Finite Group Databasebeta

← Group #10591135

Character table — Group #10591135

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222222222222244444444444444444444444441212121212121212121212121212121212121212121212127272
order1222223344666666666612121212346666666661212121212121212121212121212444488881212121212121212242424242424242444
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
χ51111-1-11111111-1-1-1-111111111-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1
χ61111-1-11111111-1-1-1-111111111-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11
χ71111-1-11111111-1-1-1-111111111-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11
χ81111-1-11111111-1-1-1-111111111-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1
χ922222222-2-22222222222-2-2-2-22-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000
χ102222222-12222-1-1-1-1-12-1-12222-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000
χ112222222-12222-1-1-1-1-12-1-12222-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000
χ122222222-1-2-222-1-1-1-1-12-1-1-2-2-2-2-1-222-1-1-1-1-1-1-111-2-2111111111100000000−i3−i3i3i3−i3−i3i3i30000000000
χ132222222-1-2-222-1-1-1-1-12-1-1-2-2-2-2-1-222-1-1-1-1-1-1-111-2-2111111111100000000i3i3−i3−i3i3i3−i3−i30000000000
χ14222222-1222-1-122222-122-1-1-1-1-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100
χ15222222-1222-1-122222-122-1-1-1-1-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-2000000001111111100
χ16222222-12-2-2-1-122222-1221111-1-2-1-1-1-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−300
χ17222222-12-2-2-1-122222-1221111-1-2-1-1-1-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−33300
χ182222-2-222-2-2222-2-2-2-2222-2-2-2-222-2-222-2-2-2-22-2-22222-2-2-2-2222200000000000000000000000000
χ192222-2-22-12222-111112-1-12222-1-2-2-2-1-11111-1-1-1-2-211-1-1-1-1111122-2-20000-1-1-1-111110000000000
χ202222-2-22-12222-111112-1-12222-1-2-2-2-1-11111-1-1-1-2-211-1-1-1-11111-2-22200001111-1-1-1-10000000000
χ212222-2-22-1-2-222-111112-1-1-2-2-2-2-12-2-2-1-11111-11122-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i30000000000
χ222222-2-22-1-2-222-111112-1-1-2-2-2-2-12-2-2-1-11111-11122-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i30000000000
χ232222-2-2-1222-1-12-2-2-2-2-122-1-1-1-1-1-211-1-11111-12211-2-2-1-1-1-11111000022-2-200000000-1-1-1-1111100
χ242222-2-2-1222-1-12-2-2-2-2-122-1-1-1-1-1-211-1-11111-12211-2-2-1-1-1-111110000-2-222000000001111-1-1-1-100
χ252222-2-2-12-2-2-1-12-2-2-2-2-1221111-1211-1-11111-1-2-2-1-1221111-1-1-1-1000000000000000033−3−3−3−33300
χ262222-2-2-12-2-2-1-12-2-2-2-2-1221111-1211-1-11111-1-2-2-1-1221111-1-1-1-10000000000000000−3−33333−3−300
χ2722-2-22-222002-2222-2-2-2-2-20000202-22-222-2-2-20000000000000000002−22−2000000002−22−22−22−200
χ2822-2-22-222002-2222-2-2-2-2-20000202-22-222-2-2-2000000000000000000−22−2200000000−22−22−22−2200
χ2922-2-22-2-1200-11222-2-21-2-233−3−3-10-11-11-1-1111003−30033−3−333−3−300002−22−200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300
χ3022-2-22-2-1200-11222-2-21-2-233−3−3-10-11-11-1-1111003−30033−3−333−3−30000−22−2200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300
χ3122-2-22-2-1200-11222-2-21-2-2−3−333-10-11-11-1-111100−3300−3−333−3−33300002−22−200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700
χ3222-2-22-2-1200-11222-2-21-2-2−3−333-10-11-11-1-111100−3300−3−333−3−3330000−22−2200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700
χ3322-2-2-2222002-22-2-222-2-2-2000020-222-2-2-222-20000000000000000002−2−22000000002−22−2−22−2200
χ3422-2-2-2222002-22-2-222-2-2-2000020-222-2-2-222-2000000000000000000−222−200000000−22−222−22−200
χ3522-2-2-22-1200-112-2-2221-2-233−3−3-101-1-1111-1-1100−330033−3−3−3−33300002−2−2200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300
χ3622-2-2-22-1200-112-2-2221-2-233−3−3-101-1-1111-1-1100−330033−3−3−3−3330000−222−200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300
χ3722-2-2-22-1200-112-2-2221-2-2−3−333-101-1-1111-1-11003−300−3−33333−3−300002−2−2200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700
