Finite Group Databasebeta

← Group #10590861

Character table — Group #10590861

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222222222444444444444444444444444444466121212121212121212121212122424242424363672
order122233446666661212121236668812121212121224242424242424242424242424242424444448812121212242424242661212444
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
χ51111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-11111-1
χ61111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1111-1-1-1-11
χ71111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-11
χ81111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-111-1
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
χ1122222-122-12-122-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10002200000000002-1-1-1-1000
χ1222222-122-12-122-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000-2-20000000000-21111000
χ1322222-122-12-122-12222-1-1-1-1-2-2-1-1-1-1-1-1-2-2-2-2111111111111000220000000000-211-1-1000
χ1422222-122-12-122-12222-1-1-1-1-2-2-1-1-1-1-1-1-2-2-2-2111111111111000-2-200000000002-1-111000
χ152222-12222-12-1-12-1-1-1-1-1-1-1-1222-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12220022-1-1-1-1-1-1-1-100000000
χ162222-12222-12-1-12-1-1-1-1-1-1-1-1222-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-200-2-21111111100000000
χ172222-12222-12-1-12-1-1-1-1-1-1-1-1-2-22-1-12-1-11111-2-2-2-21111111122200-2-2-1-1-1-1111100000000
χ182222-12222-12-1-12-1-1-1-1-1-1-1-1-2-22-1-12-1-11111-2-2-2-211111111-2-2-200221111-1-1-1-100000000
χ192222-12-2-22-12-1-121111-1-1-1-100-211-21133−3−300003333−3−3−3−322-20000-1-11133−3−300000000
χ202222-12-2-22-12-1-121111-1-1-1-100-211-21133−3−300003333−3−3−3−3-2-22000011-1-1−3−33300000000
χ212222-12-2-22-12-1-121111-1-1-1-100-211-211−3−3330000−3−3−3−3333322-20000-1-111−3−33300000000
χ222222-12-2-22-12-1-121111-1-1-1-100-211-211−3−3330000−3−3−3−33333-2-22000011-1-133−3−300000000
χ232-22-22200-2-2-22-22000022-2-22−20000002−22−222−2−222−2−222−2−22i−2i000−i2i22i−2i00−i2i2−i2i200000000
χ242-22-22200-2-2-22-22000022-2-22−20000002−22−222−2−222−2−222−2−2−2i2i000i2−i2−2i2i00i2−i2i2−i200000000
χ252-22-22200-2-2-22-22000022-2-2−22000000−22−22−2−222−2−222−2−2222i−2i000i2−i22i−2i00i2−i2i2−i200000000
χ262-22-22200-2-2-22-22000022-2-2−22000000−22−22−2−222−2−222−2−222−2i2i000−i2i2−2i2i00−i2i2−i2i200000000
χ272-22-2-1200-21-2-1123−33−3-1-1112−203−303−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ232i−2i000−i2i2−ii−i3i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ282-22-2-1200-21-2-1123−33−3-1-1112−203−303−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−2i2i000i2−i2i−ii3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ292-22-2-1200-21-2-1123−33−3-1-111−2203−303−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ232i−2i000i2−i2−ii−i3i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ302-22-2-1200-21-2-1123−33−3-1-111−2203−303−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−2i2i000−i2i2i−ii3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ312-22-2-1200-21-2-112−33−33-1-1112−20−330−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ72i−2i000−i2i2−iii3−i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ322-22-2-1200-21-2-112−33−33-1-1112−20−330−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2i2i000i2−i2i−i−i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ332-22-2-1200-21-2-112−33−33-1-111−220−330−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ72i−2i000i2−i2−iii3−i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ342-22-2-1200-21-2-112−33−33-1-111−220−330−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−2i2i000−i2i2i−i−i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ352-2-22222-2-222-2-2-222-2-22-2-2200222-2-2-200000000000000000002i−2i00000000000002i−2i000
χ362-2-22222-2-222-2-2-222-2-22-2-2200222-2-2-20000000000000000000−2i2i0000000000000−2i2i000
χ372-2-2222-22-222-2-2-2-2-2222-2-2200-2-2-22220000000000000000000000000000000000002-20
χ382-2-2222-22-222-2-2-2-2-2222-2-2200-2-2-2222000000000000000000000000000000000000-220
χ392-2-222-12-212-1-2-2122-2-2-111-100-1-1-111100003−33−33−33−33−33−30002i−2i00000000000−i3i3−ii000
χ402-2-222-12-212-1-2-2122-2-2-111-100-1-1-111100003−33−33−33−33−33−3000−2i2i00000000000i3−i3i−i000
χ412-2-222-12-212-1-2-2122-2-2-111-100-1-1-11110000−33−33−33−33−33−330002i−2i00000000000i3−i3−ii000
χ422-2-222-12-212-1-2-2122-2-2-111-100-1-1-11110000−33−33−33−33−33−33000−2i2i00000000000−i3i3i−i000
χ4344444-2-4-4-24-244-2-4-4-4-4-2-2-2-200222222000000000000000000000000000000000000000
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
χ4844-4-444004-4-4-44-400004-44-400000000000000000000000000000000000000000000000
χ4944-4-44-200-2-42-4420000-22-220000000000006−6−666−6−666−6−6600000000000000000000000
χ5044-4-44-200-2-42-4420000-22-22000000000000−666−6−666−6−666−600000000000000000000000
χ5144-4-4-240042-42-2-423−23−2323-22-2200023−230−2323000000000000000000000000000000000000000
χ5244-4-4-240042-42-2-4−232323−23-22-22000−2323023−23000000000000000000000000000000000000000
χ5344-4-4-2-200-2222-2223−23−23231-11-1000−3303−300006−6−66−2ζ5+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
χ5444-4-4-2-200-2222-2223−23−23231-11-1000−3303−30000−666−62ζ5−2ζ7+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
χ5544-4-4-2-200-2222-22−232323−231-11-10003−30−3300006−6−66ζ5−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
χ5644-4-4-2-200-2222-22−232323−231-11-10003−30−330000−666−6−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
χ574-44-44-2002-424-4-20000-2-22222−2200000022−2222−22−2−222−2−222−2−22200000000000000000000000
χ584-44-44-2002-424-4-20000-2-222−2222000000−2222−222222−2−222−2−222−2−200000000000000000000000
χ594-44-4-2-200222-22-223−2323−2311-1-122−220−330−332ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000000000000000000
χ604-44-4-2-200222-22-223−2323−2311-1-1−22220−330−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000000000000000000
χ614-44-4-2-200222-22-2−2323−232311-1-122−2203−303−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000000000000000000
χ624-44-4-2-200222-22-2−2323−232311-1-1−222203−303−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000000000000000000
χ634-4-444-2-4424-2-4-42-4-444-222-200222-2-2-2000000000000000000000000000000000000000
χ644-4-44-244-4-4-2422-4-2-222-222-2004-2-2-422000000000000000000000000000000000000000
χ654-4-44-24-44-4-2422-422-2-2-222-200-4224-2-2000000000000000000000000000000000000000
χ664-4-44-2-24-42-2-2222-2-2221-1-1100-2112-1-1000023−2323−23−33−33−33−3300000000000000000000000
χ674-4-44-2-24-42-2-2222-2-2221-1-1100-2112-1-10000−2323−23233−33−33−33−300000000000000000000000
χ684-4-44-2-2-442-2-222222-2-21-1-11002-1-1-211000000003-33-3-33-3300000000000000000000000
χ694-4-44-2-2-442-2-222222-2-21-1-11002-1-1-21100000000-33-333-33-300000000000000000000000

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