Finite Group Databasebeta

← Group #13167806

Character table — Group #13167806

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222244444444444488888888888888888889912121212121218181818181818242424242424242424242424363636363636363636364848484848487272108108
order123334666333666812121224243612121212122424242424242424242424244422224422244121266666666121212126668881212242466661212242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1111-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-11111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-11-1-1-1-111-1-1-1-11111-1-1-1-11-1-11-1-1-1-111-1-111-1-1-1-111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111111111-1-11-1111-1-11-11-1-1-11-11-111111-11-1-11-1-11-11-1-1-11-1111-11-1-1-1
χ61111111111111111111111111111111111111111-1-11-1-1-11-1-1-11-11-1-11-11-1-1-1-1-11-11-1-1-11-1-11-11-1-11-1-1-11-1-1111
χ71111111111111111111111111111111111111111-1-1-1111-11-1-11-11-1-1-11-111111-11-11-1-11-1-11-11-1-1-1111-11-11-1-1
χ81111111111111111111111111111111111111111-1-1-11-1-1-11-11-11-1-1-1-11-11-1-1-1-1-11-11-11-1-11-11-1-1-1-11-1-1-111-111
χ9111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111111111-11-111-1-1-11-11111-1-1-111-1-11-11-1-11-1-11-1
χ10111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-111-1-1-1-1111-11-1-1-111-11-111-1-1-111-1-1-1-11-1-11-1111-11
χ11111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-111-11-11-1-1-1-111-11-1111-1-11-11-11-1-1-111-1-1-1-1-111-11-1111-1
χ12111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-11-111-11111111-11-11-1-1111-11-1111-1-1-111-1-1-11-111-1-1-1-11
χ13111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-1-1111111-1-1-1-1-1-1-11-11-111-111111-1-1-1-11-11
χ14111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11-11-1-11111-1-111-1-1-1-1-1-1111-1-111111-11-1-11-11-1
χ15111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-11-1-1-1-1-1-111-1-11111-1-1111-1-1111-1-11-1111-1-11
χ16111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-11-1-1-1-1-1-1-1-1-1111111-11-11-111-111-1-1-1111-111-1
χ1722222-22222222220-2-2-20022-2-2-2-2-200000000000022000000-22-2-2222000000000000-22-2000-22000000000000
χ1822222-22222222220-2-2-20022-2-2-2-2-200000000000022000000-2-222-222000000000000-2-220002-2000000000000
χ1922222-22222222220-2-2-20022-2-2-2-2-2000000000000-2-2000000222-2-2-2-2000000000000222000-2-2000000000000
χ2022222-22222222220-2-2-20022-2-2-2-2-2000000000000-2-20000002-2-222-2-20000000000002-2-200022000000000000
χ212222-122-122-1-1-12-122-1222-1-1-12-1-1-12-122-1-1-1-1-1-1-1-1000222020020200020-12-12-10-10200-10020-1000-1-1-10-10-100
χ222222-122-122-1-1-12-122-1222-1-1-12-1-1-12-122-1-1-1-1-1-1-1-10002-2-20200-20-200020-1-21-210-10200100-201000-1110-10100
χ232222-122-122-1-1-12-122-1222-1-1-12-1-1-12-122-1-1-1-1-1-1-1-1000-2220-200-20-2000-2012-12-1010-200100-2010001-1-1010100
χ242222-122-122-1-1-12-122-1222-1-1-12-1-1-12-122-1-1-1-1-1-1-1-1000-2-2-20-200202000-201-21-21010-200-10020-1000111010-100
χ252222-122-122-1-1-12-1-22-12-2-2-1-1-12-1-1-1-21-2-21111111100022-20-200-20-200020-12-1-21010-200100201000-1-11010-100
χ262222-122-122-1-1-12-1-22-12-2-2-1-1-12-1-1-1-21-2-2111111110002-220-20020200020-1-212-1010-200-100-20-1000-11-1010100
χ272222-122-122-1-1-12-1-22-12-2-2-1-1-12-1-1-1-21-2-211111111000-22-20200202000-2012-1-210-10200-100-20-10001-110-10100
χ282222-122-122-1-1-12-1-22-12-2-2-1-1-12-1-1-1-21-2-211111111000-2-220200-20-2000-201-212-10-1020010020100011-10-10-100
