Finite Group Databasebeta

← Group #10591134

Character table — Group #10591134

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222222222222244444444444444444444444441212121212121212121212121212121212121212121212127272
order122233444466666612121212121212122366666666666121212121212121212121212444488881212121212121212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1
χ6111111-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11
χ7111111-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11
χ8111111-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1
χ922222222-2-22222222222-2-2-2-2-22-2-2-2-222-2-2-2-22-2-222-2-2-2-2222200000000000000000000000000
χ10222222-2-2-2-2222222-2-2-2-2-2-2-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000
χ1122222-12222222-1-1-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000
χ1222222-12222222-1-1-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000
χ1322222-122-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-1-2-211-1-11111-111221111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i30000000000
χ1422222-122-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-1-2-211-1-11111-111221111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i30000000000
χ1522222-1-2-222222-1-1-111112222-2-1-2-211-1-11111-1-1-1-2-2-1-1-1-1111122-2-20000-1-1-1-111110000000000
χ1622222-1-2-222222-1-1-111112222-2-1-2-211-1-11111-1-1-1-2-2-1-1-1-11111-2-22200001111-1-1-1-10000000000
χ1722222-1-2-2-2-2222-1-1-11111-2-2-2-22-122-1-1-1-1-1-1-1-1-111-2-21111111100000000−i3−i3i3i3i3i3−i3−i30000000000
χ1822222-1-2-2-2-2222-1-1-11111-2-2-2-22-122-1-1-1-1-1-1-1-1-111-2-21111111100000000i3i3−i3−i3−i3−i3i3i30000000000
χ192222-122222-1-1-12222222-1-1-1-12-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100
χ202222-122222-1-1-12222222-1-1-1-12-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000001111111100
χ212222-1222-2-2-1-1-122222221111-2-111-2-2-1-11111-1-2-2-1-11111-1-1-1-1000000000000000033−3−333−3−300
χ222222-1222-2-2-1-1-122222221111-2-111-2-2-1-11111-1-2-2-1-11111-1-1-1-10000000000000000−3−333−3−33300
χ232222-12-2-222-1-1-1222-2-2-2-2-1-1-1-1-2-111-2-2-1-11111-12211-1-1-1-11111000022-2-200000000-1-1-1-1111100
χ242222-12-2-222-1-1-1222-2-2-2-2-1-1-1-1-2-111-2-2-1-11111-12211-1-1-1-111110000-2-222000000001111-1-1-1-100
χ252222-12-2-2-2-2-1-1-1222-2-2-2-211112-1-1-122-1-1-1-1-1-1-1-2-21111111111000000000000000033−3−3−3−33300
χ262222-12-2-2-2-2-1-1-1222-2-2-2-211112-1-1-122-1-1-1-1-1-1-1-2-211111111110000000000000000−3−33333−3−300
χ272-22-222002-2-2-222-2-2000022-2-2020000-2-2000022-20022-2-20000002i−2i000000002i−2i2i−2i0000000000
χ282-22-222002-2-2-222-2-2000022-2-2020000-2-2000022-20022-2-2000000−2i2i00000000−2i2i−2i2i0000000000
