Finite Group Databasebeta

← Group #13139939

Character table — Group #13139939

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order12222234466646612121212336666666666121212123666666666121212121212121212121212121244448888121212121212121224242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-1111111-1-1-111-1-111111-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-111
χ61111-1-1111111-1-1-111-1-111111-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1
χ71111-1-1111111-1-1-111-1-111111-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1111-1-1
χ81111-1-1111111-1-1-111-1-111111-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1-111
χ922222222222222222222-122-1-1-1-1-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ1022222222222222222222-122-1-1-1-1-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ112222222222222222222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ122222222222222222222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ132222222-2-2222-222-2-2-2-2222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-222-2-2-2-22-122-1-1-1-1-12-1-1-2-2-2-2-122-1-1-1-1-1-1-111-2-2111111111100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ152222222-2-2222-222-2-2-2-22-122-1-1-1-1-12-1-1-2-2-2-2-122-1-1-1-1-1-1-111-2-2111111111100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ162222222-2-2222-222-2-2-2-2-12-1-122222-1221111-1-1-1-1-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−3000000
χ172222222-2-2222-222-2-2-2-2-12-1-122222-1221111-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−333000000
χ182222-2-2222222-2-2-222-2-22-122-111112-1-12222-1-2-2-1-11111-1-1-1-2-211-1-1-1-1111122-2-20000-1-1-1-1111100000000000000
χ192222-2-2222222-2-2-222-2-22-122-111112-1-12222-1-2-2-1-11111-1-1-1-2-211-1-1-1-11111-2-22200001111-1-1-1-100000000000000
χ202222-2-2222222-2-2-222-2-2-12-1-12-2-2-2-2-122-1-1-1-1-111-1-11111-12211-2-2-1-1-1-11111000022-2-200000000-1-1-1-11111000000
χ212222-2-2222222-2-2-222-2-2-12-1-12-2-2-2-2-122-1-1-1-1-111-1-11111-12211-2-2-1-1-1-111110000-2-222000000001111-1-1-1-1000000
χ222222-2-22-2-22222-2-2-2-22222222-2-2-2-2222-2-2-2-22-2-222-2-2-2-22-2-22222-2-2-2-22222000000000000000000000000000000
χ232222-2-22-2-22222-2-2-2-2222-122-111112-1-1-2-2-2-2-1-2-2-1-11111-11122-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i300000000000000
χ242222-2-22-2-22222-2-2-2-2222-122-111112-1-1-2-2-2-2-1-2-2-1-11111-11122-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i300000000000000
χ252222-2-22-2-22222-2-2-2-222-12-1-12-2-2-2-2-1221111-111-1-11111-1-2-2-1-1221111-1-1-1-1000000000000000033−3−3−3−333000000
χ262222-2-22-2-22222-2-2-2-222-12-1-12-2-2-2-2-1221111-111-1-11111-1-2-2-1-1221111-1-1-1-10000000000000000−3−33333−3−3000000
χ2722-2-22-22002-2-202-20000222-2222-2-2-2-2-2000022-22-222-2-2-20000000000000000002−22−2000000002−22−22−22−2000000
χ2822-2-22-22002-2-202-20000222-2222-2-2-2-2-2000022-22-222-2-2-2000000000000000000−22−2200000000−22−22−22−22000000
χ2922-2-22-22002-2-202-20000-12-11222-2-21-2-233−3−3-1-11-11-1-1111003−30033−3−333−3−300002−22−200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ3022-2-22-22002-2-202-20000-12-11222-2-21-2-233−3−3-1-11-11-1-1111003−30033−3−333−3−30000−22−2200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ3122-2-22-22002-2-202-20000-12-11222-2-21-2-2−3−333-1-11-11-1-111100−3300−3−333−3−33300002−22−200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ3222-2-22-22002-2-202-20000-12-11222-2-21-2-2−3−333-1-11-11-1-111100−3300−3−333−3−3330000−22−2200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ3322-2-2-222002-2-20-220000222-22-2-222-2-2-200002-222-2-2-222-20000000000000000002−2−22000000002−22−2−22−22000000
