Finite Group Databasebeta

← Group #13167809

Character table — Group #13167809

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222244444444444488888888888888888889912121212121218181818181818242424242424242424242424363636363636363636364848484848487272108108
order123334666333666812121224243612121212122424242424242424242424244422444422244121266661212121212121212666888121224246612121212242422
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-111-1-111
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
χ51111111111111111111111111111111111111111-1-11-11-111-11-11-1-1-11-11-11-11-111111-1-1-11-11-1-1-11-11-1111-1-1-1
χ61111111111111111111111111111111111111111-1-11-11-1-1-1-1-11-11-1-11-11-11-11-1-1-1-1-1-11-1-1-11-11-1-11-11-1-1-1-1111
χ71111111111111111111111111111111111111111-1-1-11-1111-1-11-11-1-1-11-11-11-111111-11-1-1-11-11-1-1-11-1111-11-1-1
χ81111111111111111111111111111111111111111-1-1-11-11-1-1-11-11-1-1-1-11-11-11-11-1-1-1-11-1-1-11-11-1-1-1-11-11-1-11-111
χ9111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-111111111-11-1-11-1111-1-1111-1-1-111-1-11-1-111-1-1-11-1
χ10111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-111-1-1-1-1111-11-1-11-11-1-111-1-11-111-1-1-1-11-1-11-1111-11
χ11111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-111-11-11-1-1-1-111-11-111-11-111-1-1-1-11-111-1-1-1-1-111-11-1111-1
χ12111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111111-11-111-11-1-1-111111-1-1-111-1-1-111-1-11-1-1-11
χ13111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11-11-1-1-11111-1-1-1-111-1-11-1-11-111-11111-1-11-1-11-11
χ14111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-11-11-1-11111-1-1-1-1-1-111-11-111-1-111111-1-1-111-11-1
χ15111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-11-1-1-1-1-1-1111111-1-1-11-111-1-1111-1-1111-11-1-11
χ16111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-11-1-1-1-1-1-1-11111-1-1111-1-11-111-111-1-111-11-111-1
χ1722222-22222222220-2-2-20022-2-2-2-2-200000000000022000000-22-2-22220000000000002-2-2000-22000000000000
χ1822222-22222222220-2-2-20022-2-2-2-2-200000000000022000000-2-222-222000000000000-22-20002-2000000000000
χ1922222-22222222220-2-2-20022-2-2-2-2-2000000000000-2-2000000222-2-2-2-2000000000000222000-2-2000000000000
χ2022222-22222222220-2-2-20022-2-2-2-2-2000000000000-2-20000002-2-222-2-2000000000000-2-2200022000000000000
χ212222-12-1222-1-1-1-122-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-12222220020000-1-122-1-1-1-122000000-120000-1-1-1-1-1-1000000
χ222222-12-1222-1-1-1-122-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-2-2-2-20020000-1-1-2-21111-2-2000000-120000-1-11111000000
χ232222-12-1222-1-1-1-122-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-2-22-22-200-20000112-2-11-112-20000001-2000011-11-11000000
χ242222-12-1222-1-1-1-122-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-2-2-22-2200-2000011-221-11-1-220000001-20000111-11-1000000
χ252222-12-1222-1-1-1-12-2-12211-1-1-1-12-1-1-2-2-2-211111111222-2-220020000-1-12-2-111-1-22000000-1-2000011-111-1000000
χ262222-12-1222-1-1-1-12-2-12211-1-1-1-12-1-1-2-2-2-21111111122-222-20020000-1-1-221-1-112-2000000-1-20000111-1-11000000
χ272222-12-1222-1-1-1-12-2-12211-1-1-1-12-1-1-2-2-2-211111111-2-222-2-200-200001122-1-111-2-2000000120000-1-1-1-111000000
