Finite Group Databasebeta

← Group #10591165

Character table — Group #10591165

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222222222222244444444444444444444444444441212121212121212121212122424242424247272
order1222334466666612121212234666666666661212121212121212121212121212888824242424242424242466121224
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
χ5111111111111111111-11-1-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-11-1
χ6111111111111111111-11-1-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11-1-111-11
χ7111111111111111111-11-1-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-1-11
χ8111111111111111111-11-1-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-1111-1
χ9222222-2-2222222-2-2-2-222-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000
χ10222222-2-2222222-2-2-2-2-222-2-2-2-222-2-2-2-22-2-22222-2-2-2-2222200000000000000000000
χ1122222-12222-12-1-122222-1222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-100
χ1222222-12222-12-1-122222-1222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000-2-2111100
χ1322222-12222-12-1-12222-2-1-2-2-211-1-11111-1-1-1-2-211-1-1-1-111110000000000002-2-1-11100
χ1422222-12222-12-1-12222-2-1-2-2-211-1-11111-1-1-1-2-211-1-1-1-11111000000000000-2211-1-100
χ1522222-1-2-222-12-1-1-2-2-2-22-1-222-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000−i3i3−i3i300
χ1622222-1-2-222-12-1-1-2-2-2-22-1-222-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000i3−i3i3−i300
χ1722222-1-2-222-12-1-1-2-2-2-2-2-12-2-211-1-11111-11122-1-11111-1-1-1-100000000000000−i3i3i3−i300
χ1822222-1-2-222-12-1-1-2-2-2-2-2-12-2-211-1-11111-11122-1-11111-1-1-1-100000000000000i3−i3−i3i300
χ192222-1222-1-12-122-1-1-1-12-12-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ202222-1222-1-12-122-1-1-1-12-12-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ212222-1222-1-12-122-1-1-1-1-2-1-211-2-2-1-11111-12211-2-2-1-1-1-1111122-2-2-1-1-1-1111100000000
χ222222-1222-1-12-122-1-1-1-1-2-1-211-2-2-1-11111-12211-2-2-1-1-1-11111-2-2221111-1-1-1-100000000
χ232222-12-2-2-1-12-12211112-1-2-1-122-1-1-1-1-1-1-1-2-211-2-211111111000033−3−333−3−300000000
χ242222-12-2-2-1-12-12211112-1-2-1-122-1-1-1-1-1-1-1-2-211-2-2111111110000−3−333−3−33300000000
χ252222-12-2-2-1-12-1221111-2-1211-2-2-1-11111-1-2-2-1-1221111-1-1-1-1000033−3−3−3−33300000000
χ262222-12-2-2-1-12-1221111-2-1211-2-2-1-11111-1-2-2-1-1221111-1-1-1-10000−3−33333−3−300000000
χ2722-2-2222-2-2-2-222-222-2-20200000-2-2000022-2000022-2-20000002i−2i00002i−2i2i−2i00000000
χ2822-2-2222-2-2-2-222-222-2-20200000-2-2000022-2000022-2-2000000−2i2i0000−2i2i−2i2i00000000
χ2922-2-222-22-2-2-222-2-2-2220200000-2-200002-220000-2-22200002-2002-22-2000000000000
χ3022-2-222-22-2-2-222-2-2-2220200000-2-200002-220000-2-2220000-2200-22-22000000000000
χ3122-2-2-122-211-2-12-2-1-1110-10−i3i30011−i3−i3i3i3-12-2−i3i300-1-111−i3−i3i3i3002i−2i3−3−33−ii−ii00000000
χ3222-2-2-122-211-2-12-2-1-1110-10−i3i30011−i3−i3i3i3-12-2−i3i300-1-111−i3−i3i3i300−2i2i−333−3i−ii−i00000000
χ3322-2-2-122-211-2-12-2-1-1110-10i3−i30011i3i3−i3−i3-12-2i3−i300-1-111i3i3−i3−i3002i−2i−333−3−ii−ii00000000
