Finite Group Databasebeta

← Group #13140040

Character table — Group #13140040

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order1222223446661212121246612123366666666663666666666121212121212121212121212121212122222666666668888242424242424242424661212
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
χ51111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ61111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ71111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-11-1-111
χ81111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111-111-1-1
χ92222222222222222222222-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000
χ102222222222222222222222-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000000000
χ11222222222222222222222-12-1222222-12-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ12222222222222222222222-12-1222222-12-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
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
χ142222222-2-2222-2-2-2-2-222-2-22-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-2-211-2-211111111110000−i3−i3i3i3−i3−i3i3i3000000000000000000
χ152222222-2-2222-2-2-2-2-222-2-22-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-2-211-2-211111111110000i3i3−i3−i3i3i3−i3−i3000000000000000000
χ162222222-2-2222-2-2-2-2-222-2-2-12-1222222-12-1-1-1-1-1-1-1-1-1-1-111-2-211-2-21111111100000000000000000000000000−i3i3−i3i3
χ172222222-2-2222-2-2-2-2-222-2-2-12-1222222-12-1-1-1-1-1-1-1-1-1-1-111-2-211-2-21111111100000000000000000000000000i3−i3i3−i3
χ182222-2-22222222222-2-2-2-2-22-12-1-111112-12-1-2-2-1-11111-122-1-1-2-211-1-1-1-1111122-2-2-1-1-1-11111000000000000000000
χ192222-2-22222222222-2-2-2-2-22-12-1-111112-12-1-2-2-1-11111-122-1-1-2-211-1-1-1-11111-2-2221111-1-1-1-1000000000000000000
χ202222-2-22222222222-2-2-2-2-2-12-122-2-2-2-2-12-1-111-1-11111-1-1-12211-2-2-1-1-1-111110000000000000000000000002-2-1-111
χ212222-2-22222222222-2-2-2-2-2-12-122-2-2-2-2-12-1-111-1-11111-1-1-12211-2-2-1-1-1-11111000000000000000000000000-2211-1-1
χ222222-2-22-2-2222-2-2-2-22-2-22222222-2-2-2-22222-2-222-2-2-2-22-2-2-2-22222-2-2-2-22222000000000000000000000000000000
χ232222-2-22-2-2222-2-2-2-22-2-2222-12-1-111112-12-1-2-2-1-11111-1-2-21122-1-11111-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000000000
χ242222-2-22-2-2222-2-2-2-22-2-2222-12-1-111112-12-1-2-2-1-11111-1-2-21122-1-11111-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000000000
χ252222-2-22-2-2222-2-2-2-22-2-222-12-122-2-2-2-2-12-1-111-1-11111-111-2-2-1-1221111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ262222-2-22-2-2222-2-2-2-22-2-222-12-122-2-2-2-2-12-1-111-1-11111-111-2-2-1-1221111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ272-22-20022-2-2-2222-2-20000022-2-2-2000022-2200-2-2000022-22-2000022-2-20000002-200002-22-2000000000000000000
χ282-22-20022-2-2-2222-2-20000022-2-2-2000022-2200-2-2000022-22-2000022-2-2000000-220000-22-22000000000000000000
χ292-22-20022-2-2-2222-2-2000002-1-211−i3−i3i3i32-1-2-10011−i3−i3i3i3-12-2-1100−i3i3-1-111−i3−i3i3i3002-2−i3i3−i3i3-11-11000000000000000000
χ302-22-20022-2-2-2222-2-2000002-1-211−i3−i3i3i32-1-2-10011−i3−i3i3i3-12-2-1100−i3i3-1-111−i3−i3i3i300-22i3−i3i3−i31-11-1000000000000000000
χ312-22-20022-2-2-2222-2-2000002-1-211i3i3−i3−i32-1-2-10011i3i3−i3−i3-12-2-1100i3−i3-1-111i3i3−i3−i3002-2i3−i3i3−i3-11-11000000000000000000
χ322-22-20022-2-2-2222-2-2000002-1-211i3i3−i3−i32-1-2-10011i3i3−i3−i3-12-2-1100i3−i3-1-111i3i3−i3−i300-22−i3i3−i3i31-11-1000000000000000000
χ332-22-2002-22-2-22-2-2220000022-2-2-2000022-2200-2-200002-22-220000-2-22200002-2002-2-220000000000000000000000
χ342-22-2002-22-2-22-2-2220000022-2-2-2000022-2200-2-200002-22-220000-2-2220000-2200-222-20000000000000000000000
χ352-22-2002-22-2-22-2-222000002-1-211−i3−i3i3i32-1-2-10011−i3−i3i3i3-1-221-100i3−i311-1-1i3i3−i3−i32-200-111-1−i3i3i3−i3000000000000000000
χ362-22-2002-22-2-22-2-222000002-1-211−i3−i3i3i32-1-2-10011−i3−i3i3i3-1-221-100i3−i311-1-1i3i3−i3−i3-22001-1-11i3−i3−i3i3000000000000000000
χ372-22-2002-22-2-22-2-222000002-1-211i3i3−i3−i32-1-2-10011i3i3−i3−i3-1-221-100−i3i311-1-1−i3−i3i3i32-200-111-1i3−i3−i3i3000000000000000000
χ382-22-2002-22-2-22-2-222000002-1-211i3i3−i3−i32-1-2-10011i3i3−i3−i3-1-221-100−i3i311-1-1−i3−i3i3i3-22001-1-11−i3i3i3−i3000000000000000000
χ392-2-222-22002-2-2000002-20022-22-22-22-2-2-2222-22-22-22-2-200000000000000000000000000002−22−222−2−222−2−2000000
χ402-2-222-22002-2-2000002-20022-22-22-22-2-2-2222-22-22-22-2-20000000000000000000000000000−22−22−2−222−2−222000000
χ412-2-22-222002-2-200000-220022-22-2-22-22-2-222-222-2-22-22-200000000000000000000000000002−2−2222−2−2−2−222000000
χ422-2-22-222002-2-200000-220022-22-2-22-22-2-222-222-2-22-22-20000000000000000000000000000−222−2−2−22222−2−2000000
