Finite Group Databasebeta

← Group #13140035

Character table — Group #13140035

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order122222344666121212124661212336666666666366666666612121212121212121212121212121212222266666666888824242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
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
χ51111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ61111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ71111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-11-1-111
χ81111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111-111-1-1
χ92222222222222222222222-12-1-1-1-1-1-1-122-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000
χ102222222222222222222222-12-1-1-1-1-1-1-122-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000000000
χ11222222222222222222222-12-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ12222222222222222222222-12-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
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
χ142222222-2-2222-2-2-2-2-222-2-22-12-1-1-1-1-1-1-122-122-1-1-1-1-1-1-11111-2-2-2-2111111110000−i3−i3i3i3−i3−i3i3i3000000000000000000
χ152222222-2-2222-2-2-2-2-222-2-22-12-1-1-1-1-1-1-122-122-1-1-1-1-1-1-11111-2-2-2-2111111110000i3i3−i3−i3i3i3−i3−i3000000000000000000
χ162222222-2-2222-2-2-2-2-222-2-2-12-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000000000000000−i3i3−i3i3
χ172222222-2-2222-2-2-2-2-222-2-2-12-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000000000000000i3−i3i3−i3
χ182222-2-22222222222-2-2-2-2-22-12-1-11111-122-1-2-2-1-11111-1-1-11122-2-2-1-1-1-1111122-2-2-1-1-1-11111000000000000000000
χ192222-2-22222222222-2-2-2-2-22-12-1-11111-122-1-2-2-1-11111-1-1-11122-2-2-1-1-1-11111-2-2221111-1-1-1-1000000000000000000
χ202222-2-22222222222-2-2-2-2-2-12-122-2-2-2-22-1-1-111-1-11111-122-2-2-1-111-1-1-1-111110000000000000000000000002-2-1-111
χ212222-2-22222222222-2-2-2-2-2-12-122-2-2-2-22-1-1-111-1-11111-122-2-2-1-111-1-1-1-11111000000000000000000000000-2211-1-1
χ222222-2-22-2-2222-2-2-2-22-2-22222222-2-2-2-22222-2-222-2-2-2-22-2-222-2-222-2-2-2-22222000000000000000000000000000000
χ232222-2-22-2-2222-2-2-2-22-2-2222-12-1-11111-122-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000000000
χ242222-2-22-2-2222-2-2-2-22-2-2222-12-1-11111-122-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000000000
χ252222-2-22-2-2222-2-2-2-22-2-222-12-122-2-2-2-22-1-1-111-1-11111-1-2-22211-1-11111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ262222-2-22-2-2222-2-2-2-22-2-222-12-122-2-2-2-22-1-1-111-1-11111-1-2-22211-1-11111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ2722-2-22-22002-2-2000002-2002222-222-2-2-2-2-222-22-222-2-2-20000000000000000000000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2000000
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χ2922-2-2-222002-2-200000-22002222-2-2-222-2-2-22-222-2-2-222-20000000000000000000000000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2000000
χ3022-2-2-222002-2-200000-22002222-2-2-222-2-2-22-222-2-2-222-20000000000000000000000000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2000000
χ312-2-220022-2-2-2222-2-20000022-2-2-200002-22200-2-2000022-2002-20022-2-20000002-200002-22-2000000000000000000
χ322-2-220022-2-2-2222-2-20000022-2-2-200002-22200-2-2000022-2002-20022-2-2000000-220000-22-22000000000000000000
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χ342-2-220022-2-2-2222-2-2000002-1-211−i3i3−i3i3-1-22-10011−i3i3−i3i3-1-11−i3i32-200-1-111−i3−i3i3i300-22i3−i3i3−i31-11-1000000000000000000
χ352-2-220022-2-2-2222-2-2000002-1-211i3−i3i3−i3-1-22-10011i3−i3i3−i3-1-11i3−i32-200-1-111i3i3−i3−i3002-2i3−i3i3−i3-11-11000000000000000000
χ362-2-220022-2-2-2222-2-2000002-1-211i3−i3i3−i3-1-22-10011i3−i3i3−i3-1-11i3−i32-200-1-111i3i3−i3−i300-22−i3i3−i3i31-11-1000000000000000000
χ372-2-22002-22-2-22-2-2220000022-2-2-200002-22200-2-200002-2200-2200-2-22200002-2002-2-220000000000000000000000
χ382-2-22002-22-2-22-2-2220000022-2-2-200002-22200-2-200002-2200-2200-2-2220000-2200-222-20000000000000000000000
χ392-2-22002-22-2-22-2-222000002-1-211−i3i3−i3i3-1-22-10011−i3i3−i3i3-11-1i3−i3-220011-1-1i3i3−i3−i32-200-111-1−i3i3i3−i3000000000000000000
χ402-2-22002-22-2-22-2-222000002-1-211−i3i3−i3i3-1-22-10011−i3i3−i3i3-11-1i3−i3-220011-1-1i3i3−i3−i3-22001-1-11i3−i3−i3i3000000000000000000
χ412-2-22002-22-2-22-2-222000002-1-211i3−i3i3−i3-1-22-10011i3−i3i3−i3-11-1−i3i3-220011-1-1−i3−i3i3i32-200-111-1i3−i3−i3i3000000000000000000
χ422-2-22002-22-2-22-2-222000002-1-211i3−i3i3−i3-1-22-10011i3−i3i3−i3-11-1−i3i3-220011-1-1−i3−i3i3i3-22001-1-11−i3i3i3−i3000000000000000000
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
χ454444-4-44444444444-4-4-4-4-4-2-2-2-2-22222-2-2-212211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000
