Finite Group Databasebeta

← Group #11752354

Character table — Group #11752354

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222224444444444444444444455558888888888888888881010101010102020202020202020303030303030303060606060
order12223446662456610101012121212151530303030303044441010202020203030303060606060606060604412121212246612121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ4111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii
χ51111111111-1-11-1-111111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1
χ61111111111-1-11-1-111111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11-1-111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii
χ81111111111-1-11-1-111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−i
χ911111-1-11111-1111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-1-1-11-11-1
χ1011111-1-11111-1111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-1-1-11111-11-11
χ1111111-1-11111-1111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1ii−i−i−i−iiii−i−ii
χ1211111-1-11111-1111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1−i−iiiii−i−i−iii−i
χ1311111-1-1111-111-1-1111-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-11111-1-1-1-1-11-11
χ1411111-1-1111-111-1-1111-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-1-1-111111-11-1
χ1511111-1-1111-111-1-1111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111ii−i−i−i−iii−iii−i
χ1611111-1-1111-111-1-1111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111−i−iiiii−i−ii−i−ii
χ172222-122-1-1-1222-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1000000000000
χ182222-122-1-1-1222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2111111000000000000
χ192222-122-1-1-1-2-2211222-1-111-1-1-1-1-1-1-1-12222-2-222-2-21111-1-1-1-1111122-1-1-1-1-2-211-1-111000000000000
χ202222-122-1-1-1-2-2211222-1-111-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-11111-2-2111122-1-111-1-1000000000000
χ212222-1-2-2-1-1-12-22-1-12221111-1-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-111111111-2-2-1-1-1-1-221111-1-1000000000000
χ222222-1-2-2-1-1-12-22-1-12221111-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1111111112211112-2-1-1-1-111000000000000
χ232222-1-2-2-1-1-1-2221122211-1-1-1-1-1-1-1-1-1-12222-2-2-2-22211111111-1-1-1-1-2-2-1-1-1-12-2-1-11111000000000000
χ242222-1-2-2-1-1-1-2221122211-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211111111-1-1-1-1221111-2211-1-1-1-1000000000000
χ2522-2-22002-2-200200-22-2000022-2-222-2-22i−2i2i−2i000000000000000000002i2i−2i−2i000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900000000
χ2622-2-22002-2-200200-22-2000022-2-222-2-22i−2i2i−2i000000000000000000002i2i−2i−2i00000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900000000
χ2722-2-22002-2-200200-22-2000022-2-222-2-2−2i2i−2i2i00000000000000000000−2i−2i2i2i00000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900000000
χ2822-2-22002-2-200200-22-2000022-2-222-2-2−2i2i−2i2i00000000000000000000−2i−2i2i2i000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900000000
χ292-22-222i−2i-22-2002002-2-22i−2i002222-2-2-2-22i−2i−2i2i002i−2i0000002i2i−2i−2i00002-22i−2i2i−2i00002-200000000000000
χ302-22-222i−2i-22-2002002-2-22i−2i002222-2-2-2-2−2i2i2i−2i002i−2i0000002i2i−2i−2i0000-22−2i2i−2i2i0000-2200000000000000
χ312-22-22−2i2i-22-2002002-2-2−2i2i002222-2-2-2-22i−2i−2i2i00−2i2i000000−2i−2i2i2i0000-222i−2i2i−2i0000-2200000000000000
χ322-22-22−2i2i-22-2002002-2-2−2i2i002222-2-2-2-2−2i2i2i−2i00−2i2i000000−2i−2i2i2i00002-2−2i2i−2i2i00002-200000000000000
χ332-22-2-12i−2i1-11002−i3i32-2-2−ii3−3-1-1-1-111112i−2i−2i2i002i−2i00−i3−i3i3i3−i−iii33−3−32-2−ii−ii00−i3i3-113−3000000000000
χ342-22-2-12i−2i1-11002−i3i32-2-2−ii3−3-1-1-1-11111−2i2i2i−2i002i−2i00−i3−i3i3i3−i−iii33−3−3-22i−ii−i00i3−i31-1−33000000000000
χ352-22-2-12i−2i1-11002i3−i32-2-2−ii−33-1-1-1-111112i−2i−2i2i002i−2i00i3i3−i3−i3−i−iii−3−3332-2−ii−ii00i3−i3-11−33000000000000
χ362-22-2-12i−2i1-11002i3−i32-2-2−ii−33-1-1-1-11111−2i2i2i−2i002i−2i00i3i3−i3−i3−i−iii−3−333-22i−ii−i00−i3i31-13−3000000000000
χ372-22-2-1−2i2i1-11002−i3i32-2-2i−i−33-1-1-1-111112i−2i−2i2i00−2i2i00−i3−i3i3i3ii−i−i−3−333-22−ii−ii00i3−i31-13−3000000000000
χ382-22-2-1−2i2i1-11002−i3i32-2-2i−i−33-1-1-1-11111−2i2i2i−2i00−2i2i00−i3−i3i3i3ii−i−i−3−3332-2i−ii−i00−i3i3-11−33000000000000
χ392-22-2-1−2i2i1-11002i3−i32-2-2i−i3−3-1-1-1-111112i−2i−2i2i00−2i2i00i3i3−i3−i3ii−i−i33−3−3-22−ii−ii00−i3i31-1−33000000000000
χ402-22-2-1−2i2i1-11002i3−i32-2-2i−i3−3-1-1-1-11111−2i2i2i−2i00−2i2i00i3i3−i3−i3ii−i−i33−3−32-2i−ii−i00i3−i3-113−3000000000000
χ412-2-22200-2-2200200-2-22000022-2-2-2-22222-2-2000000000000000000002-2-220000000000002i−2i2i−2i0000
χ422-2-22200-2-2200200-2-22000022-2-2-2-22222-2-2000000000000000000002-2-22000000000000−2i2i−2i2i0000