χ29222-122-122-12-1-1-122-12222-1-1-1-12-1-1-12-1-122-1-1-1-1-1-100202220020200020-10-12-12-10200-10020-1000-10-1-1-10-1000
χ30222-122-122-12-1-1-122-12222-1-1-1-12-1-1-12-1-122-1-1-1-1-1-10020-2-2200-20-200020-101-21-2-10200100-201000-1011-101000
χ31222-122-122-12-1-1-122-12222-1-1-1-12-1-1-12-1-122-1-1-1-1-1-100-2022-200-20-2000-2010-12-1210-200100-20100010-1-1101000
χ32222-122-122-12-1-1-122-12222-1-1-1-12-1-1-12-1-122-1-1-1-1-1-100-20-2-2-200202000-20101-21-210-200-10020-1000101110-1000
χ33222-122-122-12-1-1-12-2-122-2-2-1-1-1-12-1-11-211-2-211111100202-2-20020200020-10-121-210-200-100-20-1000-10-11101000
χ34222-122-122-12-1-1-12-2-122-2-2-1-1-1-12-1-11-211-2-21111110020-22-200-20-200020-101-2-1210-200100201000-101-110-1000
χ35222-122-122-12-1-1-12-2-122-2-2-1-1-1-12-1-11-211-2-211111100-202-2200-20-2000-2010-121-2-1020010020100010-11-10-1000
χ36222-122-122-12-1-1-12-2-122-2-2-1-1-1-12-1-11-211-2-211111100-20-22200202000-20101-2-12-10200-100-20-1000101-1-101000
χ3722-122222-1-1-122-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-12222002220000-1-1-1-122000022-1-1-10020000-1-1-1-100-1-10000
χ3822-122222-1-1-122-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-122-2-200-2-220000-1-111-2-20000-2-211-10020000-1-11100110000
χ3922-122222-1-1-122-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-2-22-2002-2-2000011-112-200002-2-11100-2000011-1100-110000
χ4022-122222-1-1-122-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2200-22-20000111-1-220000-221-1100-20000111-1001-10000
χ4122-122222-1-1-122-1-1-222-111-1-12-1-1-1-1-2-21111-2-21111222-200-2220000-1-1-112-20000-221-1-100-2000011-11001-10000
χ4222-122222-1-1-122-1-1-222-111-1-12-1-1-1-1-2-21111-2-2111122-22002-220000-1-11-1-2200002-2-11-100-20000111-100-110000
χ4322-122222-1-1-122-1-1-222-111-1-12-1-1-1-1-2-21111-2-21111-2-22200-2-2-2000011-1-1220000-2-21110020000-1-1-1-100110000
χ4422-122222-1-1-122-1-1-222-111-1-12-1-1-1-1-2-21111-2-21111-2-2-2-20022-200001111-2-2000022-1-110020000-1-11100-1-10000
χ454444-2-44-244-2-2-24-20-42-400-2-22-4222000000000000000000000040-40000000000000000-200002000000000000
χ464444-2-44-244-2-2-24-20-42-400-2-22-42220000000000000000000000-404000000000000000020000-2000000000000
χ47444-24-4-244-24-2-2-2402-4-400-2-222-42200000000000000000000040-40000000000000000-2000020000000000000
χ48444-24-4-244-24-2-2-2402-4-400-2-222-422000000000000000000000-404000000000000000020000-20000000000000
χ49444-2-24-2-24-2-211-2-24-2-2444111-2-211-2-2-2-2-2-21111110000440000000000000-2-2-2-2000000000000000011000000
χ50444-2-24-2-24-2-211-2-24-2-2444111-2-211-2-2-2-2-2-21111110000-4-4000000000000022220000000000000000-1-1000000
χ51444-2-24-2-24-2-211-2-2-4-2-24-4-4111-2-211222222-1-1-1-1-1-100004-40000000000000-2-22200000000000000001-1000000
χ52444-2-24-2-24-2-211-2-2-4-2-24-4-4111-2-211222222-1-1-1-1-1-10000-44000000000000022-2-20000000000000000-11000000
χ5344-244-444-2-2-244-2-20-4-4200-2-2-4222200000000000044000000-40000-2-200000000000020000000000000000000
χ5444-244-444-2-2-244-2-20-4-4200-2-2-42222000000000000-4-40000004000022000000000000-20000000000000000000
χ5544-24-244-2-2-21-2-2-2144-2-2-2-211-2-21114-2-2-211-2-211110004000400000000-20-200000-20-200000000000100010000
χ5644-24-244-2-2-21-2-2-2144-2-2-2-211-2-21114-2-2-211-2-21111000-4000-4000000002020000020200000000000-1000-10000
χ5744-24-244-2-2-21-2-2-21-44-2-22211-2-2111-4222-1-122-1-1-1-10004000-400000000-20-200000202000000000001000-10000
χ5844-24-244-2-2-21-2-2-21-44-2-22211-2-2111-4222-1-122-1-1-1-1000-400040000000020200000-20-200000000000-100010000
