Finite Group Databasebeta

← Group #10591173

Character table — Group #10591173

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222222222222244444444444444444444444441212121212121212121212121212121212121212121212127272
order12223344446666661212121212121212236666666666612121212121212121212121222446666888812121212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
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
χ5111111-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-1
χ6111111-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11
χ7111111-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11
χ8111111-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-1
χ922222222-2-22222222222-2-2-2-2-22-2-2-2-222-2-2-2-2222-2-2-2-2-2-2222200000000000000000000000000
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
χ1122222-1222222-1-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-10000000000
χ1222222-1222222-1-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111000011110000000000
χ1322222-122-2-222-1-12-1-1-1-1-1-2-2-2-2-2-1-2-211-1-11111-122111111-1-1-1-10000−i3−i3i3i30000−i3−i3i3i30000000000
χ1422222-122-2-222-1-12-1-1-1-1-1-2-2-2-2-2-1-2-211-1-11111-122111111-1-1-1-10000i3i3−i3−i30000i3i3−i3−i30000000000
χ1522222-1-2-22222-1-12-111112222-2-1-2-211-1-11111-1-2-2-1-1-1-1-1-1111122-2-2-1-1-1-1000011110000000000
χ1622222-1-2-22222-1-12-111112222-2-1-2-211-1-11111-1-2-2-1-1-1-1-1-11111-2-22211110000-1-1-1-10000000000
χ1722222-1-2-2-2-222-1-12-11111-2-2-2-22-122-1-1-1-1-1-1-1-1-1-2-211111111110000−i3−i3i3i30000i3i3−i3−i30000000000
χ1822222-1-2-2-2-222-1-12-11111-2-2-2-22-122-1-1-1-1-1-1-1-1-1-2-211111111110000i3i3−i3−i30000−i3−i3i3i30000000000
χ192222-122222-1-122-122222-1-1-1-12-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-100
χ202222-122222-1-122-122222-1-1-1-12-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-2-2-200001111111100
χ212222-1222-2-2-1-122-1222221111-2-111-2-2-1-11111-1-1-1-2-21111-1-1-1-1000000000000000033−3−333−3−300
χ222222-1222-2-2-1-122-1222221111-2-111-2-2-1-11111-1-1-1-2-21111-1-1-1-10000000000000000−3−333−3−33300
χ232222-12-2-222-1-122-12-2-2-2-2-1-1-1-1-2-111-2-2-1-11111-11122-1-1-1-111110000000022-2-20000-1-1-1-1111100
χ242222-12-2-222-1-122-12-2-2-2-2-1-1-1-1-2-111-2-2-1-11111-11122-1-1-1-1111100000000-2-22200001111-1-1-1-100
χ252222-12-2-2-2-2-1-122-12-2-2-2-211112-1-1-122-1-1-1-1-1-1-111-2-211111111000000000000000033−3−3−3−33300
χ262222-12-2-2-2-2-1-122-12-2-2-2-211112-1-1-122-1-1-1-1-1-1-111-2-2111111110000000000000000−3−33333−3−300
χ272-22-2222i−2i002-22-2-2-22i2i−2i−2i00000200002-20000-22i−2i0000002i2i−2i−2i000000002−2−i2i200002−22−2−i2i2−i2i200
χ282-22-2222i−2i002-22-2-2-22i2i−2i−2i00000200002-20000-22i−2i0000002i2i−2i−2i00000000−22i2−i20000−22−22i2−i2i2−i200
χ292-22-222−2i2i002-22-2-2-2−2i−2i2i2i00000200002-20000-2−2i2i000000−2i−2i2i2i000000002−2i2−i200002−22−2i2−i2i2−i200
χ302-22-222−2i2i002-22-2-2-2−2i−2i2i2i00000200002-20000-2−2i2i000000−2i−2i2i2i00000000−22−i2i20000−22−22−i2i2−i2i200
χ312-22-2-122i−2i00-112-21-22i2i−2i−2i33−3−30-1−i3i300-11−i3−i3i3i31−ii0033−3−3−i−iii000000002−2−i2i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700
χ322-22-2-122i−2i00-112-21-22i2i−2i−2i33−3−30-1−i3i300-11−i3−i3i3i31−ii0033−3−3−i−iii00000000−22i2−i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700
χ332-22-2-122i−2i00-112-21-22i2i−2i−2i−3−3330-1i3−i300-11i3i3−i3−i31−ii00−3−333−i−iii000000002−2−i2i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300
χ342-22-2-122i−2i00-112-21-22i2i−2i−2i−3−3330-1i3−i300-11i3i3−i3−i31−ii00−3−333−i−iii00000000−22i2−i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300
χ352-22-2-12−2i2i00-112-21-2−2i−2i2i2i33−3−30-1i3−i300-11i3i3−i3−i31i−i0033−3−3ii−i−i000000002−2i2−i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700
χ362-22-2-12−2i2i00-112-21-2−2i−2i2i2i33−3−30-1i3−i300-11i3i3−i3−i31i−i0033−3−3ii−i−i00000000−22−i2i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700
χ372-22-2-12−2i2i00-112-21-2−2i−2i2i2i−3−3330-1−i3i300-11−i3−i3i3i31i−i00−3−333ii−i−i000000002−2i2−i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300
