Finite Group Databasebeta

← Group #13139971

Character table — Group #13139971

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order12222234466612121212466121233666666666636666666661212121212121212121212121212121244448888121212121212121224242424242424244412121212
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
χ51111-1-11111111111-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-111
χ61111-1-11111111111-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1
χ71111-1-11111111111-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1111-1-1
χ81111-1-11111111111-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1-111
χ92222222222222222222222-12-122222-1-12-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-12-122222-1-12-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ12222222222222222222222-12-12-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ132222222-2-2222-2-2-2-2-222-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-2-2-2-2-222-2-22-12-122222-1-12-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000000000000000−i3i3−i3i3
χ152222222-2-2222-2-2-2-2-222-2-22-12-122222-1-12-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000000000000000i3−i3i3−i3
χ162222222-2-2222-2-2-2-2-222-2-2-12-12-1-1-1-1-122-1-122-1-1-1-1-1-1-11111-2-2-2-21111111100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ172222222-2-2222-2-2-2-2-222-2-2-12-12-1-1-1-1-122-1-122-1-1-1-1-1-1-11111-2-2-2-21111111100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ182222-2-22222222222-2-2-2-2-22-12-1-2-2-2-22-1-12-111-1-11111-122-2-2-1-111-1-1-1-111110000000000000000000000002-211-1-1
χ192222-2-22222222222-2-2-2-2-22-12-1-2-2-2-22-1-12-111-1-11111-122-2-2-1-111-1-1-1-11111000000000000000000000000-22-1-111
χ202222-2-22222222222-2-2-2-2-2-12-121111-122-1-1-2-2-1-11111-1-1-11122-2-2-1-1-1-1111122-2-20000-1-1-1-1111100000000000000
χ212222-2-22222222222-2-2-2-2-2-12-121111-122-1-1-2-2-1-11111-1-1-11122-2-2-1-1-1-11111-2-22200001111-1-1-1-100000000000000
χ222222-2-22-2-2222-2-2-2-22-2-2222222-2-2-2-222222-2-222-2-2-2-22-2-222-2-222-2-2-2-22222000000000000000000000000000000
χ232222-2-22-2-2222-2-2-2-22-2-2222-12-1-2-2-2-22-1-12-111-1-11111-1-2-22211-1-11111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ242222-2-22-2-2222-2-2-2-22-2-2222-12-1-2-2-2-22-1-12-111-1-11111-1-2-22211-1-11111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ252222-2-22-2-2222-2-2-2-22-2-222-12-121111-122-1-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i300000000000000
χ262222-2-22-2-2222-2-2-2-22-2-222-12-121111-122-1-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i300000000000000
χ2722-2-22-22002-2-2000002-200222222-2-2-2-2-2-222-22-222-2-2-2000000000000000000002−22−20000000022−2−222−2−2000000
χ2822-2-22-22002-2-2000002-200222222-2-2-2-2-2-222-22-222-2-2-200000000000000000000−22−2200000000−2−222−2−222000000
χ2922-2-2-222002-2-200000-22002222-2-222-2-2-2-22-222-2-2-222-2000000000000000000002−2−220000000022−2−2−2−222000000
χ3022-2-2-222002-2-200000-22002222-2-222-2-2-2-22-222-2-2-222-200000000000000000000−222−200000000−2−22222−2−2000000
χ312-22-20022-2-2-2222-2-20000022-2-200002-22-2200-2-2000022-2002-20022-2-20000002i−2i000000002i−2i2i−2i00000000000000
χ322-22-20022-2-2-2222-2-20000022-2-200002-22-2200-2-2000022-2002-20022-2-2000000−2i2i00000000−2i2i−2i2i00000000000000