χ432-2-22200-2-2200200-2-22000022-2-2-2-222-2-22200000000000000000000-222-20000000000002-2-220000
χ442-2-22200-2-2200200-2-22000022-2-2-2-222-2-22200000000000000000000-222-2000000000000-222-20000
χ45444444444444-144-1-1-14444-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-4-4-1-4-4-1-1-144-4-4-1-1-1-1-1-1-1-1000011-1-1111111-1-1-1-1111100000000000000000000000000
χ4744444-4-44444-4-144-1-1-1-4-4-4-4-1-1-1-1-1-1-1-10000-1-11111-1-1-1-11111111100000000000000000000000000
χ4844444-4-4444-44-1-4-4-1-1-1-4-444-1-1-1-1-1-1-1-100001111-1-111111111-1-1-1-100000000000000000000000000
χ494444-244-2-2-244-1-2-2-1-1-1-2-2-2-21−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
χ504444-244-2-2-244-1-2-2-1-1-1-2-2-2-21+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
χ514444-244-2-2-2-4-4-122-1-1-1-2-2221−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
χ524444-244-2-2-2-4-4-122-1-1-1-2-2221+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
χ534444-2-4-4-2-2-24-4-1-2-2-1-1-122221−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
χ544444-2-4-4-2-2-24-4-1-2-2-1-1-122221+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
χ554444-2-4-4-2-2-2-44-122-1-1-122-2-21−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
χ564444-2-4-4-2-2-2-44-122-1-1-122-2-21+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
χ5744-4-4-200-22200400-44-40000-2-222-2-2224i−4i4i−4i00000000000000000000−2i−2i2i2i00000000000000000000
χ5844-4-4-200-22200400-44-40000-2-222-2-222−4i4i−4i4i000000000000000000002i2i−2i−2i00000000000000000000
χ594-44-444i−4i-44-400-100-1114i−4i00-1-1-1-111110000−55−ii−i5i5−555−5−i−iii−i5i5i5−i500000000000000000000000000
χ604-44-444i−4i-44-400-100-1114i−4i00-1-1-1-1111100005−5−iii5−i55−5−55−i−iiii5−i5−i5i500000000000000000000000000
χ614-44-44−4i4i-44-400-100-111−4i4i00-1-1-1-111110000−55i−ii5−i5−555−5ii−i−ii5−i5−i5i500000000000000000000000000
χ624-44-44−4i4i-44-400-100-111−4i4i00-1-1-1-1111100005−5i−i−i5i55−5−55ii−i−i−i5i5i5−i500000000000000000000000000
χ634-44-4-24i−4i2-2200-1−2i32i3-111−2i2i23−231−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i15200005−5−iii5−i5ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ14+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
χ644-44-4-24i−4i2-2200-1−2i32i3-111−2i2i23−231+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i1520000−55−ii−i5i5ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ38+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
χ654-44-4-24i−4i2-2200-12i3−2i3-111−2i2i−23231−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i1520000−55−ii−i5i5−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ14+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
χ664-44-4-24i−4i2-2200-12i3−2i3-111−2i2i−23231+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i15200005−5−iii5−i5−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ38+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
χ674-44-4-2−4i4i2-2200-1−2i32i3-1112i−2i−23231−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i15200005−5i−i−i5i5ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−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
χ684-44-4-2−4i4i2-2200-1−2i32i3-1112i−2i−23231+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i1520000−55i−ii5−i5ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−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
χ694-44-4-2−4i4i2-2200-12i3−2i3-1112i−2i23−231−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i1520000−55i−ii5−i5−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−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
χ704-44-4-2−4i4i2-2200-12i3−2i3-1112i−2i23−231+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i15200005−5i−i−i5i5−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−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
χ714-4-44-20022-200400-4-440000-2-22222-2-244-4-400000000000000000000-222-200000000000000000000
χ724-4-44-20022-200400-4-440000-2-22222-2-2-4-444000000000000000000002-2-2200000000000000000000
χ7388-8-88008-8-800-2002-220000-2-222-2-222000000000000000000000000000000000000000000000000
χ7488-8-8-400-44400-2002-2200001−i151+i15−1+i15−1−i151−i151+i15−1+i15−1−i15000000000000000000000000000000000000000000000000
χ7588-8-8-400-44400-2002-2200001+i151−i15−1−i15−1+i151+i151−i15−1−i15−1+i15000000000000000000000000000000000000000000000000
χ768-8-88800-8-8800-20022-20000-2-22222-2-2000000000000000000000000000000000000000000000000
χ778-8-88-40044-400-20022-200001−i151+i15−1+i15−1−i15−1+i15−1−i151−i151+i15000000000000000000000000000000000000000000000000
χ788-8-88-40044-400-20022-200001+i151−i15−1−i15−1+i15−1−i15−1+i151+i151−i15000000000000000000000000000000000000000000000000

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