Finite Group Databasebeta

← Group #13140185

Character table — Group #13140185

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order1222223446666666412121212336666661212121236666666666612121212121212121212121212122222666666668888242424242424242424661212
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
χ51111-1-111111-1-1-1-11-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ61111-1-111111-1-1-1-11-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ71111-1-111111-1-1-1-11-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-11-1-111
χ81111-1-111111-1-1-1-11-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1000000000000-2-2-2-211111111000000
χ132222222-2-22222222-2-2-2-2-222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ142222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000000000000000−i3i3−i3i3
χ152222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000000000000000i3−i3i3−i3
χ162222222-2-22222222-2-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−3000000
χ172222222-2-22222222-2-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−333000000
χ182222-2-222222-2-2-2-22-222-2-22-122-12-1-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-111110000000000000000000000002-2-1-111
χ192222-2-222222-2-2-2-22-222-2-22-122-12-1-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-11111000000000000000000000000-2211-1-1
χ202222-2-222222-2-2-2-22-222-2-2-12-1-12-122-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-1111100000000000022-2-2-1-1-1-11111000000
χ212222-2-222222-2-2-2-22-222-2-2-12-1-12-122-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-11111000000000000-2-2221111-1-1-1-1000000
χ222222-2-22-2-222-2-2-2-222-2-22222222222-2-2-2-22-2-2-2-222-2-2-2-22-2-22222-2-2-2-22222000000000000000000000000000000
χ232222-2-22-2-222-2-2-2-222-2-2222-122-12-1-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ242222-2-22-2-222-2-2-2-222-2-2222-122-12-1-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ252222-2-22-2-222-2-2-2-222-2-222-12-1-12-1221111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-1000000000000000033−3−3−3−333000000
χ262222-2-22-2-222-2-2-2-222-2-222-12-1-12-1221111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-10000000000000000−3−33333−3−3000000
χ272-22-20022-2-2-20000202-20022-2-2-222-222-2-220000-2-2000022-2000022-2-20000002-2000022-2-2000000000000000000
χ282-22-20022-2-2-20000202-20022-2-2-222-222-2-220000-2-2000022-2000022-2-2000000-220000-2-222000000000000000000
χ292-22-2002-22-2-2000020-220022-2-2-222-2-2-22220000-2-200002-220000-2-22200002-20022-2-20000000000000000000000
χ302-22-2002-22-2-2000020-220022-2-2-222-2-2-22220000-2-200002-220000-2-2220000-2200-2-2220000000000000000000000
χ312-2-222-22002-222-2-2-200000222-2-2-2-22000022-22-22-222-2-2-2000000000000000000000000002−22−22−22−22−22−2000000
χ322-2-222-22002-222-2-2-200000222-2-2-2-22000022-22-22-222-2-2-200000000000000000000000000−22−22−22−22−22−22000000
χ332-2-222-22002-222-2-2-200000-12-11-21-223−33−3-1-112-2-11-1-1111003−3003−33−333−3−30000000000002−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ342-2-222-22002-222-2-2-200000-12-11-21-223−33−3-1-112-2-11-1-1111003−3003−33−333−3−3000000000000−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ352-2-222-22002-222-2-2-200000-12-11-21-22−33−33-1-112-2-11-1-111100−3300−33−33−3−3330000000000002−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ362-2-222-22002-222-2-2-200000-12-11-21-22−33−33-1-112-2-11-1-111100−3300−33−33−3−333000000000000−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ372-2-22-222002-2-2-222-200000222-2-2-2-2200002-22-222-2-2-222-2000000000000000000000000002−2−222−22−2−22−22000000
χ382-2-22-222002-2-2-222-200000222-2-2-2-2200002-22-222-2-2-222-200000000000000000000000000−222−2−22−222−22−2000000
χ392-2-22-222002-2-2-222-200000-12-11-21-223−33−3-11-1-22-1111-1-1100−33003−33−3−3−3330000000000002−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ402-2-22-222002-2-2-222-200000-12-11-21-223−33−3-11-1-22-1111-1-1100−33003−33−3−3−333000000000000−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ412-2-22-222002-2-2-222-200000-12-11-21-22−33−33-11-1-22-1111-1-11003−300−33−3333−3−30000000000002−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ422-2-22-222002-2-2-222-200000-12-11-21-22−33−33-11-1-22-1111-1-11003−300−33−3333−3−3000000000000−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ444444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ454444-4-444444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000
χ464444-4-44-4-444-4-4-4-444-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000
χ4744-4-400400-440000-40000044-444-4-4-4000040000-440000-400000000000000000000000000000000000000000000
