Finite Group Databasebeta

← Group #10590850

Character table — Group #10590850

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222222222222244444444444444444444444444441212121212121212121212122424242424247272
order122233446666661212121236668812121212121224242424242424242424242424242424246688121224242424441212121224
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-1-111-11
χ61111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1111-1-11-1
χ71111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1111-1
χ81111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1111-1-1-11
χ9222222-2-2222222-2-2-2-2222200-2-2-2-2-2-200000000000000002-22200-2-2000000000000
χ10222222-2-2222222-2-2-2-2222200-2-2-2-2-2-20000000000000000-22-2-20022000000000000
χ1122222-1222-1-1-122-1-1-1-1-1-1-1-1222-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000
χ1222222-1222-1-1-122-1-1-1-1-1-1-1-1222-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-211-2-211111100000000
χ1322222-1222-1-1-122-1-1-1-1-1-1-1-1-2-22-1-12-1-11111-2-2-2-21111111122-1-1-2-2-1-1111100000000
χ1422222-1222-1-1-122-1-1-1-1-1-1-1-1-2-22-1-12-1-11111-2-2-2-211111111-2-2112211-1-1-1-100000000
χ1522222-1-2-22-1-1-1221111-1-1-1-100-211-21133−3−300003333−3−3−3−32-2-1-1001133−3−300000000
χ1622222-1-2-22-1-1-1221111-1-1-1-100-211-21133−3−300003333−3−3−3−3-221100-1-1−3−33300000000
χ1722222-1-2-22-1-1-1221111-1-1-1-100-211-211−3−3330000−3−3−3−333332-2-1-10011−3−33300000000
χ1822222-1-2-22-1-1-1221111-1-1-1-100-211-211−3−3330000−3−3−3−33333-221100-1-133−3−300000000
χ192222-1222-1222-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-100
χ202222-1222-1222-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2111100
χ212222-1222-1222-1-12222-1-1-1-1-2-2-1-1-1-1-1-1-2-2-2-21111111111110000000000002-211-1-100
χ222222-1222-1222-1-12222-1-1-1-1-2-2-1-1-1-1-1-1-2-2-2-2111111111111000000000000-22-1-11100
χ232-22-2222-2-2-2-22-2222-2-22-2-222i−2i222-2-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000
χ242-22-2222-2-2-2-22-2222-2-22-2-22−2i2i222-2-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ252-22-222-22-2-2-22-22-2-2222-2-2200-2-2-2222000000000000000000002-2002-22-200000000
χ262-22-222-22-2-2-22-22-2-2222-2-2200-2-2-222200000000000000000000-2200-22-2200000000
χ272-22-22-12-2-211-1-22-1-111-111-12i−2i2-1-1-211−ii−ii2i2i−2i−2i−i−iii−i−iii00−i3i300−i3i33−3−3300000000
χ282-22-22-12-2-211-1-22-1-111-111-12i−2i2-1-1-211−ii−ii2i2i−2i−2i−i−iii−i−iii00i3−i300i3−i3−333−300000000
χ292-22-22-12-2-211-1-22-1-111-111-1−2i2i2-1-1-211i−ii−i−2i−2i2i2iii−i−iii−i−i00−i3i300−i3i3−333−300000000
χ302-22-22-12-2-211-1-22-1-111-111-1−2i2i2-1-1-211i−ii−i−2i−2i2i2iii−i−iii−i−i00i3−i300i3−i33−3−3300000000
χ312-22-22-1-22-211-1-2211-1-1-111-100-2112-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i300−i3i32-2i3−i3-11-1100000000
χ322-22-22-1-22-211-1-2211-1-1-111-100-2112-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i300i3−i3-22−i3i31-11-100000000
χ332-22-22-1-22-211-1-2211-1-1-111-100-2112-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i300−i3i3-22i3−i31-11-100000000
χ342-22-22-1-22-211-1-2211-1-1-111-100-2112-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i300i3−i32-2−i3i3-11-1100000000
χ352-22-2-122-21-2-221-122-2-2-111-12i−2i-1-1-11112i−2i2i−2i−i−iii−i−iii−i−iii000000000000003−3−i3i300
