Finite Group Databasebeta

← Group #13139952

Character table — Group #13139952

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order12222234466666664121212123366666612121212366666666666121212121212121212121212121244448888121212121212121224242424242424244412121212
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
χ51111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ61111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ71111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ81111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
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
χ142222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000000000−i3i3−i3i3
χ152222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000000000i3−i3i3−i3
χ162222222-2-22222222-2-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-211111111000000000000000033−3−333−3−3000000
χ172222222-2-22222222-2-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-2111111110000000000000000−3−333−3−333000000
χ182222-2-22222-2-2-2-222-222-2-22-122-12-1-12222-1-2-211-1-11111-1-2-2-1-111-1-1-1-111110000000000000000000000002-2-1-111
χ192222-2-22222-2-2-2-222-222-2-22-122-12-1-12222-1-2-211-1-11111-1-2-2-1-111-1-1-1-11111000000000000000000000000-2211-1-1
χ202222-2-22222-2-2-2-222-222-2-2-12-1-12-122-1-1-1-1-111-2-2-1-11111-11122-2-2-1-1-1-11111000022-2-200000000-1-1-1-11111000000
χ212222-2-22222-2-2-2-222-222-2-2-12-1-12-122-1-1-1-1-111-2-2-1-11111-11122-2-2-1-1-1-111110000-2-222000000001111-1-1-1-1000000
χ222222-2-22-2-22-2-2-2-2222-2-22222222222-2-2-2-22-2-2-2-222-2-2-2-2222-2-222-2-2-2-22222000000000000000000000000000000
χ232222-2-22-2-22-2-2-2-2222-2-2222-122-12-1-1-2-2-2-2-1-2-211-1-11111-12211-1-11111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ242222-2-22-2-22-2-2-2-2222-2-2222-122-12-1-1-2-2-2-2-1-2-211-1-11111-12211-1-11111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ252222-2-22-2-22-2-2-2-2222-2-222-12-1-12-1221111-111-2-2-1-11111-1-1-1-2-2221111-1-1-1-1000000000000000033−3−3−3−333000000
χ262222-2-22-2-22-2-2-2-2222-2-222-12-1-12-1221111-111-2-2-1-11111-1-1-1-2-2221111-1-1-1-10000000000000000−3−33333−3−3000000
χ272-22-20022-2-200002-202-20022-2-2-22-2222-2-220000-2-200002002-20022-2-20000002i−2i000000002i2i−2i−2i00000000000000
χ282-22-20022-2-200002-202-20022-2-2-22-2222-2-220000-2-200002002-20022-2-2000000−2i2i00000000−2i−2i2i2i00000000000000
χ292-22-2002-22-200002-20-220022-2-2-22-22-2-22220000-2-20000200-2200-2-22200002i−2i0000002i2i−2i−2i000000000000000000
χ302-22-2002-22-200002-20-220022-2-2-22-22-2-22220000-2-20000200-2200-2-2220000−2i2i000000−2i−2i2i2i000000000000000000
χ312-2-222-2200-222-2-2-2200000222-22-2-2-2000022-22-22-222-2-2-2000000000000000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2000000
χ322-2-222-2200-222-2-2-2200000222-22-2-2-2000022-22-22-222-2-2-2000000000000000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2000000
χ332-2-222-2200-222-2-2-2200000-12-1121-2-23−33−3-1-112-2-11-1-11113−300003−33−333−3−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ342-2-222-2200-222-2-2-2200000-12-1121-2-23−33−3-1-112-2-11-1-11113−300003−33−333−3−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ352-2-222-2200-222-2-2-2200000-12-1121-2-2−33−33-1-112-2-11-1-1111−330000−33−33−3−3330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ362-2-222-2200-222-2-2-2200000-12-1121-2-2−33−33-1-112-2-11-1-1111−330000−33−33−3−3330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ372-2-22-22200-2-2-222-2200000222-22-2-2-200002-22-222-2-2-222-2000000000000000000−i2i2i2−i200000000−i2i2−i2i2i2−i2i2−i2000000
χ382-2-22-22200-2-2-222-2200000222-22-2-2-200002-22-222-2-2-222-2000000000000000000i2−i2−i2i200000000i2−i2i2−i2−i2i2−i2i2000000
χ392-2-22-22200-2-2-222-2200000-12-1121-2-23−33−3-11-1-22-1111-1-11−3300003−33−3−3−3330000−i2i2i2−i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ402-2-22-22200-2-2-222-2200000-12-1121-2-23−33−3-11-1-22-1111-1-11−3300003−33−3−3−3330000i2−i2−i2i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ412-2-22-22200-2-2-222-2200000-12-1121-2-2−33−33-11-1-22-1111-1-113−30000−33−3333−3−30000−i2i2i2−i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ422-2-22-22200-2-2-222-2200000-12-1121-2-2−33−33-11-1-22-1111-1-113−30000−33−3333−3−30000i2−i2−i2i200000000−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
χ454444-4-44444-4-4-4-444-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-2221111-1-1-1-1000000000000000000000000000000
χ464444-4-44-4-44-4-4-4-4444-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4744-4-40040040000-4-40000044-44-4-44-4000040000-440000-400000000000000000000000000000000000000000000