χ3422-2-2-222002-2-20-220000222-22-2-222-2-2-200002-222-2-2-222-2000000000000000000−222−200000000−22−222−22−2000000
χ3522-2-2-222002-2-20-220000-12-112-2-2221-2-233−3−3-11-1-1111-1-1100−330033−3−3−3−33300002−2−2200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ3622-2-2-222002-2-20-220000-12-112-2-2221-2-233−3−3-11-1-1111-1-1100−330033−3−3−3−3330000−222−200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ3722-2-2-222002-2-20-220000-12-112-2-2221-2-2−3−333-11-1-1111-1-11003−300−3−33333−3−300002−2−2200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ3822-2-2-222002-2-20-220000-12-112-2-2221-2-2−3−333-11-1-1111-1-11003−300−3−33333−3−30000−222−200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ392-22-20022-2-2-220002-20022-2-2-2000022-22-22-2200-2-2000022-200002-22-20000002i−2i000000002i−2i2i−2i00000000000000
χ402-22-20022-2-2-220002-20022-2-2-2000022-22-22-2200-2-2000022-200002-22-2000000−2i2i00000000−2i2i−2i2i00000000000000
χ412-22-20022-2-2-220002-2002-1-2-21−i3i3−i3i32-112-22-2-10011−i3i3−i3i3-1-1100−i3i3-11-11−i3i3−i3i3002i−2i00003−33−3−ii−ii00000000000000
χ422-22-20022-2-2-220002-2002-1-2-21−i3i3−i3i32-112-22-2-10011−i3i3−i3i3-1-1100−i3i3-11-11−i3i3−i3i300−2i2i0000−33−33i−ii−i00000000000000
χ432-22-20022-2-2-220002-2002-1-2-21i3−i3i3−i32-112-22-2-10011i3−i3i3−i3-1-1100i3−i3-11-11i3−i3i3−i3002i−2i0000−33−33−ii−ii00000000000000
χ442-22-20022-2-2-220002-2002-1-2-21i3−i3i3−i32-112-22-2-10011i3−i3i3−i3-1-1100i3−i3-11-11i3−i3i3−i300−2i2i00003−33−3i−ii−i00000000000000
χ452-22-2002-22-2-22000-220022-2-2-2000022-2-22-22200-2-200002-220000-22-2200002i−2i0000002i−2i−2i2i000000000000000000
χ462-22-2002-22-2-22000-220022-2-2-2000022-2-22-22200-2-200002-220000-22-220000−2i2i000000−2i2i2i−2i000000000000000000
χ472-22-2002-22-2-22000-22002-1-2-21−i3i3−i3i32-11-22-22-10011−i3i3−i3i3-11-100i3−i31-11-1i3−i3i3−i32i−2i000000−iii−i3−3−3300000000000000
χ482-22-2002-22-2-22000-22002-1-2-21−i3i3−i3i32-11-22-22-10011−i3i3−i3i3-11-100i3−i31-11-1i3−i3i3−i3−2i2i000000i−i−ii−333−300000000000000
χ492-22-2002-22-2-22000-22002-1-2-21i3−i3i3−i32-11-22-22-10011i3−i3i3−i3-11-100−i3i31-11-1−i3i3−i3i32i−2i000000−iii−i−333−300000000000000
χ502-22-2002-22-2-22000-22002-1-2-21i3−i3i3−i32-11-22-22-10011i3−i3i3−i3-11-100−i3i31-11-1−i3i3−i3i3−2i2i000000i−i−ii3−3−3300000000000000
χ514444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ524444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ534444-4-4444444-4-4-444-4-4-2-2-2-2-22222-2-2-2-2-2-2-212211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000
χ544444-4-44-4-44444-4-4-4-444-2-2-2-2-22222-2-2-2222212211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000
χ5544-4-44-44004-4-404-400004-24-4-2-2-222-4220000-24-4-22-2-222200000000000000000000000000000000000000000000
χ5644-4-44-44004-4-404-40000-2-2-22-2-2-2222222323−23−231-221-111-1-1-10023−2300−3−333−3−333000000000000000000000000000000
χ5744-4-44-44004-4-404-40000-2-2-22-2-2-222222−23−2323231-221-111-1-1-100−23230033−3−333−3−3000000000000000000000000000000
χ5844-4-4-444004-4-40-4400004-24-4-222-2-2-4220000-2-44-2222-2-2200000000000000000000000000000000000000000000