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
χ454444-4-44444444444-4-4-4-4-4-2-2-2-2-22222-2-2-212211-1-1-1-11-2-2-2-222221111-1-1-1-1000000000000000000000000000000
χ464444-4-44-4-4444-4-4-4-44-4-444-2-2-2-2-22222-2-2-212211-1-1-1-112222-2-2-2-2-1-1-1-11111000000000000000000000000000000
χ4744-4-400400-44-4000000000444-440000-4-4-4400-440000-40000000000000000000000000000000000000000000000
χ4844-4-400400-44-40000000004-242-2−2i32i32i3−2i3-42-4-2002-2−2i32i32i3−2i320000000000000000000000000000000000000000000000
χ4944-4-400400-44-40000000004-242-22i3−2i3−2i32i3-42-4-2002-22i3−2i3−2i32i320000000000000000000000000000000000000000000000
χ5044-4-400400-44-4000000000-24-2-4400002-42-2002-200002000023−2300000023−2323−23000000000000000000000000000000
χ5144-4-400400-44-4000000000-24-2-4400002-42-2002-2000020000−2323000000−2323−2323000000000000000000000000000000
χ5244-4-400400-44-4000000000-2-2-22-2−2i32i32i3−2i3222100-11i3−i3−i3i3-1000023−23003i−3i3i−3i−33−33000000000000000000000000000000
χ5344-4-400400-44-4000000000-2-2-22-2−2i32i32i3−2i3222100-11i3−i3−i3i3-10000−232300−3i3i−3i3i3−33−3000000000000000000000000000000
χ5444-4-400400-44-4000000000-2-2-22-22i3−2i3−2i32i3222100-11−i3i3i3−i3-1000023−2300−3i3i−3i3i−33−33000000000000000000000000000000
χ5544-4-400400-44-4000000000-2-2-22-22i3−2i3−2i32i3222100-11−i3i3i3−i3-10000−2323003i−3i3i−3i3−33−3000000000000000000000000000000
χ564-44-40044-4-4-4444-4-400000-242-4-40000-242-200220000-2-224-40000-2-2220000000000000000000000000000000000
χ574-44-40044-4-4-4444-4-400000-2-2222−2i3−2i32i32i3-2-22100-1-1i3i3−i3−i31-22-2200−2i32i311-1-1i3i3−i3−i3000000000000000000000000000000
χ584-44-40044-4-4-4444-4-400000-2-22222i32i3−2i3−2i3-2-22100-1-1−i3−i3i3i31-22-22002i3−2i311-1-1−i3−i3i3i3000000000000000000000000000000
χ594-44-4004-44-4-44-4-44400000-242-4-40000-242-200220000-22-2-44000022-2-20000000000000000000000000000000000
χ604-44-4004-44-4-44-4-44400000-2-2222−2i3−2i32i32i3-2-22100-1-1i3i3−i3−i312-22-2002i3−2i3-1-111−i3−i3i3i3000000000000000000000000000000
χ614-44-4004-44-4-44-4-44400000-2-22222i32i3−2i3−2i3-2-22100-1-1−i3−i3i3i312-22-200−2i32i3-1-111i3i3−i3−i3000000000000000000000000000000
χ624-4-444-44004-4-4000004-4004-2-4-22-22-22-424-24-4-22-22-2220000000000000000000000000000000000000000000000
χ634-4-444-44004-4-4000004-400-2424-44-44-42-4-2-2-22-22-22-2220000000000000000000000000000000000000000000000
χ644-4-444-44004-4-4000004-400-2-22-22-22-2222-21-221-11-11-1-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000
χ654-4-444-44004-4-4000004-400-2-22-22-22-2222-21-221-11-11-1-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000
χ664-4-44-444004-4-400000-44004-2-4-222-22-2-424-2-44-222-22-220000000000000000000000000000000000000000000000
χ674-4-44-444004-4-400000-4400-2424-4-44-442-4-2-22-2-222-22-220000000000000000000000000000000000000000000000
χ684-4-44-444004-4-400000-4400-2-22-222-22-222-212-21-1-11-11-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000
χ694-4-44-444004-4-400000-4400-2-22-222-22-222-212-21-1-11-11-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000
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
χ786-6-666-6-300-33333−3333−330-3333−33000000000000000000000000000000000000000000000000002−22−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000
χ796-6-666-6-300-33333−3333−330-3333−3300000000000000000000000000000000000000000000000000−22−22−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000
χ806-6-666-6-300-333−3333−33330-33−3333000000000000000000000000000000000000000000000000002−22−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000
χ816-6-666-6-300-333−3333−33330-33−333300000000000000000000000000000000000000000000000000−22−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000
χ826-6-66-66-300-33333−3333−3303-3−3333000000000000000000000000000000000000000000000000002−2−22ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000
χ836-6-66-66-300-33333−3333−3303-3−333300000000000000000000000000000000000000000000000000−222−2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000
χ846-6-66-66-300-333−3333−333303-333−33000000000000000000000000000000000000000000000000002−2−22ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000
χ856-6-66-66-300-333−3333−333303-333−3300000000000000000000000000000000000000000000000000−222−2−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000
χ861212-12-1200-6006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-1200-6006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-1212-1200-612-1266-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-1212-1200-6-121266-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000

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