Finite Group Databasebeta

← Group #13169425

Character table — Group #13169425

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612124436661212121212121212121212122444412121212121212122244444466661212121212121212121212121212121244661212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-111-1-11111-1-1-1-111-1-1111111-1-11-11111-1-111-1-11-1-1-1-1-111-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111-11-11-1-1111111-1-1-1-1-1-1111111-1-111-1111-1-111-1-111-11-1-1-1-1-1-111-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-11111111111111111-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-11-11-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1-1-111-1-111-1-1-11-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1111-1-1-1-1-111-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1111
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1-1-111-1-1-1-111-1-1-111111-1-1-1-1111-111-1-1-1-111111-1-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1111111-1-111-1-1-1-1-1-1-1-1111-111-1-11111-1-1-1111-1-111-1-111-11-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-111-1-111-1-1111111-1-1-11-1-111-1-1-1-111-1111-1-111-1-1-1-1-111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-111-1-1-1-1-1-111-1-1-1-1111111-1-1111-1-1-1-1-11111-1-11-111-1-1-1-111-1-11-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1
χ17222222-1-12222-1-122-1-122-1-122-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-102222222200002222000000002-12-1-1-100-1-1-1-1-1-1-1-100-1-1-1-1000000000
χ18222222-1-12222-1-122-1-122-1-122-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-102-22-222-2-20000-2-2-2-2000000002-1-21-1100-1-111-1-111001111000000000
χ19222222-1-12222-1-122-1-122-1-122-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-22-22-2-2220000-2-2-2-200000000-212-11-10011-1-111-1-1001111000000000
χ20222222-1-12222-1-122-1-122-1-122-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-2-2-2-2-2-2-2-20000222200000000-21-2111001111111100-1-1-1-1000000000
χ21222222-1-12222-1-122-1-12-2-1-122-1-12-1-11100-1-1-1-1-2-2-2-211111111022-2-2-2-2-2-20000-2-222000000002-12-11100-1-1-1-111110011-1-1000000000
χ22222222-1-12222-1-122-1-12-2-1-122-1-12-1-11100-1-1-1-1-2-2-2-21111111102-2-22-2-222000022-2-2000000002-1-211-100-1-11111-1-100-1-111000000000
χ23222222-1-12222-1-122-1-12-2-1-122-1-12-1-11100-1-1-1-1-2-2-2-2111111110-222-222-2-2000022-2-200000000-212-1-110011-1-1-1-11100-1-111000000000
χ24222222-1-12222-1-122-1-12-2-1-122-1-12-1-11100-1-1-1-1-2-2-2-2111111110-2-22222220000-2-22200000000-21-21-1-1001111-1-1-1-10011-1-1000000000
χ2522222-1222-12-1222-12-1-122-1-1-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-12020200-1-122-1-1000000222-1-1-100-1202-1-100-1-100-1-102000000-1-1000-10
χ2622222-1222-12-1222-12-1-122-1-1-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-120-20-2001122-1-1000000-2-22-1-1-1001-20-2-1-1001100110-20000001100010
χ2722222-1222-12-1222-12-1-122-1-1-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2020200-1-1-2-211000000-2-2-211100-12021100-1-100-1-10-20000001100010
χ2822222-1222-12-1222-12-1-122-1-1-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20-20-20011-2-21100000022-2111001-20-2110011001102000000-1-1000-10