χ5944-4-4-444004-4-40-440000-2-2-22-222-2-22222323−23−2312-21-1-1-111-100−232300−3−33333−3−3000000000000000000000000000000
χ6044-4-4-444004-4-40-440000-2-2-22-222-2-2222−23−23232312-21-1-1-111-10023−230033−3−3−3−333000000000000000000000000000000
χ614-44-40044-4-4-440004-400-2422-40000-24-4-22-22-200220000-24-40000-22-220000000000000000000000000000000000
χ624-44-40044-4-4-440004-400-2-2222−2i32i3−2i32i3-2-22-22-22100-1-1i3−i3i3−i31-2200−2i32i31-11-1i3−i3i3−i3000000000000000000000000000000
χ634-44-40044-4-4-440004-400-2-22222i3−2i32i3−2i3-2-22-22-22100-1-1−i3i3−i3i31-22002i3−2i31-11-1−i3i3−i3i3000000000000000000000000000000
χ644-44-4004-44-4-44000-4400-2422-40000-24-42-22-2-200220000-2-4400002-22-20000000000000000000000000000000000
χ654-44-4004-44-4-44000-4400-2-2222−2i32i3−2i32i3-2-222-22-2100-1-1i3−i3i3−i312-2002i3−2i3-11-11−i3i3−i3i3000000000000000000000000000000
χ664-44-4004-44-4-44000-4400-2-22222i3−2i32i3−2i3-2-222-22-2100-1-1−i3i3−i3i312-200−2i32i3-11-11i3−i3i3−i3000000000000000000000000000000
χ674-4-4400400-44-4000000044-44-40000-4-440000400-440000-400000000000000000000000000000000000000000000
χ684-4-4400400-44-400000004-2-442−2i32i32i3−2i3-42-20000-2002-2−2i32i32i3−2i3200000000000000000000000000000000000000000000
χ694-4-4400400-44-400000004-2-4422i3−2i3−2i32i3-42-20000-2002-22i3−2i3−2i32i3200000000000000000000000000000000000000000000
χ704-4-4400400-44-40000000-242-2-400002-4423−23−2323-2002-20000200000023−23−23230000000000000000000000000000000000
χ714-4-4400400-44-40000000-242-2-400002-44−232323−23-2002-200002000000−232323−230000000000000000000000000000000000
χ724-4-4400400-44-40000000-2-22-22−2i32i32i3−2i322-223−23−2323100-11i3−i3−i3i3-1000000−333−3−3i3i3i−3i000000000000000000000000000000
χ734-4-4400400-44-40000000-2-22-22−2i32i32i3−2i322-2−232323−23100-11i3−i3−i3i3-10000003−3−333i−3i−3i3i000000000000000000000000000000
χ744-4-4400400-44-40000000-2-22-222i3−2i3−2i32i322-223−23−2323100-11−i3i3i3−i3-1000000−333−33i−3i−3i3i000000000000000000000000000000
χ754-4-4400400-44-40000000-2-22-222i3−2i3−2i32i322-2−232323−23100-11−i3i3i3−i3-10000003−3−33−3i3i3i−3i000000000000000000000000000000
χ76666666-366-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000000000000000000022-1-1-1-1
χ77666666-366-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000000000000000000-2-21111
χ78666666-3-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3
χ79666666-3-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3
χ806666-6-6-366-3-3-3-633-3-33300000000000000000000000000000000000000000000000000000000000000002-211-1-1
χ816666-6-6-366-3-3-3-633-3-3330000000000000000000000000000000000000000000000000000000000000000-22-1-111
χ826666-6-6-3-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000000000000000000000−i3i3i3−i3
χ836666-6-6-3-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000000000000000000000i3−i3−i3i3
χ841212-12-1212-12-600-6660-6600000000000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-12-1212-600-66606-600000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-1200-612-1266-6000-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-1200-6-121266-60006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121200-6006-660000063−630000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-121200-6006-6600000−63630000000000000000000000000000000000000000000000000000000000000000000000

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