Finite Group Databasebeta

← Group #10591093

Character table — Group #10591093

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222222222222244444444444444444444444444412121212121212121212121224242424242436363636
order1222334444666666121212122366666666666121212121212121212121212121288882424242424242424246612124444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-1111111111111-11-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1
χ6111111-1-1111111111111-11-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-111
χ7111111-1-1111111111111-11-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111
χ8111111-1-1111111111111-11-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1
χ922222222-2-2222222-2-2-2-2-22-2-2-2-222-2-2-2-22-2-22222-2-2-2-222220000000000000000000000
χ10222222-2-2-2-2222222-2-2-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ1122222-1222222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000
χ1222222-1222222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000-2-211110000
χ1322222-122-2-222-12-1-1-2-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-100000000000000−i3i3−i3i30000
χ1422222-122-2-222-12-1-1-2-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-100000000000000i3−i3i3−i30000
χ1522222-1-2-22222-12-1-12222-2-1-2-211-1-11111-1-1-1-2-211-1-1-1-111110000000000002-2-1-1110000
χ1622222-1-2-22222-12-1-12222-2-1-2-211-1-11111-1-1-1-2-211-1-1-1-11111000000000000-2211-1-10000
χ1722222-1-2-2-2-222-12-1-1-2-2-2-22-122-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000−i3i3i3−i30000
χ1822222-1-2-2-2-222-12-1-1-2-2-2-22-122-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000i3−i3−i3i30000
χ192222-122222-1-12-122-1-1-1-12-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ202222-122222-1-12-122-1-1-1-12-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ212222-1222-2-2-1-12-1221111-2-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-1000033−3−333−3−30000000000
χ222222-1222-2-2-1-12-1221111-2-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-10000−3−333−3−3330000000000
χ232222-12-2-222-1-12-122-1-1-1-1-2-111-2-2-1-11111-12211-2-2-1-1-1-1111122-2-2-1-1-1-111110000000000
χ242222-12-2-222-1-12-122-1-1-1-1-2-111-2-2-1-11111-12211-2-2-1-1-1-11111-2-2221111-1-1-1-10000000000
χ252222-12-2-2-2-2-1-12-12211112-1-1-122-1-1-1-1-1-1-1-2-211-2-211111111000033−3−3−3−3330000000000
χ262222-12-2-2-2-2-1-12-12211112-1-1-122-1-1-1-1-1-1-1-2-211-2-2111111110000−3−33333−3−30000000000
χ2722-2-222002-2-2-2-222-222-2-2020000-2-2000022-2000022-2-20000000000000000000000002i−2i
χ2822-2-222002-2-2-2-222-222-2-2020000-2-2000022-2000022-2-2000000000000000000000000−2i2i
χ2922-2-22200-22-2-2-222-2-2-222020000-2-200002-220000-2-22200000000000000000000002i−2i00
χ3022-2-22200-22-2-2-222-2-2-222020000-2-200002-220000-2-2220000000000000000000000−2i2i00
χ312-22-2222i−2i002-22-2-2-200000200002-20000-2002i−2i2i−2i00002i2i−2i−2i2−2−i2i22−22−2−i2i2−i2i20000000000
χ322-22-2222i−2i002-22-2-2-200000200002-20000-2002i−2i2i−2i00002i2i−2i−2i−22i2−i2−22−22i2−i2i2−i20000000000
χ332-22-222−2i2i002-22-2-2-200000200002-20000-200−2i2i−2i2i0000−2i−2i2i2i2−2i2−i22−22−2i2−i2i2−i20000000000
χ342-22-222−2i2i002-22-2-2-200000200002-20000-200−2i2i−2i2i0000−2i−2i2i2i−22−i2i2−22−22−i2i2−i2i20000000000