χ362-22-2-122-21-2-221-122-2-2-111-12i−2i-1-1-11112i−2i2i−2i−i−iii−i−iii−i−iii00000000000000−33i3−i300
χ372-22-2-122-21-2-221-122-2-2-111-1−2i2i-1-1-1111−2i2i−2i2iii−i−iii−i−iii−i−i000000000000003−3i3−i300
χ382-22-2-122-21-2-221-122-2-2-111-1−2i2i-1-1-1111−2i2i−2i2iii−i−iii−i−iii−i−i00000000000000−33−i3i300
χ394444-24-4-4-2444-2-2-4-4-4-4-2-2-2-200222222000000000000000000000000000000000000
χ404444-2-244-2-2-2-2-2-2-2-2-2-2111144-211-211-2-2-2-2-2-2-2-21111111100000000000000000000
χ414444-2-244-2-2-2-2-2-2-2-2-2-21111-4-4-211-21122222222-1-1-1-1-1-1-1-100000000000000000000
χ424444-2-2-4-4-2-2-2-2-2-222221111002-1-12-1-12323−23−230000−3−3−3−3333300000000000000000000
χ434444-2-2-4-4-2-2-2-2-2-222221111002-1-12-1-1−23−23232300003333−3−3−3−300000000000000000000
χ4444-4-4440044-4-4-4-4000044-4-400000000000000000000000000000000000000000000
χ4544-4-44-2004-222-4-423−2323−23-2-22200023−23023−23000000000000000000000000000000000000
χ4644-4-44-2004-222-4-4−2323−2323-2-222000−23230−2323000000000000000000000000000000000000
χ4744-4-4-2400-24-4-4220000-2-222000000000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i600000000000000000000
χ4844-4-4-2400-24-4-4220000-2-222000000000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i600000000000000000000
χ4944-4-4-2-200-2-2222223−2323−2311-1-1000−330−330000i6−i6i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ2300000000000000000000
χ5044-4-4-2-200-2-2222223−2323−2311-1-1000−330−330000−i6i6−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ2300000000000000000000
χ5144-4-4-2-200-2-22222−2323−232311-1-10003−303−30000i6−i6i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ2300000000000000000000
χ5244-4-4-2-200-2-22222−2323−232311-1-10003−303−30000−i6i6−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ2300000000000000000000
χ534-44-4-24-442-4-442-2-4-444-222-200222-2-2-2000000000000000000000000000000000000
χ544-44-4-2-24-4222-22-2-2-2221-1-114i−4i-2112-1-1−2i2i−2i2i−2i−2i2i2iii−i−iii−i−i00000000000000000000
χ554-44-4-2-24-4222-22-2-2-2221-1-11−4i4i-2112-1-12i−2i2i−2i2i2i−2i−2i−i−iii−i−iii00000000000000000000
χ564-44-4-2-2-44222-22-222-2-21-1-11002-1-1-211−2i32i32i3−2i30000i3i3−i3−i3−i3−i3i3i300000000000000000000
χ574-44-4-2-2-44222-22-222-2-21-1-11002-1-1-2112i3−2i3−2i32i30000−i3−i3i3i3i3i3−i3−i300000000000000000000
χ584-4-444400-4-44-44-400004-44-400000000000000000000000000000000000000000000
χ594-4-444-200-42-224-423−23−2323-22-2200023−230−2323000000000000000000000000000000000000
χ604-4-444-200-42-224-4−232323−23-22-22000−2323023−23000000000000000000000000000000000000
χ614-4-44-24002-44-4-220000-22-220000000000006−6−666−6−666−6−6600000000000000000000
χ624-4-44-24002-44-4-220000-22-22000000000000−666−6−666−6−666−600000000000000000000
χ634-4-44-2-20022-22-2223−23−23231-11-1000−3303−300006−6−66ζ5−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+ζ2300000000000000000000
χ644-4-44-2-20022-22-2223−23−23231-11-1000−3303−30000−666−6−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−ζ2300000000000000000000
χ654-4-44-2-20022-22-22−232323−231-11-10003−30−3300006−6−66−2ζ5+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+2ζ13−2ζ2300000000000000000000
χ664-4-44-2-20022-22-22−232323−231-11-10003−30−330000−666−62ζ5−2ζ7+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+2ζ2300000000000000000000

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