χ5944-2-244-24-21-2-2-21-24-24-2-2-211-21-211-2411-2-2-2-21111004000400000000-20-200000-20-2000000000001000100000
χ6044-2-244-24-21-2-2-21-24-24-2-2-211-21-211-2411-2-2-2-2111100-4000-4000000002020000020200000000000-1000-100000
χ6144-2-244-24-21-2-2-21-2-4-24-22211-21-2112-4-1-12222-1-1-1-1004000-400000000-20-200000202000000000001000-100000
χ6244-2-244-24-21-2-2-21-2-4-24-22211-21-2112-4-1-12222-1-1-1-100-400040000000020200000-20-200000000000-1000100000
χ634-44440-4-4-4444-4-4-40000004-4000000000000000004i−4i000000000004i−4i00000000000000000000000000000000
χ644-44440-4-4-4444-4-4-40000004-400000000000000000−4i4i00000000000−4i4i00000000000000000000000000000000
χ654-4-2440-4-42-2-24-42200006−6-2200000006−66−60066−6−64i−4i00000000000−2i2i00000000000000000000i6−i60000000000
χ664-4-2440-4-42-2-24-42200006−6-2200000006−66−60066−6−6−4i4i000000000002i−2i00000000000000000000−i6i60000000000
χ674-4-2440-4-42-2-24-4220000−66-220000000−66−6600−6−6664i−4i00000000000−2i2i00000000000000000000−i6i60000000000
χ684-4-2440-4-42-2-24-4220000−66-220000000−66−6600−6−666−4i4i000000000002i−2i00000000000000000000i6−i60000000000
χ69888-4-4-8-4-48-4-422-4-4044-80022-244-2-200000000000000000000000000000000000000000000000000000000000
χ7088-48-4-88-4-4-42-4-4-420-844002244-2-2-200000000000000000000000000000000000000000000000000000000000
χ7188-4-48-8-48-42-4-4-42-404-8400224-24-2-200000000000000000000000000000000000000000000000000000000000
χ7288-4-4-48-4-4-42222228-4-4-4-4-4-1-1222-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000
χ7388-4-4-48-4-4-4222222-8-4-4-444-1-1222-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000
χ7488-4-4-4-8-4-4-4222222044400-1-1-2-2-2110000000033−3333−3300000000000000000000000000000000000000000000000
χ7588-4-4-4-8-4-4-4222222044400-1-1-2-2-21100000000−3333−333300000000000000000000000000000000000000000000000
χ768-888-40-84-88-4-44-84000000-440000000000000000000000000000000000000000000000000000000000000000
χ778-88-4804-8-8-48-444-8000000-440000000000000000000000000000000000000000000000000000000000000000
χ788-88-4-4044-8-4-42-2440000002-20000000000032−3232−32−323200000000000000000000000000000000000000000000000
χ798-88-4-4044-8-4-42-2440000002-200000000000−3232−323232−3200000000000000000000000000000000000000000000000
χ808-8-48-40-844-42-444-2000026−262-2000000026−26−6600−6−66600000000000000000000000000000000000000000000000
χ818-8-48-40-844-42-444-20000−26262-20000000−26266−60066−6−600000000000000000000000000000000000000000000000
χ828-8-4-4804-842-4-44-24000026−262-20000000−6626−2600−6−66600000000000000000000000000000000000000000000000
χ838-8-4-4804-842-4-44-240000−26262-200000006−6−26260066−6−600000000000000000000000000000000000000000000000
χ848-8-4-4-40444222-2-2-2000026−26-1100033−3300−66−6632−322ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7+2ζ13−2ζ2300000000000000000000000000000000000000000000000
χ858-8-4-4-40444222-2-2-2000026−26-11000−333300−66−66−3232−ζ5+ζ7−2ζ13+2ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−2ζ5+2ζ7−ζ13+ζ2300000000000000000000000000000000000000000000000
χ868-8-4-4-40444222-2-2-20000−2626-1100033−33006−66−6−3232−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7−2ζ13+2ζ2300000000000000000000000000000000000000000000000
χ878-8-4-4-40444222-2-2-20000−2626-11000−3333006−66−632−32ζ5−ζ7+2ζ13−2ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ232ζ5−2ζ7+ζ13−ζ2300000000000000000000000000000000000000000000000

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