Finite Group Databasebeta

← Group #10591174

Character table — Group #10591174

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222222222222244444444444444444444444441212121212121212121212121212121212121212121212127272
order1222223344666666666612121212346666666661212121212121212121212121212444488881212121212121212242424242424242424
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
χ51111-1-111111111-1-1-1-11111111-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1
χ61111-1-111111111-1-1-1-11111111-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11
χ71111-1-111111111-1-1-1-11111111-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11
χ81111-1-111111111-1-1-1-11111111-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1
χ922222222-2-22222222222-2-2-2-22-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000
χ102222222-12222-1-12222-12-1-1-1-1-12-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100
χ112222222-12222-1-12222-12-1-1-1-1-12-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-2000000001111111100
χ122222222-1-2-222-1-12222-121111-1-2-1-1-1-1-1-1-1-1-111-2-2-2-211111111000000000000000033−3−333−3−300
χ132222222-1-2-222-1-12222-121111-1-2-1-1-1-1-1-1-1-1-111-2-2-2-2111111110000000000000000−3−333−3−33300
χ14222222-1222-1-122-1-1-1-12-12222-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000
χ15222222-1222-1-122-1-1-1-12-12222-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000
χ16222222-12-2-2-1-122-1-1-1-12-1-2-2-2-2-1-222-1-1-1-1-1-1-1-2-211111111111100000000−i3−i3i3i3−i3−i3i3i30000000000
χ17222222-12-2-2-1-122-1-1-1-12-1-2-2-2-2-1-222-1-1-1-1-1-1-1-2-211111111111100000000i3i3−i3−i3i3i3−i3−i30000000000
χ182222-2-222-2-22222-2-2-2-222-2-2-2-222-2-222-2-2-2-2222-2-222-2-2-2-2222200000000000000000000000000
χ192222-2-22-12222-1-1-2-2-2-2-12-1-1-1-1-1-211-1-11111-11122-2-2-1-1-1-11111000022-2-200000000-1-1-1-1111100
χ202222-2-22-12222-1-1-2-2-2-2-12-1-1-1-1-1-211-1-11111-11122-2-2-1-1-1-111110000-2-222000000001111-1-1-1-100
χ212222-2-22-1-2-222-1-1-2-2-2-2-121111-1211-1-11111-1-1-1-2-2221111-1-1-1-1000000000000000033−3−3−3−33300
χ222222-2-22-1-2-222-1-1-2-2-2-2-121111-1211-1-11111-1-1-1-2-2221111-1-1-1-10000000000000000−3−33333−3−300
χ232222-2-2-1222-1-12211112-12222-1-2-2-2-1-11111-1-2-2-1-111-1-1-1-1111122-2-20000-1-1-1-111110000000000
χ242222-2-2-1222-1-12211112-12222-1-2-2-2-1-11111-1-2-2-1-111-1-1-1-11111-2-22200001111-1-1-1-10000000000
χ252222-2-2-12-2-2-1-12211112-1-2-2-2-2-12-2-2-1-11111-12211-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i30000000000
χ262222-2-2-12-2-2-1-12211112-1-2-2-2-2-12-2-2-1-11111-12211-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i30000000000
χ272-22-200222-2-2-2-2-200002222-2-22000-2-200002002-20022-2-20000002-2000000002-22-20000000000
χ282-22-200222-2-2-2-2-200002222-2-22000-2-200002002-20022-2-2000000-2200000000-22-220000000000
χ292-22-20022-22-2-2-2-2000022-2-2222000-2-20000200-2200-2-22200002-20000002-22-200000000000000
χ302-22-20022-22-2-2-2-2000022-2-2222000-2-20000200-2200-2-2220000-22000000-22-2200000000000000
χ312-22-200-122-211-2-2−i3−i3i3i32-122-2-2-100011−i3−i3i3i3-100-11−i3i3-1-111−i3−i3i3i3002-20000−i3i3i3−i3-11-110000000000
χ322-22-200-122-211-2-2−i3−i3i3i32-122-2-2-100011−i3−i3i3i3-100-11−i3i3-1-111−i3−i3i3i300-220000i3−i3−i3i31-11-10000000000
χ332-22-200-122-211-2-2i3i3−i3−i32-122-2-2-100011i3i3−i3−i3-100-11i3−i3-1-111i3i3−i3−i3002-20000i3−i3−i3i3-11-110000000000
χ342-22-200-122-211-2-2i3i3−i3−i32-122-2-2-100011i3i3−i3−i3-100-11i3−i3-1-111i3i3−i3−i300-220000−i3i3i3−i31-11-10000000000
χ352-22-200-12-2211-2-2−i3−i3i3i32-1-2-222-100011−i3−i3i3i3-1001-1i3−i311-1-1i3i3−i3−i32-2000000-11-11−i3i3i3−i30000000000
χ362-22-200-12-2211-2-2−i3−i3i3i32-1-2-222-100011−i3−i3i3i3-1001-1i3−i311-1-1i3i3−i3−i3-220000001-11-1i3−i3−i3i30000000000
χ372-22-200-12-2211-2-2i3i3−i3−i32-1-2-222-100011i3i3−i3−i3-1001-1−i3i311-1-1−i3−i3i3i32-2000000-11-11i3−i3−i3i30000000000
χ382-22-200-12-2211-2-2i3i3−i3−i32-1-2-222-100011i3i3−i3−i3-1001-1−i3i311-1-1−i3−i3i3i3-220000001-11-1−i3i3i3−i30000000000
χ392-2-222-222002-22-22-22-2-2-20000202-22-22-22-2-2000000000000000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i200