χ4844-4-40040040000-4-4000004-2-442-4-220000-200002-200002000023−23000023−2323−23000000000000000000000000000000
χ4944-4-40040040000-4-4000004-2-442-4-220000-200002-2000020000−23230000−2323−2323000000000000000000000000000000
χ5044-4-40040040000-4-400000-242-2-424-423−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000
χ5144-4-40040040000-4-400000-242-2-424-4−232323−23-200002-200002000000−232323−230000000000000000000000000000000000
χ5244-4-40040040000-4-400000-2-22-222-2223−23−232310000-113-33-3-1000023−23−333−3−33−33000000000000000000000000000000
χ5344-4-40040040000-4-400000-2-22-222-2223−23−232310000-11-33-33-10000−2323−333−33−33−3000000000000000000000000000000
χ5444-4-40040040000-4-400000-2-22-222-22−232323−2310000-113-33-3-10000−23233−3−333−33−3000000000000000000000000000000
χ5544-4-40040040000-4-400000-2-22-222-22−232323−2310000-11-33-33-1000023−233−3−33−33−33000000000000000000000000000000
χ564-44-40044-4-400004-404-4004-2-4-4242-244-4-4-20000220000-200-2200-2-2220000000000000000000000000000000000
χ574-44-40044-4-400004-404-400-2422-4-2-44-2-222-20000220000-2004-400-2-2220000000000000000000000000000000000
χ584-44-40044-4-400004-404-400-2-2222-22-2-2-22210000-1-13-3-33100-220011-1-1-333-3000000000000000000000000000000
χ594-44-40044-4-400004-404-400-2-2222-22-2-2-22210000-1-1-333-3100-220011-1-13-3-33000000000000000000000000000000
χ604-44-4004-44-400004-40-44004-2-4-4242-2-4-444-20000220000-2002-20022-2-20000000000000000000000000000000000
χ614-44-4004-44-400004-40-4400-2422-4-2-4422-2-2-20000220000-200-440022-2-20000000000000000000000000000000000
χ624-44-4004-44-400004-40-4400-2-2222-22-222-2-210000-1-13-3-331002-200-1-1113-3-33000000000000000000000000000000
χ634-44-4004-44-400004-40-4400-2-2222-22-222-2-210000-1-1-333-31002-200-1-111-333-3000000000000000000000000000000
χ644-4-444-4400-444-4-4-44000004-24-4-2-4220000-24-4-22-22-2-222200000000000000000000000000000000000000000000
χ654-4-444-4400-444-4-4-4400000-2-2-22-222223−2323−231-22-221-111-1-1-123−230000−33−33−3−333000000000000000000000000000000
χ664-4-444-4400-444-4-4-4400000-2-2-22-2222−2323−23231-22-221-111-1-1-1−232300003−33−333−3−3000000000000000000000000000000
χ674-4-44-44400-4-4-444-44000004-24-4-2-4220000-2-442-2-2222-2-2200000000000000000000000000000000000000000000
χ684-4-44-44400-4-4-444-4400000-2-2-22-222223−2323−2312-22-21-1-1-111-1−23230000−33−3333−3−3000000000000000000000000000000
χ694-4-44-44400-4-4-444-4400000-2-2-22-2222−2323−232312-22-21-1-1-111-123−2300003−33−3−3−333000000000000000000000000000000
χ70666666-366-3-3-3-3-3-3-36-3-3-3-30000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-100000000000000
χ71666666-366-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-200001111111100000000000000
χ72666666-3-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i300000000000000
χ73666666-3-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i300000000000000
χ746666-6-6-366-33333-3-3-6-3-3330000000000000000000000000000000000000022-2-20000-1-1-1-1111100000000000000
χ756666-6-6-366-33333-3-3-6-3-33300000000000000000000000000000000000000-2-22200001111-1-1-1-100000000000000
χ766666-6-6-3-6-6-33333-3-3633-3-30000000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i300000000000000
χ776666-6-6-3-6-6-33333-3-3633-3-30000000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i300000000000000
χ786-66-600-36-63−3i33i3−3i33i3-330-33−3i33i300000000000000000000000000000000000000002i−2i00003−3−33−i−iii00000000000000
χ796-66-600-36-63−3i33i3−3i33i3-330-33−3i33i30000000000000000000000000000000000000000−2i2i0000−333−3ii−i−i00000000000000
χ806-66-600-36-633i3−3i33i3−3i3-330-333i3−3i300000000000000000000000000000000000000002i−2i0000−333−3−i−iii00000000000000
χ816-66-600-36-633i3−3i33i3−3i3-330-333i3−3i30000000000000000000000000000000000000000−2i2i00003−3−33ii−i−i00000000000000
χ826-66-600-3-663−3i33i3−3i33i3-3303-33i3−3i3000000000000000000000000000000000000002i−2i000000−i−iii3−3−3300000000000000
χ836-66-600-3-663−3i33i3−3i33i3-3303-33i3−3i300000000000000000000000000000000000000−2i2i000000ii−i−i−333−300000000000000
χ846-66-600-3-6633i3−3i33i3−3i3-3303-3−3i33i3000000000000000000000000000000000000002i−2i000000−i−iii−333−300000000000000
χ856-66-600-3-6633i3−3i33i3−3i3-3303-3−3i33i300000000000000000000000000000000000000−2i2i000000ii−i−i3−3−3300000000000000
χ861212-12-1200-600-6−6i36i36i3−6i3660000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-1200-600-66i3−6i3−6i36i3660000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121212-12-6006-6-6666-60000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-1212-600666-6-66-60000000000000000000000000000000000000000000000000000000000000000000000000

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