χ2922222-1222-12-1222-12-1-1-22-1-1-12-1-12-1-2-222-1-1-1-1-2111-2-2111111-2020-2001122-1-1000000-2-2-211100-120-2-1-100-1-100110200000011000-10
χ3022222-1222-12-1222-12-1-1-22-1-1-12-1-12-1-2-222-1-1-1-1-2111-2-2111111-20-20200-1-122-1-100000022-2111001-202-1-1001100-1-10-2000000-1-100010
χ3122222-1222-12-1222-12-1-1-22-1-1-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-21111112020-20011-2-211000000222-1-1-100-120-21100-1-100110-2000000-1-100010
χ3222222-1222-12-1222-12-1-1-22-1-1-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-211111120-20200-1-1-2-211000000-2-22-1-1-1001-20211001100-1-10200000011000-10
χ332222-1222-12-1222-12-12-12-12-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-122020-1-100-1-12200002200-12-1-1-120020-1-1-1-100-1-100200000-1-10000-100
χ342222-1222-12-1222-12-12-12-12-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-12-20-201100-1-1220000-2-200-12-1-11-200-20-1-111001100-200000110000100
χ352222-1222-12-1222-12-12-12-12-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-22020-1-10011-2-20000-2-2001-211-12002011-1-100-1-100-200000110000100
χ362222-1222-12-1222-12-12-12-12-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-20110011-2-2000022001-2111-200-201111001100200000-1-10000-100
χ372222-1222-12-1222-12-12-1-2-12-1-1-12-1-12-2-222-1-1-1-11-21111-2-21111-220-201100-1-1220000-2-2001-211-1200-20-1-1-1-1001100200000110000-100
χ382222-1222-12-1222-12-12-1-2-12-1-1-12-1-12-2-222-1-1-1-11-21111-2-21111-2-2020-1-100-1-122000022001-2111-20020-1-11100-1-100-200000-1-10000100
χ392222-1222-12-1222-12-12-1-2-12-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-21111220-20110011-2-200002200-12-1-1-1200-2011-1-1001100-200000-1-10000100
χ402222-1222-12-1222-12-12-1-2-12-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-211112-2020-1-10011-2-20000-2-200-12-1-11-20020111100-1-100200000110000-100
χ412-22-2222-222-2-2-22-2-22220-2-2-22-2-2-22200002-2-220000000000000000000000000002-22i−2i2i−2i0000000000000000000000002-22i−2i2i−2i00000
χ422-22-2222-222-2-2-22-2-22220-2-2-22-2-2-22200002-2-220000000000000000000000000002-2−2i2i−2i2i0000000000000000000000002-2−2i2i−2i2i00000
χ432-22-2222-222-2-2-22-2-22220-2-2-22-2-2-22200002-2-22000000000000000000000000000-222i−2i−2i2i000000000000000000000000-222i−2i−2i2i00000
χ442-22-2222-222-2-2-22-2-22220-2-2-22-2-2-22200002-2-22000000000000000000000000000-22−2i2i2i−2i000000000000000000000000-22−2i2i2i−2i00000
χ452-2-222222-2-2-2-2-2-2222220222-2-2-2-2-2-2002i−2i22-2-20000000000000000000002i−2i2i−2i2-200000000000000002i−2i00000000002-20000002i−2i000
χ462-2-222222-2-2-2-2-2-2222220222-2-2-2-2-2-2002i−2i22-2-20000000000000000000002i−2i2i−2i-2200000000000000002i−2i0000000000-22000000−2i2i000
χ472-2-222222-2-2-2-2-2-2222220222-2-2-2-2-2-200−2i2i22-2-2000000000000000000000−2i2i−2i2i2-20000000000000000−2i2i00000000002-2000000−2i2i000
χ482-2-222222-2-2-2-2-2-2222220222-2-2-2-2-2-200−2i2i22-2-2000000000000000000000−2i2i−2i2i-220000000000000000−2i2i0000000000-220000002i−2i000
χ4944444-2-2-24-24-2-2-24-2-21-24-21-2-2-21-2-21-2-20011114-2-2-2-2-21111110040400-2-2000000000000000000-2-20-20000110011000000000000000