χ3822-2-2-22-1200-112-2-2221-2-2−3−333-101-1-1111-1-11003−300−3−33333−3−30000−222−200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700
χ392-22-200222-2-2-2-2000022-22-22-22000-2-2000022-200002-22-20000002i−2i000000002i−2i2i−2i0000000000
χ402-22-200222-2-2-2-2000022-22-22-22000-2-2000022-200002-22-2000000−2i2i00000000−2i2i−2i2i0000000000
χ412-22-20022-22-2-2-2000022-2-22-222000-2-200002-220000-22-2200002i−2i0000002i−2i2i−2i00000000000000
χ422-22-20022-22-2-2-2000022-2-22-222000-2-200002-220000-22-220000−2i2i000000−2i2i−2i2i00000000000000
χ432-22-2002-12-2-2-21−i3i3−i3i32-112-22-2-100011−i3i3−i3i3-1-1100−i3i3-11-11−i3i3−i3i3002i−2i00003−3−33−ii−ii0000000000
χ442-22-2002-12-2-2-21−i3i3−i3i32-112-22-2-100011−i3i3−i3i3-1-1100−i3i3-11-11−i3i3−i3i300−2i2i0000−333−3i−ii−i0000000000
χ452-22-2002-12-2-2-21i3−i3i3−i32-112-22-2-100011i3−i3i3−i3-1-1100i3−i3-11-11i3−i3i3−i3002i−2i0000−333−3−ii−ii0000000000
χ462-22-2002-12-2-2-21i3−i3i3−i32-112-22-2-100011i3−i3i3−i3-1-1100i3−i3-11-11i3−i3i3−i300−2i2i00003−3−33i−ii−i0000000000
χ472-22-2002-1-22-2-21−i3i3−i3i32-11-22-22-100011−i3i3−i3i3-11-100i3−i31-11-1i3−i3i3−i32i−2i000000−ii−ii3−3−330000000000
χ482-22-2002-1-22-2-21−i3i3−i3i32-11-22-22-100011−i3i3−i3i3-11-100i3−i31-11-1i3−i3i3−i3−2i2i000000i−ii−i−333−30000000000
χ492-22-2002-1-22-2-21i3−i3i3−i32-11-22-22-100011i3−i3i3−i3-11-100−i3i31-11-1−i3i3−i3i32i−2i000000−ii−ii−333−30000000000
χ502-22-2002-1-22-2-21i3−i3i3−i32-11-22-22-100011i3−i3i3−i3-11-100−i3i31-11-1−i3i3−i3i3−2i2i000000i−ii−i3−3−330000000000
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
χ534444-4-4-2-244-2-2-22222-2-2-2-2-2-2-21-42211-1-1-1-11-2-222221111-1-1-1-100000000000000000000000000
χ544444-4-4-2-2-4-4-2-2-22222-2-2-22222142211-1-1-1-1122-2-2-2-2-1-1-1-1111100000000000000000000000000
χ5544-4-44-44-2004-4-2-2-222-4220000-204-4-22-2-22220000000000000000000000000000000000000000
χ5644-4-44-4-2-200-22-2-2-2222222323−23−2310-221-111-1-1-10023−2300−3−333−3−33300000000000000000000000000
χ5744-4-44-4-2-200-22-2-2-222222−23−23232310-221-111-1-1-100−23230033−3−333−3−300000000000000000000000000
χ5844-4-4-444-2004-4-222-2-2-4220000-20-44-2222-2-220000000000000000000000000000000000000000
χ5944-4-4-44-2-200-22-222-2-22222323−23−23102-21-1-1-111-100−232300−3−33333−3−300000000000000000000000000
χ6044-4-4-44-2-200-22-222-2-2222−23−232323102-21-1-1-111-10023−230033−3−3−3−33300000000000000000000000000
χ614-44-400-244-422-40000-24-4-22-22-2000220000-24-40000-22-22000000000000000000000000000000
χ624-44-400-24-4422-40000-24-42-22-2-2000220000-2-4400002-22-2000000000000000000000000000000
χ634-44-400-2-24-4222−2i32i3−2i32i3-2-22-22-221000-1-1i3−i3i3−i31-2200−2i32i31-11-1i3−i3i3−i300000000000000000000000000
χ644-44-400-2-24-42222i3−2i32i3−2i3-2-22-22-221000-1-1−i3i3−i3i31-22002i3−2i31-11-1−i3i3−i3i300000000000000000000000000
χ654-44-400-2-2-44222−2i32i3−2i32i3-2-222-22-21000-1-1i3−i3i3−i312-2002i3−2i3-11-11−i3i3−i3i300000000000000000000000000
χ664-44-400-2-2-442222i3−2i32i3−2i3-2-222-22-21000-1-1−i3i3−i3i312-200−2i32i3-11-11i3−i3i3−i300000000000000000000000000
χ674-4-44004400-44-40000-4-4400004000-440000-40000000000000000000000000000000000000000
χ684-4-44004-200-442−2i32i32i3−2i3-42-20000-20002-2−2i32i32i3−2i320000000000000000000000000000000000000000
χ694-4-44004-200-4422i3−2i3−2i32i3-42-20000-20002-22i3−2i3−2i32i320000000000000000000000000000000000000000
χ704-4-4400-24002-2-400002-4423−23−2323-20002-20000200000023−23−2323000000000000000000000000000000
χ714-4-4400-24002-2-400002-44−232323−23-20002-200002000000−232323−23000000000000000000000000000000
χ724-4-4400-2-2002-22−2i32i32i3−2i322-223−23−23231000-11i3−i3−i3i3-1000000−333−3−3i3i3i−3i00000000000000000000000000
χ734-4-4400-2-2002-22−2i32i32i3−2i322-2−232323−231000-11i3−i3−i3i3-10000003−3−333i−3i−3i3i00000000000000000000000000
χ744-4-4400-2-2002-222i3−2i3−2i32i322-223−23−23231000-11−i3i3i3−i3-1000000−333−33i−3i−3i3i00000000000000000000000000
χ754-4-4400-2-2002-222i3−2i3−2i32i322-2−232323−231000-11−i3i3i3−i3-10000003−3−33−3i3i3i−3i00000000000000000000000000

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