Finite Group Databasebeta

← Group #10590800

Character table — Group #10590800

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222222222444444444444444444444444444466121212121212121212121212122424242424363672
order12223344666666121212123666881212121212122424242424242424242424242424242444444881212121224242424412121212444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-111-1-111-1
χ61111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11-1-111-1-11
χ71111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-11
χ81111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-11111-1
χ9222222-2-2222222-2-2-2-2222200-2-2-2-2-2-2000000000000000022-2000022-2-2000000000000
χ10222222-2-2222222-2-2-2-2222200-2-2-2-2-2-20000000000000000-2-220000-2-222000000000000
χ1122222-12222-1-1-12-1-1-1-1-1-1-1-1222-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12220022-1-1-1-1-1-1-1-100000000
χ1222222-12222-1-1-12-1-1-1-1-1-1-1-1222-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-200-2-21111111100000000
χ1322222-12222-1-1-12-1-1-1-1-1-1-1-1-2-22-1-12-1-11111-2-2-2-21111111122200-2-2-1-1-1-1111100000000
χ1422222-12222-1-1-12-1-1-1-1-1-1-1-1-2-22-1-12-1-11111-2-2-2-211111111-2-2-200221111-1-1-1-100000000
χ1522222-1-2-222-1-1-121111-1-1-1-100-211-21133−3−300003333−3−3−3−322-20000-1-11133−3−300000000
χ1622222-1-2-222-1-1-121111-1-1-1-100-211-21133−3−300003333−3−3−3−3-2-22000011-1-1−3−33300000000
χ1722222-1-2-222-1-1-121111-1-1-1-100-211-211−3−3330000−3−3−3−3333322-20000-1-111−3−33300000000
χ1822222-1-2-222-1-1-121111-1-1-1-100-211-211−3−3330000−3−3−3−33333-2-22000011-1-133−3−300000000
χ192222-1222-1-1222-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10002200000000002-1-1-1-1000
χ202222-1222-1-1222-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000-2-20000000000-21111000
χ212222-1222-1-1222-12222-1-1-1-1-2-2-1-1-1-1-1-1-2-2-2-2111111111111000220000000000-2-1-111000
χ222222-1222-1-1222-12222-1-1-1-1-2-2-1-1-1-1-1-1-2-2-2-2111111111111000-2-20000000000211-1-1000
χ2322-2-222002-2-22-2-2000022-2-22−20000002−22−222−2−222−2−222−2−22-20002−22-2002−22−200000000
χ2422-2-222002-2-22-2-2000022-2-22−20000002−22−222−2−222−2−222−2−2-22000−22-2200−22−2200000000
χ2522-2-222002-2-22-2-2000022-2-2−22000000−22−22−2−222−2−222−2−2222-2000−222-200−22−2200000000
χ2622-2-222002-2-22-2-2000022-2-2−22000000−22−22−2−222−2−222−2−222-220002−2-22002−22−200000000
χ2722-2-22-1002-21-11-23−33−3-1-1112−203−303−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ232-20002−2-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ2822-2-22-1002-21-11-23−33−3-1-1112−203−303−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-22000−221-1−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ2922-2-22-1002-21-11-23−33−3-1-111−2203−303−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ232-2000−22-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ3022-2-22-1002-21-11-23−33−3-1-111−2203−303−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-220002−21-1−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ3122-2-22-1002-21-11-2−33−33-1-1112−20−330−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ72-20002−2-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ3222-2-22-1002-21-11-2−33−33-1-1112−20−330−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-22000−221-13−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ3322-2-22-1002-21-11-2−33−33-1-111−220−330−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ72-2000−22-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ3422-2-22-1002-21-11-2−33−33-1-111−220−330−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-220002−21-13−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ352-2-22222-2-2-22-2-2222-2-22-2-2200222-2-2-20000000000000000000000000000000000002i−2i0