χ3422-2-2-122-211-2-12-2-1-1110-10i3−i30011i3i3−i3−i3-12-2i3−i300-1-111i3i3−i3−i300−2i2i3−3−33i−ii−i00000000
χ3522-2-2-12-2211-2-12-211-1-10-10−i3i30011−i3−i3i3i3-1-22i3−i30011-1-1i3i3−i3−i32-200-11-11−i3i3i3−i300000000
χ3622-2-2-12-2211-2-12-211-1-10-10−i3i30011−i3−i3i3i3-1-22i3−i30011-1-1i3i3−i3−i3-22001-11-1i3−i3−i3i300000000
χ3722-2-2-12-2211-2-12-211-1-10-10i3−i30011i3i3−i3−i3-1-22−i3i30011-1-1−i3−i3i3i32-200-11-11i3−i3−i3i300000000
χ3822-2-2-12-2211-2-12-211-1-10-10i3−i30011i3i3−i3−i3-1-22−i3i30011-1-1−i3−i3i3i3-22001-11-1−i3i3i3−i300000000
χ394444-2-244-2-2-2-2-2-2-2-2-2-2414-2-2-2-21111111-2-2-2-2-2-21111111100000000000000000000
χ404444-2-244-2-2-2-2-2-2-2-2-2-2-41-4222211-1-1-1-11-2-222221111-1-1-1-100000000000000000000
χ414444-2-2-4-4-2-2-2-2-2-2222241-4-2-2-2-21111111222222-1-1-1-1-1-1-1-100000000000000000000
χ424444-2-2-4-4-2-2-2-2-2-22222-414222211-1-1-1-1122-2-2-2-2-1-1-1-1111100000000000000000000
χ4344-4-44-24-4-4-424-2244-4-40-200000220000-2-220000-2-222000000000000000000000000
χ4444-4-44-2-44-4-424-22-4-4440-200000220000-22-2000022-2-2000000000000000000000000
χ4544-4-4-2-24-4222-2-22-2-222010−2i32i300-1-1i3i3−i3−i31-22−2i32i30011-1-1i3i3−i3−i300000000000000000000
χ4644-4-4-2-24-4222-2-22-2-2220102i3−2i300-1-1−i3−i3i3i31-222i3−2i30011-1-1−i3−i3i3i300000000000000000000
χ4744-4-4-2-2-44222-2-2222-2-2010−2i32i300-1-1i3i3−i3−i312-22i3−2i300-1-111−i3−i3i3i300000000000000000000
χ4844-4-4-2-2-44222-2-2222-2-20102i3−2i300-1-1−i3−i3i3i312-2−2i32i300-1-111i3i3−i3−i300000000000000000000
χ494-44-444004-4-4-4-44000004000004-40000-40000000000000000000000000000000000
χ504-44-44-2004-42-42-200000-2000−2i32i3-22−2i32i3−2i32i320000000000000000000000000000000000
χ514-44-44-2004-42-42-200000-20002i3−2i3-222i3−2i32i3−2i320000000000000000000000000000000000
χ524-44-4-2400-22-42-4423−2323−230-200000-220000200000023−2323−23000000000000000000000000
χ534-44-4-2400-22-42-44−2323−23230-200000-2200002000000−2323−2323000000000000000000000000
χ544-44-4-2-200-22222-223−2323−2301000−2i32i31-1i3−i3i3−i3-1000000−33−333i−3i3i−3i00000000000000000000
χ554-44-4-2-200-22222-223−2323−23010002i3−2i31-1−i3i3−i3i3-1000000−33−33−3i3i−3i3i00000000000000000000
χ564-44-4-2-200-22222-2−2323−232301000−2i32i31-1i3−i3i3−i3-10000003−33−3−3i3i−3i3i00000000000000000000
χ574-44-4-2-200-22222-2−2323−2323010002i3−2i31-1−i3i3−i3i3-10000003−33−33i−3i3i−3i00000000000000000000
χ584-4-444400-444-4-4-400000400000-440000-40000000000000000000000000000000000
χ594-4-444-200-44-2-42200000-2000002-200002000023−23000023−23−232300000000000000000000
χ604-4-444-200-44-2-42200000-2000002-2000020000−23230000−232323−2300000000000000000000
χ614-4-44-24002-242-4-423−23−23230-2000002-20000200000023−23−2323000000000000000000000000
χ624-4-44-24002-242-4-4−232323−230-2000002-200002000000−232323−23000000000000000000000000
χ634-4-44-2-2002-2-222223−23−23230100000-113-3-33-1000023−23−333−3−333−300000000000000000000
χ644-4-44-2-2002-2-222223−23−23230100000-11-333-3-10000−2323−333−33−3−3300000000000000000000
χ654-4-44-2-2002-2-2222−232323−230100000-113-3-33-10000−23233−3−333−3−3300000000000000000000
χ664-4-44-2-2002-2-2222−232323−230100000-11-333-3-1000023−233−3−33−333−300000000000000000000

Here i is the imaginary unit (i² = −1).