χ332-22-20022-2-2-2222-2-200000-121-2−i3i3−i3i3-1-221-10011−i3i3−i3i3-1-11−i3i32-200-1-111−i3−i3i3i3002i−2i00003−33−3−ii−ii00000000000000
χ342-22-20022-2-2-2222-2-200000-121-2−i3i3−i3i3-1-221-10011−i3i3−i3i3-1-11−i3i32-200-1-111−i3−i3i3i300−2i2i0000−33−33i−ii−i00000000000000
χ352-22-20022-2-2-2222-2-200000-121-2i3−i3i3−i3-1-221-10011i3−i3i3−i3-1-11i3−i32-200-1-111i3i3−i3−i3002i−2i0000−33−33−ii−ii00000000000000
χ362-22-20022-2-2-2222-2-200000-121-2i3−i3i3−i3-1-221-10011i3−i3i3−i3-1-11i3−i32-200-1-111i3i3−i3−i300−2i2i00003−33−3i−ii−i00000000000000
χ372-22-2002-22-2-22-2-2220000022-2-200002-22-2200-2-200002-2200-2200-2-22200002i−2i0000002i−2i−2i2i000000000000000000
χ382-22-2002-22-2-22-2-2220000022-2-200002-22-2200-2-200002-2200-2200-2-2220000−2i2i000000−2i2i2i−2i000000000000000000
χ392-22-2002-22-2-22-2-22200000-121-2−i3i3−i3i3-1-221-10011−i3i3−i3i3-11-1i3−i3-220011-1-1i3i3−i3−i32i−2i000000−iii−i3−3−3300000000000000
χ402-22-2002-22-2-22-2-22200000-121-2−i3i3−i3i3-1-221-10011−i3i3−i3i3-11-1i3−i3-220011-1-1i3i3−i3−i3−2i2i000000i−i−ii−333−300000000000000
χ412-22-2002-22-2-22-2-22200000-121-2i3−i3i3−i3-1-221-10011i3−i3i3−i3-11-1−i3i3-220011-1-1−i3−i3i3i32i−2i000000−iii−i−333−300000000000000
χ422-22-2002-22-2-22-2-22200000-121-2i3−i3i3−i3-1-221-10011i3−i3i3−i3-11-1−i3i3-220011-1-1−i3−i3i3i3−2i2i000000i−i−ii3−3−3300000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000
χ444444444-4-4444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ454444-4-44444444444-4-4-4-4-4-2-2-2-22222-2-2-2-212211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000
χ464444-4-44-4-4444-4-4-4-44-4-444-2-2-2-22222-2-2-2-212211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4744-4-44-44004-4-4000004-4004-24-244-4-4-422-4-2-22-22-2-22220000000000000000000000000000000000000000000000
χ4844-4-44-44004-4-4000004-400-24-24-2-2222-4-42-24-4-22-2-22220000000000000000000000000000000000000000000000
χ4944-4-44-44004-4-4000004-400-2-2-2-2-2-22222221-221-111-1-1-1000000003i−3i3i−3i3i−3i3i−3i000000000000000000000000000000
χ5044-4-44-44004-4-4000004-400-2-2-2-2-2-22222221-221-111-1-1-100000000−3i3i−3i3i−3i3i−3i3i000000000000000000000000000000
χ5144-4-4-444004-4-400000-44004-24-2-4-444-422-4-22-2-2222-2-220000000000000000000000000000000000000000000000
χ5244-4-4-444004-4-400000-4400-24-2422-2-22-4-42-2-44-2222-2-220000000000000000000000000000000000000000000000
χ5344-4-4-444004-4-400000-4400-2-2-2-222-2-2222212-21-1-1-111-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000
χ5444-4-4-444004-4-400000-4400-2-2-2-222-2-2222212-21-1-1-111-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000
χ554-44-40044-4-4-4444-4-4000004-2-42000042-2-4-200220000-24-400-2200-2-2220000000000000000000000000000000000
χ564-44-40044-4-4-4444-4-400000-2-222−2i32i3−2i32i3-22-22100-1-1i3−i3i3−i31-22−2i32i3-220011-1-1i3i3−i3−i3000000000000000000000000000000
χ574-44-40044-4-4-4444-4-400000-2-2222i3−2i32i3−2i3-22-22100-1-1−i3i3−i3i31-222i3−2i3-220011-1-1−i3−i3i3i3000000000000000000000000000000
χ584-44-4004-44-4-44-4-444000004-2-42000042-2-4-200220000-2-44002-20022-2-20000000000000000000000000000000000
χ594-44-4004-44-4-44-4-44400000-2-222−2i32i3−2i32i3-22-22100-1-1i3−i3i3−i312-22i3−2i32-200-1-111−i3−i3i3i3000000000000000000000000000000
χ604-44-4004-44-4-44-4-44400000-2-2222i3−2i32i3−2i3-22-22100-1-1−i3i3−i3i312-2−2i32i32-200-1-111i3i3−i3−i3000000000000000000000000000000
χ614-4-4400400-44-400000000044-4-40000-44-44400-440000-40000000000000000000000000000000000000000000000