χ362-2-22222-2-2-22-2-2222-2-22-2-2200222-2-2-2000000000000000000000000000000000000−2i2i0
χ372-2-2222-22-2-22-2-22-2-2222-2-2200-2-2-222200000000000000000002-2000000000002-200000
χ382-2-2222-22-2-22-2-22-2-2222-2-2200-2-2-22220000000000000000000-2200000000000-2200000
χ392-2-22-12-22112-2-2-1-2-222-111-100111-1-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30002-200000000000-11−i3i3000
χ402-2-22-12-22112-2-2-1-2-222-111-100111-1-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000-22000000000001-1i3−i3000
χ412-2-22-12-22112-2-2-1-2-222-111-100111-1-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30002-200000000000-11i3−i3000
χ422-2-22-12-22112-2-2-1-2-222-111-100111-1-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000-22000000000001-1−i3i3000
χ434444-24-4-4-2-2444-2-4-4-4-4-2-2-2-200222222000000000000000000000000000000000000000
χ444444-2-244-2-2-2-2-2-2-2-2-2-2111144-211-211-2-2-2-2-2-2-2-21111111100000000000000000000000
χ454444-2-244-2-2-2-2-2-2-2-2-2-21111-4-4-211-21122222222-1-1-1-1-1-1-1-100000000000000000000000
χ464444-2-2-4-4-2-2-2-2-2-222221111002-1-12-1-12323−23−230000−3−3−3−3333300000000000000000000000
χ474444-2-2-4-4-2-2-2-2-2-222221111002-1-12-1-1−23−23232300003333−3−3−3−300000000000000000000000
χ4844-4-4-2400-22-44-420000-2-22222−2200000022−2222−22−2−222−2−222−2−22200000000000000000000000
χ4944-4-4-2400-22-44-420000-2-222−2222000000−2222−222222−2−222−2−222−2−200000000000000000000000
χ5044-4-4-2-200-222-22223−2323−2311-1-122−220−330−332ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000000000000000000
χ5144-4-4-2-200-222-22223−2323−2311-1-1−22220−330−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000000000000000000
χ5244-4-4-2-200-222-222−2323−232311-1-122−2203−303−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000000000000000000
χ5344-4-4-2-200-222-222−2323−232311-1-1−222203−303−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000000000000000000
χ544-44-44400-44-4-44-400004-44-400000000000000000000000000000000000000000000000
χ554-44-44-200-4422-2-423−23−2323-22-2200023−230−2323000000000000000000000000000000000000000
χ564-44-44-200-4422-2-4−232323−23-22-22000−2323023−23000000000000000000000000000000000000000
χ574-44-4-24002-2-4-4420000-22-22000000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ584-44-4-24002-2-4-4420000-22-22000000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ594-44-4-2-2002-222-2223−23−23231-11-1000−3303−30000i6−i6−i6i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ2300000000000000000000000
χ604-44-4-2-2002-222-2223−23−23231-11-1000−3303−30000−i6i6i6−i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ2300000000000000000000000
χ614-44-4-2-2002-222-22−232323−231-11-10003−30−330000i6−i6−i6i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ2300000000000000000000000
χ624-44-4-2-2002-222-22−232323−231-11-10003−30−330000−i6i6i6−i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ2300000000000000000000000
χ634-4-444-24-4-4-4-2224-2-222-222-2004-2-2-422000000000000000000000000000000000000000
χ644-4-444-2-44-4-4-222422-2-2-222-200-4224-2-2000000000000000000000000000000000000000
χ654-4-44-244-4224-4-4-244-4-4-222-200-2-2-2222000000000000000000000000000000000000000
χ664-4-44-2-24-422-222-2-2-2221-1-1100-2112-1-1000000003i−3i3i−3i−3i3i−3i3i00000000000000000000000
χ674-4-44-2-24-422-222-2-2-2221-1-1100-2112-1-100000000−3i3i−3i3i3i−3i3i−3i00000000000000000000000
χ684-4-44-2-2-4422-222-222-2-21-1-11002-1-1-2110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i300000000000000000000000
χ694-4-44-2-2-4422-222-222-2-21-1-11002-1-1-21100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i300000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.