χ292-22-22200-22-2-222-2-20000-2-222020000-2-200002-2200-2-22200002i−2i0000002i−2i2i−2i00000000000000
χ302-22-22200-22-2-222-2-20000-2-222020000-2-200002-2200-2-2220000−2i2i000000−2i2i−2i2i00000000000000
χ312-22-22-1002-2-2-22-111−i3−i3i3i322-2-20-100−i3i311−i3−i3i3i3-1-1100-1-111−i3−i3i3i3002i−2i00003−3−33−ii−ii0000000000
χ322-22-22-1002-2-2-22-111−i3−i3i3i322-2-20-100−i3i311−i3−i3i3i3-1-1100-1-111−i3−i3i3i300−2i2i0000−333−3i−ii−i0000000000
χ332-22-22-1002-2-2-22-111i3i3−i3−i322-2-20-100i3−i311i3i3−i3−i3-1-1100-1-111i3i3−i3−i3002i−2i0000−333−3−ii−ii0000000000
χ342-22-22-1002-2-2-22-111i3i3−i3−i322-2-20-100i3−i311i3i3−i3−i3-1-1100-1-111i3i3−i3−i300−2i2i00003−3−33i−ii−i0000000000
χ352-22-22-100-22-2-22-111−i3−i3i3i3-2-2220-100i3−i311i3i3−i3−i3-11-10011-1-1−i3−i3i3i32i−2i000000−ii−ii3−3−330000000000
χ362-22-22-100-22-2-22-111−i3−i3i3i3-2-2220-100i3−i311i3i3−i3−i3-11-10011-1-1−i3−i3i3i3−2i2i000000i−ii−i−333−30000000000
χ372-22-22-100-22-2-22-111i3i3−i3−i3-2-2220-100−i3i311−i3−i3i3i3-11-10011-1-1i3i3−i3−i32i−2i000000−ii−ii−333−30000000000
χ382-22-22-100-22-2-22-111i3i3−i3−i3-2-2220-100−i3i311−i3−i3i3i3-11-10011-1-1i3i3−i3−i3−2i2i000000i−ii−i3−3−330000000000
χ392-2-22222i−2i002-2-2-22-22i−2i2i−2i00000200002-20000-2002i−2i00002i−2i2i−2i00002−2−i2i2000000002−22−2−i2i2−i2i200
χ402-2-22222i−2i002-2-2-22-22i−2i2i−2i00000200002-20000-2002i−2i00002i−2i2i−2i0000−22i2−i200000000−22−22i2−i2i2−i200
χ412-2-2222−2i2i002-2-2-22-2−2i2i−2i2i00000200002-20000-200−2i2i0000−2i2i−2i2i00002−2i2−i2000000002−22−2i2−i2i2−i200
χ422-2-2222−2i2i002-2-2-22-2−2i2i−2i2i00000200002-20000-200−2i2i0000−2i2i−2i2i0000−22−i2i200000000−22−22−i2i2−i2i200
χ432-2-22-122i−2i00-111-22-22i−2i2i−2i3−33−30-1−i3i300-11−i3i3−i3i3100−ii3−33−3−ii−ii00002−2−i2i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700
χ442-2-22-122i−2i00-111-22-22i−2i2i−2i3−33−30-1−i3i300-11−i3i3−i3i3100−ii3−33−3−ii−ii0000−22i2−i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700
χ452-2-22-122i−2i00-111-22-22i−2i2i−2i−33−330-1i3−i300-11i3−i3i3−i3100−ii−33−33−ii−ii00002−2−i2i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300
χ462-2-22-122i−2i00-111-22-22i−2i2i−2i−33−330-1i3−i300-11i3−i3i3−i3100−ii−33−33−ii−ii0000−22i2−i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300
χ472-2-22-12−2i2i00-111-22-2−2i2i−2i2i3−33−30-1i3−i300-11i3−i3i3−i3100i−i3−33−3i−ii−i00002−2i2−i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700
χ482-2-22-12−2i2i00-111-22-2−2i2i−2i2i3−33−30-1i3−i300-11i3−i3i3−i3100i−i3−33−3i−ii−i0000−22−i2i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700
χ492-2-22-12−2i2i00-111-22-2−2i2i−2i2i−33−330-1−i3i300-11−i3i3−i3i3100i−i−33−33i−ii−i00002−2i2−i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300
χ502-2-22-12−2i2i00-111-22-2−2i2i−2i2i−33−330-1−i3i300-11−i3i3−i3i3100i−i−33−33i−ii−i0000−22−i2i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300