χ624-4-4400400-44-40000000004-2-420000-4-224-2002-20000200000023−23000023−23−2323000000000000000000000000000000
χ634-4-4400400-44-40000000004-2-420000-4-224-2002-200002000000−23230000−232323−23000000000000000000000000000000
χ644-4-4400400-44-4000000000-242-4−2i32i32i3−2i324-4-2-2002-2−2i32i32i3−2i320000000000000000000000000000000000000000000000
χ654-4-4400400-44-4000000000-242-42i3−2i3−2i32i324-4-2-2002-22i3−2i3−2i32i320000000000000000000000000000000000000000000000
χ664-4-4400400-44-4000000000-2-222−2i32i32i3−2i32-22-2100-11i3−i3−i3i3-100000023−23−3i3i3i−3i−333−3000000000000000000000000000000
χ674-4-4400400-44-4000000000-2-222−2i32i32i3−2i32-22-2100-11i3−i3−i3i3-1000000−23233i−3i−3i3i3−3−33000000000000000000000000000000
χ684-4-4400400-44-4000000000-2-2222i3−2i3−2i32i32-22-2100-11−i3i3i3−i3-100000023−233i−3i−3i3i−333−3000000000000000000000000000000
χ694-4-4400400-44-4000000000-2-2222i3−2i3−2i32i32-22-2100-11−i3i3i3−i3-1000000−2323−3i3i3i−3i3−3−33000000000000000000000000000000
χ70666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000222200000000-1-1-1-1-1-1-1-1000000
χ71666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-20000000011111111000000
χ72666666-3-6-6-3-3-33333-6-3-3330000000000000000000000000000000000000000000000000000003−33−33−33−3000000
χ73666666-3-6-6-3-3-33333-6-3-333000000000000000000000000000000000000000000000000000000−33−33−33−33000000
χ746666-6-6-366-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000022-2-200000000-1-1-1-11111000000
χ756666-6-6-366-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000-2-222000000001111-1-1-1-1000000
χ766666-6-6-3-6-6-3-3-33333633-3-30000000000000000000000000000000000000000000000000000003−33−3−33−33000000
χ776666-6-6-3-6-6-3-3-33333633-3-3000000000000000000000000000000000000000000000000000000−33−333−33−3000000
χ7866-6-66-6-300-33333−3333−330-3333−330000000000000000000000000000000000000000002−22−200000000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000
χ7966-6-66-6-300-33333−3333−330-3333−33000000000000000000000000000000000000000000−22−2200000000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000
χ8066-6-66-6-300-333−3333−33330-33−33330000000000000000000000000000000000000000002−22−200000000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000
χ8166-6-66-6-300-333−3333−33330-33−3333000000000000000000000000000000000000000000−22−2200000000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000
χ8266-6-6-66-300-33333−3333−3303-3−33330000000000000000000000000000000000000000002−2−2200000000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000
χ8366-6-6-66-300-33333−3333−3303-3−3333000000000000000000000000000000000000000000−222−200000000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000
χ8466-6-6-66-300-333−3333−333303-333−330000000000000000000000000000000000000000002−2−2200000000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000
χ8566-6-6-66-300-333−3333−333303-333−33000000000000000000000000000000000000000000−222−200000000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000
χ8612-1212-1200-612-1266-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-1200-6-121266-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121200-6006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-121200-6006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000

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