χ382-22-2-12−2i2i00-112-21-2−2i−2i2i2i−3−3330-1−i3i300-11−i3−i3i3i31i−i00−3−333ii−i−i00000000−22−i2i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300
χ392-2-2222002-2-2-2-2-22200002-22-2020000-2-200002002-22-22-20000002-2000000002-22-20000000000
χ402-2-2222002-2-2-2-2-22200002-22-2020000-2-200002002-22-22-2000000-2200000000-22-220000000000
χ412-2-222200-22-2-2-2-2220000-22-22020000-2-20000200-22-22-2200002-2002-22-2000000000000000000
χ422-2-222200-22-2-2-2-2220000-22-22020000-2-20000200-22-22-220000-2200-22-22000000000000000000
χ432-2-222-1002-2-2-2112-1−i3i3−i3i32-22-20-100−i3i311−i3i3−i3i3-100-11-11-11−i3i3−i3i3002-2−i3i3i3−i30000-11-110000000000
χ442-2-222-1002-2-2-2112-1−i3i3−i3i32-22-20-100−i3i311−i3i3−i3i3-100-11-11-11−i3i3−i3i300-22i3−i3−i3i300001-11-10000000000
χ452-2-222-1002-2-2-2112-1i3−i3i3−i32-22-20-100i3−i311i3−i3i3−i3-100-11-11-11i3−i3i3−i3002-2i3−i3−i3i30000-11-110000000000
χ462-2-222-1002-2-2-2112-1i3−i3i3−i32-22-20-100i3−i311i3−i3i3−i3-100-11-11-11i3−i3i3−i300-22−i3i3i3−i300001-11-10000000000
χ472-2-222-100-22-2-2112-1−i3i3−i3i3-22-220-100i3−i311i3−i3i3−i3-1001-11-11-1−i3i3−i3i32-200-11-110000−i3i3i3−i30000000000
χ482-2-222-100-22-2-2112-1−i3i3−i3i3-22-220-100i3−i311i3−i3i3−i3-1001-11-11-1−i3i3−i3i3-22001-11-10000i3−i3−i3i30000000000
χ492-2-222-100-22-2-2112-1i3−i3i3−i3-22-220-100−i3i311−i3i3−i3i3-1001-11-11-1i3−i3i3−i32-200-11-110000i3−i3−i3i30000000000
χ502-2-222-100-22-2-2112-1i3−i3i3−i3-22-220-100−i3i311−i3i3−i3i3-1001-11-11-1i3−i3i3−i3-22001-11-10000−i3i3i3−i30000000000
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
χ524444-2-244-4-4-2-2-2-2-2-2-2-2-2-22222-41222211-1-1-1-11-2-222-1-1-1-1111100000000000000000000000000
χ534444-2-2-4-444-2-2-2-2-2-22222-2-2-2-2-41222211-1-1-1-1122-2-21111-1-1-1-100000000000000000000000000
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
χ5544-4-4440000-44-44-4-400000000040000-440000-400000000000000000000000000000000000000
χ5644-4-44-20000-442-2-4223−23−232300000-200002-2000020000000023−23−232300000000000000000000000000
χ5744-4-44-20000-442-2-42−232323−2300000-200002-20000200000000−232323−2300000000000000000000000000
χ5844-4-4-2400002-2-442-4000023−23−23230-200002-200002000023−23−2323000000000000000000000000000000
χ5944-4-4-2400002-2-442-40000−232323−230-200002-2000020000−232323−23000000000000000000000000000000
χ6044-4-4-2-200002-22-22223−23−232323−23−2323010000-11-333-3-10000−333−3−333−300000000000000000000000000
χ6144-4-4-2-200002-22-22223−23−2323−232323−23010000-113-3-33-100003−3−33−333−300000000000000000000000000
χ6244-4-4-2-200002-22-222−232323−2323−23−2323010000-113-3-33-10000−333−33−3−3300000000000000000000000000
χ6344-4-4-2-200002-22-222−232323−23−232323−23010000-11-333-3-100003−3−333−3−3300000000000000000000000000
χ644-44-44-24i−4i004-4-22-42−2i−2i2i2i00000-20000-22000024i−4i000000−2i−2i2i2i00000000000000000000000000
χ654-44-44-2−4i4i004-4-22-422i2i−2i−2i00000-20000-2200002−4i4i0000002i2i−2i−2i00000000000000000000000000
χ664-44-4-2-24i−4i00-22-2222−2i−2i2i2i2323−23−2301−2i32i3001-1i3i3−i3−i3-1−2i2i00−3−333ii−i−i00000000000000000000000000
χ674-44-4-2-24i−4i00-22-2222−2i−2i2i2i−23−232323012i3−2i3001-1−i3−i3i3i3-1−2i2i0033−3−3ii−i−i00000000000000000000000000
χ684-44-4-2-2−4i4i00-22-22222i2i−2i−2i2323−23−23012i3−2i3001-1−i3−i3i3i3-12i−2i00−3−333−i−iii00000000000000000000000000
χ694-44-4-2-2−4i4i00-22-22222i2i−2i−2i−23−23232301−2i32i3001-1i3i3−i3−i3-12i−2i0033−3−3−i−iii00000000000000000000000000
χ704-4-44-24004-422-4-4-240000-22-220-20000220000-2004-4-22-22000000000000000000000000000000
χ714-4-44-2400-4422-4-4-2400002-22-20-20000220000-200-442-22-2000000000000000000000000000000
χ724-4-44-2-2004-42222-2-2−2i32i3−2i32i3-22-220100−2i32i3-1-1i3−i3i3−i3100-221-11-1i3−i3i3−i300000000000000000000000000
χ734-4-44-2-2004-42222-2-22i3−2i32i3−2i3-22-2201002i3−2i3-1-1−i3i3−i3i3100-221-11-1−i3i3−i3i300000000000000000000000000
χ744-4-44-2-200-442222-2-2−2i32i3−2i32i32-22-201002i3−2i3-1-1−i3i3−i3i31002-2-11-11i3−i3i3−i300000000000000000000000000
χ754-4-44-2-200-442222-2-22i3−2i32i3−2i32-22-20100−2i32i3-1-1i3−i3i3−i31002-2-11-11−i3i3−i3i300000000000000000000000000

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