χ5044444-2-2-24-24-2-2-24-2-21-24-21-2-2-21-2-21-2-20011114-2-2-2-2-211111100-40-4002200000000000000000022020000-1-100-1-1000000000000000
χ5144444-2-2-24-24-2-2-24-2-21-2-4-21-2-2-21-2-2122001111-422222-1-1-1-1-1-10040-40022000000000000000000-2-20200001100-1-1000000000000000
χ5244444-2-2-24-24-2-2-24-2-21-2-4-21-2-2-21-2-2122001111-422222-1-1-1-1-1-100-40400-2-2000000000000000000220-20000-1-10011000000000000000
χ534444-24-2-2-24-24-2-2-241-2-241-2-2-21-2-21-2-2-2001111-24-2-211-2-2111104040-2-2000000000000000000-2-200-200011001100000000000000000
χ544444-24-2-2-24-24-2-2-241-2-241-2-2-21-2-21-2-2-2001111-24-2-211-2-211110-40-402200000000000000000022002000-1-100-1-100000000000000000
χ554444-24-2-2-24-24-2-2-241-2-2-41-2-2-21-2-21-2220011112-422-1-122-1-1-1-1040-4022000000000000000000-2-20020001100-1-100000000000000000
χ564444-24-2-2-24-24-2-2-241-2-2-41-2-2-21-2-21-2220011112-422-1-122-1-1-1-10-4040-2-20000000000000000002200-2000-1-1001100000000000000000
χ574444-2-244-2-2-2-244-2-2-2-214-2-211-2-21-2-244441111-2-211-2-2-2-21111400000000-2-2-2-200000000-2-2110000001100000000000000000000000
χ584444-2-244-2-2-2-244-2-2-2-214-2-211-2-21-2-244-4-41111-2-211-2-2-2-21111-40000000022220000000022-1-1000000-1-100000000000000000000000
χ594444-2-244-2-2-2-244-2-2-2-21-4-2-211-2-21-2-2-4-444111122-1-12222-1-1-1-1-400000000-2-2-2-20000000022-1-10000001100000000000000000000000
χ604444-2-244-2-2-2-244-2-2-2-21-4-2-211-2-21-2-2-4-4-4-4111122-1-12222-1-1-1-1400000000222200000000-2-211000000-1-100000000000000000000000
χ6144-4-4444-4-4-4444-4-4-44440-4-4-4-4444-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000000
χ6244-4-444-22-4-444-22-4-4-2-24022-4-4-2-242223−2300-22-22000023−2323−232323−23−2300000000000000000000000000000000000000000000000000000000
χ6344-4-444-22-4-444-22-4-4-2-24022-4-4-2-2422−232300-22-220000−2323−2323−23−23232300000000000000000000000000000000000000000000000000000000
χ6444-4-44-24-4-424-24-4-424-2-20-42224-2-2-420000-22-22000000000000000000023−2300000000000000000000000000000023−23000000000000000
χ6544-4-44-24-4-424-24-4-424-2-20-42224-2-2-420000-22-220000000000000000000−2323000000000000000000000000000000−2323000000000000000
χ6644-4-44-2-22-424-2-22-42-21-202-122-21-22-123−23001-11-1000023−23−33−3−333000000023−23000000000000000000000000003-300−33000000000000000
χ6744-4-44-2-22-424-2-22-42-21-202-122-21-22-123−23001-11-1000023−23−33−3−3330000000−232300000000000000000000000000-33003−3000000000000000
χ6844-4-44-2-22-424-2-22-42-21-202-122-21-22-1−2323001-11-10000−23233−333−3−3000000023−2300000000000000000000000000-3300−33000000000000000
χ6944-4-44-2-22-424-2-22-42-21-202-122-21-22-1−2323001-11-10000−23233−333−3−30000000−2323000000000000000000000000003-3003−3000000000000000
χ7044-4-4-244-42-4-244-42-4-24-202-422-24-22-40000-22-220000000000000000023−2300000000000000000000000000000023−2300000000000000000
χ7144-4-4-244-42-4-244-42-4-24-202-422-24-22-40000-22-2200000000000000000−2323000000000000000000000000000000−232300000000000000000
χ7244-4-4-24-222-4-24-222-41-2-20-12221-2-2-1223−23001-11-10000−3323−23−3−3330000023−23000000000000000000000000003-300−3300000000000000000
χ7344-4-4-24-222-4-24-222-41-2-20-12221-2-2-1223−23001-11-10000−3323−23−3−33300000−232300000000000000000000000000-33003−300000000000000000