χ464444-4-44-4-4444-4-4-4-44-4-444-2-2-2-2-22222-2-2-212211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4744-4-44-44004-4-4000004-4004-24-22-2-2222-4-4-24-4-22-2-22220000000000000000000000000000000000000000000000
χ4844-4-44-44004-4-4000004-400-24-24-444-4-4-422-2-22-22-2-22220000000000000000000000000000000000000000000000
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χ5144-4-4-444004-4-400000-44004-24-2222-2-22-4-4-2-44-2222-2-220000000000000000000000000000000000000000000000
χ5244-4-4-444004-4-400000-4400-24-24-4-4-444-422-22-2-2222-2-220000000000000000000000000000000000000000000000
χ5344-4-4-444004-4-400000-4400-2-2-2-2222-2-222212-21-1-1-111-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000
χ5444-4-4-444004-4-400000-4400-2-2-2-2222-2-222212-21-1-1-111-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000
χ554-44-400400-44-400000000044-4-440000-44-4400-440000-40000000000000000000000000000000000000000000000
χ564-44-400400-44-40000000004-2-42-2−2i32i32i3−2i324-4-2002-2−2i32i32i3−2i320000000000000000000000000000000000000000000000
χ574-44-400400-44-40000000004-2-42-22i3−2i3−2i32i324-4-2002-22i3−2i3−2i32i320000000000000000000000000000000000000000000000
χ584-44-400400-44-4000000000-242-440000-4-22-2002-20000200000023−23000023−23−2323000000000000000000000000000000
χ594-44-400400-44-4000000000-242-440000-4-22-2002-200002000000−23230000−232323−23000000000000000000000000000000
χ604-44-400400-44-4000000000-2-222-2−2i32i32i3−2i32-22100-11i3−i3−i3i3-100000023−23−3i3i3i−3i−333−3000000000000000000000000000000
χ614-44-400400-44-4000000000-2-222-2−2i32i32i3−2i32-22100-11i3−i3−i3i3-1000000−23233i−3i−3i3i3−3−33000000000000000000000000000000
χ624-44-400400-44-4000000000-2-222-22i3−2i3−2i32i32-22100-11−i3i3i3−i3-100000023−233i−3i−3i3i−333−3000000000000000000000000000000
χ634-44-400400-44-4000000000-2-222-22i3−2i3−2i32i32-22100-11−i3i3i3−i3-1000000−2323−3i3i3i−3i3−3−33000000000000000000000000000000
χ644-4-440044-4-4-4444-4-400000-242-4-4000042-2-200220000-24-400-2200-2-2220000000000000000000000000000000000
χ654-4-440044-4-4-4444-4-400000-2-2222−2i32i3−2i32i3-22-2100-1-1i3−i3i3−i31-22−2i32i3-220011-1-1i3i3−i3−i3000000000000000000000000000000
χ664-4-440044-4-4-4444-4-400000-2-22222i3−2i32i3−2i3-22-2100-1-1−i3i3−i3i31-222i3−2i3-220011-1-1−i3−i3i3i3000000000000000000000000000000
χ674-4-44004-44-4-44-4-44400000-242-4-4000042-2-200220000-2-44002-20022-2-20000000000000000000000000000000000
χ684-4-44004-44-4-44-4-44400000-2-2222−2i32i3−2i32i3-22-2100-1-1i3−i3i3−i312-22i3−2i32-200-1-111−i3−i3i3i3000000000000000000000000000000
χ694-4-44004-44-4-44-4-44400000-2-22222i3−2i32i3−2i3-22-2100-1-1−i3i3−i3i312-2−2i32i32-200-1-111i3i3−i3−i3000000000000000000000000000000
χ70666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000000000002222-1-1-1-1-1-1-1-1000000
χ71666666-366-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000000000000000-2-2-2-211111111000000
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
χ746666-6-6-366-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000000022-2-2-1-1-1-11111000000
χ756666-6-6-366-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000000000000-2-2221111-1-1-1-1000000
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
χ7866-6-66-6-300-33333−3333−330-3333−3300000000000000000000000000000000000000000000000000−i2i2−i2i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ7966-6-66-6-300-33333−3333−330-3333−3300000000000000000000000000000000000000000000000000i2−i2i2−i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ8066-6-66-6-300-333−3333−33330-33−333300000000000000000000000000000000000000000000000000−i2i2−i2i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ8166-6-66-6-300-333−3333−33330-33−333300000000000000000000000000000000000000000000000000i2−i2i2−i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ8266-6-6-66-300-33333−3333−3303-3−333300000000000000000000000000000000000000000000000000−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ8366-6-6-66-300-33333−3333−3303-3−333300000000000000000000000000000000000000000000000000i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ8466-6-6-66-300-333−3333−333303-333−3300000000000000000000000000000000000000000000000000−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ8566-6-6-66-300-333−3333−333303-333−3300000000000000000000000000000000000000000000000000i2−i2−i2i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ8612-1212-1200-6006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-1200-6006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121200-612-1266-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-121200-6-121266-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000

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