χ4844-4-400400-440000-4000004-2-44-2-4220000-200002-200002000023−23000023−2323−23000000000000000000000000000000
χ4944-4-400400-440000-4000004-2-44-2-4220000-200002-2000020000−23230000−2323−2323000000000000000000000000000000
χ5044-4-400400-440000-400000-242-242-4-423−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000
χ5144-4-400400-440000-400000-242-242-4-4−232323−23-200002-200002000000−232323−230000000000000000000000000000000000
χ5244-4-400400-440000-400000-2-22-2-222223−23−232310000-113-33-3-1000023−23−333−3−33−33000000000000000000000000000000
χ5344-4-400400-440000-400000-2-22-2-222223−23−232310000-11-33-33-10000−2323−333−33−33−3000000000000000000000000000000
χ5444-4-400400-440000-400000-2-22-2-2222−232323−2310000-113-33-3-10000−23233−3−333−33−3000000000000000000000000000000
χ5544-4-400400-440000-400000-2-22-2-2222−232323−2310000-11-33-33-1000023−233−3−33−33−33000000000000000000000000000000
χ564-44-40044-4-4-40000404-4004-2-4-424-2244-4-4-20000220000-2-220000-2-2220000000000000000000000000000000000
χ574-44-40044-4-4-40000404-400-2422-4-24-4-2-222-20000220000-24-40000-2-2220000000000000000000000000000000000
χ584-44-40044-4-4-40000404-400-2-2222-2-22-2-22210000-1-13-3-331-22000011-1-1-333-3000000000000000000000000000000
χ594-44-40044-4-4-40000404-400-2-2222-2-22-2-22210000-1-1-333-31-22000011-1-13-3-33000000000000000000000000000000
χ604-44-4004-44-4-4000040-44004-2-4-424-22-4-444-20000220000-22-2000022-2-20000000000000000000000000000000000
χ614-44-4004-44-4-4000040-4400-2422-4-24-422-2-2-20000220000-2-44000022-2-20000000000000000000000000000000000
χ624-44-4004-44-4-4000040-4400-2-2222-2-2222-2-210000-1-13-3-3312-20000-1-1113-3-33000000000000000000000000000000
χ634-44-4004-44-4-4000040-4400-2-2222-2-2222-2-210000-1-1-333-312-20000-1-111-333-3000000000000000000000000000000
χ644-4-444-44004-444-4-4-4000004-24-42-42-20000-24-4-22-22-2-222200000000000000000000000000000000000000000000
χ654-4-444-44004-444-4-4-400000-2-2-22222-223−2323−231-22-221-111-1-1-10023−2300−33−33−3−333000000000000000000000000000000
χ664-4-444-44004-444-4-4-400000-2-2-22222-2−2323−23231-22-221-111-1-1-100−2323003−33−333−3−3000000000000000000000000000000
χ674-4-44-444004-4-4-444-4000004-24-42-42-20000-2-442-2-2222-2-2200000000000000000000000000000000000000000000
χ684-4-44-444004-4-4-444-400000-2-2-22222-223−2323−2312-22-21-1-1-111-100−232300−33−3333−3−3000000000000000000000000000000
χ694-4-44-444004-4-4-444-400000-2-2-22222-2−2323−232312-22-21-1-1-111-10023−23003−33−3−3−333000000000000000000000000000000
χ70666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002222-1-1-1-1-1-1-1-1000000000000000000
χ71666666-366-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-211111111000000000000000000
χ72666666-3-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i3000000000000000000
χ73666666-3-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i3000000000000000000
χ746666-6-6-366-3-33333-3-6-3-3330000000000000000000000000000000000000022-2-2-1-1-1-11111000000000000000000
χ756666-6-6-366-3-33333-3-6-3-33300000000000000000000000000000000000000-2-2221111-1-1-1-1000000000000000000
χ766666-6-6-3-6-6-3-33333-3633-3-3000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i3000000000000000000
χ776666-6-6-3-6-6-3-33333-3633-3-3000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i3000000000000000000
χ786-66-600-36-633−3i33i3−3i33i3-30-33−3i33i300000000000000000000000000000000000000002-2−i3i3i3−i3-1-111000000000000000000
χ796-66-600-36-633−3i33i3−3i33i3-30-33−3i33i30000000000000000000000000000000000000000-22i3−i3−i3i311-1-1000000000000000000
χ806-66-600-36-6333i3−3i33i3−3i3-30-333i3−3i300000000000000000000000000000000000000002-2i3−i3−i3i3-1-111000000000000000000
χ816-66-600-36-6333i3−3i33i3−3i3-30-333i3−3i30000000000000000000000000000000000000000-22−i3i3i3−i311-1-1000000000000000000
χ826-66-600-3-6633−3i33i3−3i33i3-303-33i3−3i3000000000000000000000000000000000000002-200-1-111−i3i3i3−i3000000000000000000
χ836-66-600-3-6633−3i33i3−3i33i3-303-33i3−3i300000000000000000000000000000000000000-220011-1-1i3−i3−i3i3000000000000000000
χ846-66-600-3-66333i3−3i33i3−3i3-303-3−3i33i3000000000000000000000000000000000000002-200-1-111i3−i3−i3i3000000000000000000
χ856-66-600-3-66333i3−3i33i3−3i3-303-3−3i33i300000000000000000000000000000000000000-220011-1-1−i3i3i3−i3000000000000000000
χ861212-12-1200-6006-6−6i36i36i3−6i360000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-1200-6006-66i3−6i3−6i36i360000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121212-12-600-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-1212-600-6666-6-660000000000000000000000000000000000000000000000000000000000000000000000000

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