χ514444-2-24444-2-2-2-2-2-2-2-2-2-2-2-2-2-241-2-2-2-21111111-2-2-2-21111111100000000000000000000000000
χ524444-2-244-4-4-2-2-2-2-2-2-2-2-2-22222-41222211-1-1-1-1122-2-2-1-1-1-1111100000000000000000000000000
χ534444-2-2-4-444-2-2-2-2-2-22222-2-2-2-2-41222211-1-1-1-11-2-2221111-1-1-1-100000000000000000000000000
χ544444-2-2-4-4-4-4-2-2-2-2-2-22222222241-2-2-2-211111112222-1-1-1-1-1-1-1-100000000000000000000000000
χ5544-4-4440000-44-4-4-4400000000040000-440000-400000000000000000000000000000000000000
χ5644-4-44-20000-44-422-223−23−232300000-200002-2000020000000023−23−232300000000000000000000000000
χ5744-4-44-20000-44-422-2−232323−2300000-200002-20000200000000−232323−2300000000000000000000000000
χ5844-4-4-2400002-22-4-44000023−23−23230-200002-200002000023−23−2323000000000000000000000000000000
χ5944-4-4-2400002-22-4-440000−232323−230-200002-2000020000−232323−23000000000000000000000000000000
χ6044-4-4-2-200002-2222-223−23−232323−23−2323010000-11-333-3-10000−333−3−333−300000000000000000000000000
χ6144-4-4-2-200002-2222-223−23−2323−232323−23010000-113-3-33-100003−3−33−333−300000000000000000000000000
χ6244-4-4-2-200002-2222-2−232323−2323−23−2323010000-113-3-33-10000−333−33−3−3300000000000000000000000000
χ6344-4-4-2-200002-2222-2−232323−23−232323−23010000-11-333-3-100003−3−333−3−3300000000000000000000000000
χ644-44-4-24004-422-24-4-40000-2-2220-20000220000-24-400-2-222000000000000000000000000000000
χ654-44-4-2400-4422-24-4-4000022-2-20-20000220000-2-440022-2-2000000000000000000000000000000
χ664-44-4-2-2004-422-2-222−2i3−2i32i32i3-2-2220100−2i32i3-1-1i3i3−i3−i31-220011-1-1i3i3−i3−i300000000000000000000000000
χ674-44-4-2-2004-422-2-2222i32i3−2i3−2i3-2-22201002i3−2i3-1-1−i3−i3i3i31-220011-1-1−i3−i3i3i300000000000000000000000000
χ684-44-4-2-200-4422-2-222−2i3−2i32i32i322-2-201002i3−2i3-1-1−i3−i3i3i312-200-1-111i3i3−i3−i300000000000000000000000000
χ694-44-4-2-200-4422-2-2222i32i3−2i3−2i322-2-20100−2i32i3-1-1i3i3−i3−i312-200-1-111−i3−i3i3i300000000000000000000000000
χ704-4-444-24i−4i004-4-42-22−2i2i−2i2i00000-20000-2200002004i−4i0000−2i2i−2i2i00000000000000000000000000
χ714-4-444-2−4i4i004-4-42-222i−2i2i−2i00000-20000-220000200−4i4i00002i−2i2i−2i00000000000000000000000000
χ724-4-44-2-24i−4i00-2222-22−2i2i−2i2i23−2323−2301−2i32i3001-1i3−i3i3−i3-100−2i2i−33−33i−ii−i00000000000000000000000000
χ734-4-44-2-24i−4i00-2222-22−2i2i−2i2i−2323−2323012i3−2i3001-1−i3i3−i3i3-100−2i2i3−33−3i−ii−i00000000000000000000000000
χ744-4-44-2-2−4i4i00-2222-222i−2i2i−2i23−2323−23012i3−2i3001-1−i3i3−i3i3-1002i−2i−33−33−ii−ii00000000000000000000000000
χ754-4-44-2-2−4i4i00-2222-222i−2i2i−2i−2323−232301−2i32i3001-1i3−i3i3−i3-1002i−2i3−33−3−ii−ii00000000000000000000000000

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