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+ζ92−1+i152−1−i1521−i1521+i15200000000000000000000000000
χ724-4-44-2-4422-200-12i3−2i3−2i32i311-12-21+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i15200005−5−551-1−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+ζ116−1−i152−1+i1521+i1521−i15200000000000000000000000000
χ7388-8-88008-8-800-20000-22200-2-2-2-22222000000000000000000000000000000000000000000000000
χ7488-8-8-400-44400-20000-222001−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i15000000000000000000000000000000000000000000000000
χ7588-8-8-400-44400-20000-222001+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i15000000000000000000000000000000000000000000000000
χ768-88-8800-88-800-200002-2200-2-222-2-222000000000000000000000000000000000000000000000000
χ778-88-8-4004-4400-200002-22001−i151+i15−1+i15−1−i151−i151+i15−1+i15−1−i15000000000000000000000000000000000000000000000000
χ788-88-8-4004-4400-200002-22001+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.