χ402-2-222-222002-22-22-22-2-2-20000202-22-22-22-2-2000000000000000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i200
χ412-2-222-22-1002-2-112-22-21-23−33−3-10-11-11-11-1113−300003−33−33−33−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300
χ422-2-222-22-1002-2-112-22-21-23−33−3-10-11-11-11-1113−300003−33−33−33−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300
χ432-2-222-22-1002-2-112-22-21-2−33−33-10-11-11-11-111−330000−33−33−33−330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700
χ442-2-222-22-1002-2-112-22-21-2−33−33-10-11-11-11-111−330000−33−33−33−330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700
χ452-2-22-2222002-22-2-22-22-2-2000020-222-2-22-22-2000000000000000000−i2i2i2−i200000000−i2i2−i2i2i2−i2i2−i200
χ462-2-22-2222002-22-2-22-22-2-2000020-222-2-22-22-2000000000000000000i2−i2−i2i200000000i2−i2i2−i2−i2i2−i2i200
χ472-2-22-222-1002-2-11-22-221-23−33−3-101-1-111-11-11−3300003−33−3−33−330000−i2i2i2−i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300
χ482-2-22-222-1002-2-11-22-221-23−33−3-101-1-111-11-11−3300003−33−3−33−330000i2−i2−i2i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300
χ492-2-22-222-1002-2-11-22-221-2−33−33-101-1-111-11-113−30000−33−333−33−30000−i2i2i2−i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700
χ502-2-22-222-1002-2-11-22-221-2−33−33-101-1-111-11-113−30000−33−333−33−30000i2−i2−i2i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700
χ51444444-2-244-2-2-2-2-2-2-2-2-2-2-2-2-2-214-2-21111111-2-2-2-2-2-21111111100000000000000000000000000
χ52444444-2-2-4-4-2-2-2-2-2-2-2-2-2-222221-4-2-21111111222222-1-1-1-1-1-1-1-100000000000000000000000000
χ534444-4-4-2-244-2-2-2-22222-2-2-2-2-2-21-42211-1-1-1-1122-2-2221111-1-1-1-100000000000000000000000000
χ544444-4-4-2-2-4-4-2-2-2-22222-2-22222142211-1-1-1-11-2-222-2-2-1-1-1-1111100000000000000000000000000
χ5544-4-4004400-44-440000-4-400004000-440000-40000000000000000000000000000000000000000
χ5644-4-4004-200-442-200002-423−23−2323-20002-20000200000023−23−2323000000000000000000000000000000
χ5744-4-4004-200-442-200002-4−232323−23-20002-200002000000−232323−23000000000000000000000000000000
χ5844-4-400-24002-2-44−2i32i32i3−2i3-420000-20002-2−2i32i32i3−2i320000000000000000000000000000000000000000
χ5944-4-400-24002-2-442i3−2i3−2i32i3-420000-20002-22i3−2i3−2i32i320000000000000000000000000000000000000000
χ6044-4-400-2-2002-22-2−2i32i32i3−2i32223−23−23231000-11i3−i3−i3i3-1000000−333−3−3i3i3i−3i00000000000000000000000000
χ6144-4-400-2-2002-22-2−2i32i32i3−2i322−232323−231000-11i3−i3−i3i3-10000003−3−333i−3i−3i3i00000000000000000000000000
χ6244-4-400-2-2002-22-22i3−2i3−2i32i32223−23−23231000-11−i3i3i3−i3-1000000−333−33i−3i−3i3i00000000000000000000000000
χ6344-4-400-2-2002-22-22i3−2i3−2i32i322−232323−231000-11−i3i3i3−i3-10000003−3−33−3i3i3i−3i00000000000000000000000000
χ644-44-4004-24-4-4-4220000-24-2-222-2000220000-2004-400-2-222000000000000000000000000000000
χ654-44-4004-2-44-4-4220000-2422-2-2-2000220000-200-440022-2-2000000000000000000000000000000
χ664-44-400-2-24-42222−2i3−2i32i32i3-2-2-2-2221000-1-1i3i3−i3−i3100-22−2i32i311-1-1i3i3−i3−i300000000000000000000000000
χ674-44-400-2-24-422222i32i3−2i3−2i3-2-2-2-2221000-1-1−i3−i3i3i3100-222i3−2i311-1-1−i3−i3i3i300000000000000000000000000
χ684-44-400-2-2-442222−2i3−2i32i32i3-2-222-2-21000-1-1i3i3−i3−i31002-22i3−2i3-1-111−i3−i3i3i300000000000000000000000000
χ694-44-400-2-2-4422222i32i3−2i3−2i3-2-222-2-21000-1-1−i3−i3i3i31002-2−2i32i3-1-111i3i3−i3−i300000000000000000000000000
χ704-4-444-4-2400-224-4-22-22-420000-204-4-22-22-2220000000000000000000000000000000000000000
χ714-4-444-4-2-200-22-22-22-222223−2323−2310-221-11-11-1-123−230000−33−33−33−3300000000000000000000000000
χ724-4-444-4-2-200-22-22-22-2222−2323−232310-221-11-11-1-1−232300003−33−33−33−300000000000000000000000000
χ734-4-44-44-2400-224-42-22-2-420000-20-44-222-22-220000000000000000000000000000000000000000
χ744-4-44-44-2-200-22-222-22-22223−2323−23102-21-1-11-11-1−23230000−33−333−33−300000000000000000000000000
χ754-4-44-44-2-200-22-222-22-222−2323−2323102-21-1-11-11-123−2300003−33−3−33−3300000000000000000000000000

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