χ282222-12-1222-1-1-1-12-2-12211-1-1-1-12-1-1-2-2-2-211111111-2-2-2-22200-2000011-2-211-1-122000000120000-1-111-1-1000000
χ29222-12222-1-12-12-1-1222-122-1-12-1-1-1-12-1-1-122-1-1-1-1-1-10002022200202000-102020-12-12-10-100020-1000-10-1-1-10-100
χ30222-12222-1-12-12-1-1222-122-1-12-1-1-1-12-1-1-122-1-1-1-1-1-1000202-2-200-20-2000-102020-1-21-2101000-201000-10-1110100
χ31222-12222-1-12-12-1-1222-122-1-12-1-1-1-12-1-1-122-1-1-1-1-1-1000-20-22200-20-200010-20-2012-12-101000-201000101-1-10100
χ32222-12222-1-12-12-1-1222-122-1-12-1-1-1-12-1-1-122-1-1-1-1-1-1000-20-2-2-20020200010-20-201-21-210-100020-1000101110-100
χ33222-12222-1-12-12-1-1-222-1-2-2-1-12-1-1-1-1-2111-2-211111100020-22-200-20-2000-1020-2012-1-2101000201000-101-110-100
χ34222-12222-1-12-12-1-1-222-1-2-2-1-12-1-1-1-1-2111-2-211111100020-2-2200202000-1020-201-212-10-1000-20-1000-1011-10100
χ35222-12222-1-12-12-1-1-222-1-2-2-1-12-1-1-1-1-2111-2-2111111000-2022-20020200010-2020-12-1-210-1000-20-100010-1-110100
χ36222-12222-1-12-12-1-1-222-1-2-2-1-12-1-1-1-1-2111-2-2111111000-202-2200-20-200010-2020-1-212-10100020100010-11-10-100
χ3722-12222-12-1-12-12-122-1222-1-1-12-1-1-1-12-1-1-1-122-1-1-1-1002020220202000-102020-10-12-12-100020-1000-10-10-1-1-1000
χ3822-12222-12-1-12-12-122-1222-1-1-12-1-1-1-12-1-1-1-122-1-1-1-1002020-2-20-20-2000-102020-101-21-21000-201000-10-10111000
χ3922-12222-12-1-12-12-122-1222-1-1-12-1-1-1-12-1-1-1-122-1-1-1-100-20-20220-20-200010-20-2010-12-121000-2010001010-1-11000
χ4022-12222-12-1-12-12-122-1222-1-1-12-1-1-1-12-1-1-1-122-1-1-1-100-20-20-2-2020200010-20-20101-21-2-100020-1000101011-1000
χ4122-12222-12-1-12-12-1-22-12-2-2-1-1-12-1-1-11-21111-2-211110020-202-20202000-1020-2010-121-2-1000-20-1000-1010-111000
χ4222-12222-12-1-12-12-1-22-12-2-2-1-1-12-1-1-11-21111-2-211110020-20-220-20-2000-1020-20101-2-121000201000-10101-1-1000
χ4322-12222-12-1-12-12-1-22-12-2-2-1-1-12-1-1-11-21111-2-2111100-20202-20-20-200010-2020-10-121-2100020100010-10-11-1000
χ4422-12222-12-1-12-12-1-22-12-2-2-1-1-12-1-1-11-21111-2-2111100-2020-22020200010-2020-101-2-12-1000-20-100010-101-11000
χ454444-2-4-2444-2-2-2-2402-4-400-2-222-42200000000000044000000-40000-2-200000000000000200000000000000000
χ464444-2-4-2444-2-2-2-2402-4-400-2-222-422000000000000-4-4000000400002200000000000000-200000000000000000
χ47444-24-444-2-24-24-2-20-4-4200-2-2-42222000000000000000000000040-4000000000000000-2000002000000000000
χ48444-24-444-2-24-24-2-20-4-4200-2-2-422220000000000000000000000-404000000000000000200000-2000000000000
χ49444-2-24-24-2-2-21-21-24-24-2-2-211-21-2114-2-2-2-2-21111110004040000000000-20-20-20-2000000000000000101000000
χ50444-2-24-24-2-2-21-21-24-24-2-2-211-21-2114-2-2-2-2-2111111000-40-400000000002020202000000000000000-10-1000000
χ51444-2-24-24-2-2-21-21-2-4-24-22211-21-211-422222-1-1-1-1-1-100040-40000000000-20-2020200000000000000010-1000000
χ52444-2-24-24-2-2-21-21-2-4-24-22211-21-211-422222-1-1-1-1-1-1000-40400000000002020-20-2000000000000000-101000000
χ5344-244-44-24-2-24-24-20-42-400-2-22-422200000000000000000000040-4000000000000000-20000020000000000000
χ5444-244-44-24-2-24-24-20-42-400-2-22-4222000000000000000000000-404000000000000000200000-20000000000000
χ5544-24-24-2-24-21-21-2-24-2-24-2-2111-2-211-24-2-211-2-21111004040000000000-20-20-20-20000000000000001010000000