χ352-22-2-122i−2i00-1121-2-23−33−30-1−i3i300-11−i3−i3i3i3100−ii2i−2i3−33−3−i−iii2−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ362-22-2-122i−2i00-1121-2-23−33−30-1−i3i300-11−i3−i3i3i3100−ii2i−2i3−33−3−i−iii−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ372-22-2-122i−2i00-1121-2-2−33−330-1i3−i300-11i3i3−i3−i3100−ii2i−2i−33−33−i−iii2−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ382-22-2-122i−2i00-1121-2-2−33−330-1i3−i300-11i3i3−i3−i3100−ii2i−2i−33−33−i−iii−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ392-22-2-12−2i2i00-1121-2-23−33−30-1i3−i300-11i3i3−i3−i3100i−i−2i2i3−33−3ii−i−i2−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
χ402-22-2-12−2i2i00-1121-2-23−33−30-1i3−i300-11i3i3−i3−i3100i−i−2i2i3−33−3ii−i−i−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ412-22-2-12−2i2i00-1121-2-2−33−330-1−i3i300-11−i3−i3i3i3100i−i−2i2i−33−33ii−i−i2−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ422-22-2-12−2i2i00-1121-2-2−33−330-1−i3i300-11−i3−i3i3i3100i−i−2i2i−33−33ii−i−i−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ434444-2-24444-2-2-2-2-2-2-2-2-2-241-2-2-2-21111111-2-2-2-2-2-2111111110000000000000000000000
χ444444-2-244-4-4-2-2-2-2-2-22222-41222211-1-1-1-1122-2-2-2-2-1-1-1-111110000000000000000000000
χ454444-2-2-4-444-2-2-2-2-2-2-2-2-2-2-41222211-1-1-1-11-2-222221111-1-1-1-10000000000000000000000
χ464444-2-2-4-4-4-4-2-2-2-2-2-2222241-2-2-2-21111111222222-1-1-1-1-1-1-1-10000000000000000000000
χ4744-4-44-2004-4-4-424-2244-4-40-20000220000-2-220000-2-22200000000000000000000000000
χ4844-4-44-200-44-4-424-22-4-4440-20000220000-22-2000022-2-200000000000000000000000000
χ4944-4-4-24004-422-4-24-4-2-2220-20000220000-24-40000-2-22200000000000000000000000000
χ5044-4-4-2400-4422-4-24-422-2-20-20000220000-2-44000022-2-200000000000000000000000000
χ5144-4-4-2-2004-4222-2-22-2-222010000-1-13-33-31-22000011-1-13-33-30000000000000000000000
χ5244-4-4-2-2004-4222-2-22-2-222010000-1-1-33-331-22000011-1-1-33-330000000000000000000000
χ5344-4-4-2-200-44222-2-2222-2-2010000-1-13-33-312-20000-1-111-33-330000000000000000000000
χ5444-4-4-2-200-44222-2-2222-2-2010000-1-1-33-3312-20000-1-1113-33-30000000000000000000000
χ554-44-44-24i−4i004-4-2-42200000-20000-2200002004i−4i−2i2i0000−2i−2i2i2i0000000000000000000000
χ564-44-44-2−4i4i004-4-2-42200000-20000-220000200−4i4i2i−2i00002i2i−2i−2i0000000000000000000000
χ574-44-4-2-24i−4i00-22-222223−2323−2301−2i32i3001-1i3i3−i3−i3-100−2i2i−2i2i−33−33ii−i−i0000000000000000000000
χ584-44-4-2-24i−4i00-22-2222−2323−2323012i3−2i3001-1−i3−i3i3i3-100−2i2i−2i2i3−33−3ii−i−i0000000000000000000000
χ594-44-4-2-2−4i4i00-22-222223−2323−23012i3−2i3001-1−i3−i3i3i3-1002i−2i2i−2i−33−33−i−iii0000000000000000000000
χ604-44-4-2-2−4i4i00-22-2222−2323−232301−2i32i3001-1i3i3−i3−i3-1002i−2i2i−2i3−33−3−i−iii0000000000000000000000
χ614-4-44440000-44-4-4-440000040000-440000-4000000000000000000000000000000000000
χ624-4-444-20000-442-42-200000-200−2i32i32-2−2i32i32i3−2i32000000000000000000000000000000000000
χ634-4-444-20000-442-42-200000-2002i3−2i32-22i3−2i3−2i32i32000000000000000000000000000000000000
χ644-4-44-2400002-2-42-4423−23−23230-200002-20000200000023−23−232300000000000000000000000000
χ654-4-44-2400002-2-42-44−232323−230-200002-200002000000−232323−2300000000000000000000000000
χ664-4-44-2-200002-2222-223−23−23230100−2i32i3-11i3−i3−i3i3-1000000−333−3−3i3i3i−3i0000000000000000000000
χ674-4-44-2-200002-2222-223−23−232301002i3−2i3-11−i3i3i3−i3-1000000−333−33i−3i−3i3i0000000000000000000000
χ684-4-44-2-200002-2222-2−232323−230100−2i32i3-11i3−i3−i3i3-10000003−3−333i−3i−3i3i0000000000000000000000
χ694-4-44-2-200002-2222-2−232323−2301002i3−2i3-11−i3i3i3−i3-10000003−3−33−3i3i3i−3i0000000000000000000000

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