χ5644-24-24-2-24-21-21-2-24-2-24-2-2111-2-211-24-2-211-2-2111100-40-400000000002020202000000000000000-10-10000000
χ5744-24-24-2-24-21-21-2-2-4-2-2422111-2-2112-422-1-122-1-1-1-10040-40000000000-20-2020200000000000000010-10000000
χ5844-24-24-2-24-21-21-2-2-4-2-2422111-2-2112-422-1-122-1-1-1-100-40400000000002020-20-2000000000000000-1010000000
χ5944-2-2444-2-21-2-2-2-2144-2-24411-2-2111-2-211-2-2-2-2111100000044000000000000000-2-2-2-200000000000000110000
χ6044-2-2444-2-21-2-2-2-2144-2-24411-2-2111-2-211-2-2-2-21111000000-4-4000000000000000222200000000000000-1-10000
χ6144-2-2444-2-21-2-2-2-21-44-2-2-4-411-2-211122-1-12222-1-1-1-10000004-4000000000000000-2-222000000000000001-10000
χ6244-2-2444-2-21-2-2-2-21-44-2-2-4-411-2-211122-1-12222-1-1-1-1000000-4400000000000000022-2-200000000000000-110000
χ634-44440-4-4-4444-4-4-40000004-4000000000000000004i−4i000000000004i−4i00000000000000000000000000000000
χ644-44440-4-4-4444-4-4-40000004-400000000000000000−4i4i00000000000−4i4i00000000000000000000000000000000
χ654-444-202-4-44-2-222-400006−6-220000000006−66−666−6−64i−4i00000000000−2i2i00000000000000000000i6−i60000000000
χ664-444-202-4-44-2-222-400006−6-220000000006−66−666−6−6−4i4i000000000002i−2i00000000000000000000−i6i60000000000
χ674-444-202-4-44-2-222-40000−66-22000000000−66−66−6−6664i−4i00000000000−2i2i00000000000000000000−i6i60000000000
χ684-444-202-4-44-2-222-40000−66-22000000000−66−66−6−666−4i4i000000000002i−2i00000000000000000000i6−i60000000000
χ69888-4-4-8-48-4-4-42-42-404-8400224-24-2-200000000000000000000000000000000000000000000000000000000000
χ7088-48-4-8-4-48-42-42-4-4044-80022-244-2-200000000000000000000000000000000000000000000000000000000000
χ7188-4-48-88-4-42-4-4-4-420-844002244-2-2-200000000000000000000000000000000000000000000000000000000000
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
χ768-88-480-8-84-48-4-844000000-440000000000000000000000000000000000000000000000000000000000000000
χ778-88-4-404-84-4-424-24000026−262-200000000026−26−66−6−66600000000000000000000000000000000000000000000000
χ788-88-4-404-84-4-424-240000−26262-2000000000−26266−666−6−600000000000000000000000000000000000000000000000
χ798-8-4880-84-8-4-484-84000000-440000000000000000000000000000000000000000000000000000000000000000
χ808-8-48-4044-8-42-4-244000026−262-2000000000−6626−26−6−66600000000000000000000000000000000000000000000000
χ818-8-48-4044-8-42-4-2440000−26262-20000000006−6−262666−6−600000000000000000000000000000000000000000000000
χ828-8-4-480-8442-4-444-20000002-2000000032−32000032−32−323200000000000000000000000000000000000000000000000
χ838-8-4-480-8442-4-444-20000002-20000000−32320000−323232−3200000000000000000000000000000000000000000000000
χ848-8-4-4-40444222-2-2-2000026−26-1100033−330032−32−66−662ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7+2ζ13−2ζ2300000000000000000000000000000000000000000000000
χ858-8-4-4-40444222-2-2-2000026−26-11000−333300−3232−66−66−ζ5+ζ7−2ζ13+2ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−2ζ5+2ζ7−ζ13+ζ2300000000000000000000000000000000000000000000000
χ868-8-4-4-40444222-2-2-20000−2626-1100033−3300−32326−66−6−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7−2ζ13+2ζ2300000000000000000000000000000000000000000000000
χ878-8-4-4-40444222-2-2-20000−2626-11000−33330032−326−66−6ζ5−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.