χ7444-4-4-24-222-4-24-222-41-2-20-12221-2-2-12−2323001-11-100003−3−232333−3−30000023−2300000000000000000000000000-3300−3300000000000000000
χ7544-4-4-24-222-4-24-222-41-2-20-12221-2-2-12−2323001-11-100003−3−232333−3−300000−2323000000000000000000000000003-3003−300000000000000000
χ764-44-444-2244-4-42-2-4-4-2-24022-4422-4-2-20000-222-20000000000000000000000000004-40000000000000000000000000000-22000000000
χ774-44-444-2244-4-42-2-4-4-2-24022-4422-4-2-20000-222-2000000000000000000000000000-4400000000000000000000000000002-2000000000
χ784-44-44-24-44-2-42-44-424-2-20-422-2-4224-20000-222-200000000000000000000000000000004i−4i0000000000000000000000000000−2i2i00000
χ794-44-44-24-44-2-42-44-424-2-20-422-2-4224-20000-222-20000000000000000000000000000000−4i4i00000000000000000000000000002i−2i00000
χ804-44-4-244-4-242-4-442-4-24-202-42-22-42-240000-222-2000000000000000000000000000004i−4i0000000000000000000000000000−2i2i0000000
χ814-44-4-244-4-242-4-442-4-24-202-42-22-42-240000-222-200000000000000000000000000000−4i4i00000000000000000000000000002i−2i0000000
χ824-4-4444-2-2-4-4-4-42244-2-240-2-24-422-4220000-2-22200000000000000000000000004-40000000000000000000000000000-2200000000000
χ834-4-4444-2-2-4-4-4-42244-2-240-2-24-422-4220000-2-2220000000000000000000000000-4400000000000000000000000000002-200000000000
χ844-4-444-244-42-42-4-44-24-2-204-2-22-422-42004i−4i-2-2220000000000000000000004i−4i−2i2i000000000000000000−2i2i00000000000000000000000
χ854-4-444-244-42-42-4-44-24-2-204-2-22-422-4200−4i4i-2-222000000000000000000000−4i4i2i−2i0000000000000000002i−2i00000000000000000000000
χ864-4-44-24442-42-4-4-4-24-24-20-24-222-422-4004i−4i-2-222000000000000000000000−2i2i4i−4i000000000000000000−2i2i00000000000000000000000
χ874-4-44-24442-42-4-4-4-24-24-20-24-222-422-400−4i4i-2-2220000000000000000000002i−2i−4i4i0000000000000000002i−2i00000000000000000000000
χ884-4-44-2-2442222-4-4-2-2-2-210-2-21-122-122004i−4i11-1-1003i−3i00003i−3i3i−3i000000000−2i2i−2i2i00000000003-3000000i−i00000000000000000000000
χ894-4-44-2-2442222-4-4-2-2-2-210-2-21-122-122004i−4i11-1-100−3i3i0000−3i3i−3i3i000000000−2i2i−2i2i0000000000-33000000i−i00000000000000000000000
χ904-4-44-2-2442222-4-4-2-2-2-210-2-21-122-12200−4i4i11-1-1003i−3i00003i−3i3i−3i0000000002i−2i2i−2i0000000000-33000000−ii00000000000000000000000
χ914-4-44-2-2442222-4-4-2-2-2-210-2-21-122-12200−4i4i11-1-100−3i3i0000−3i3i−3i3i0000000002i−2i2i−2i00000000003-3000000−ii00000000000000000000000
χ928888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-48-844-4-48-844-4-42044-2-2-4-424400002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4444-4-4-44442220-2-2-2-2222-2-243−4300-11-110000−2323−232333−3−300000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-4444-4-4-44442220-2-2-2-2222-2-2−434300-11-11000023−2323−23−3−33300000000000000000000000000000000000000000000000000000000
χ978-88-88-4-448-4-844-4-84-42-404-24-44-24-4200002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-48-44-484-84-44-82-4-40-244-4-2442-400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-48-8-4-444-8844-4-42044-2244-2-4-400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-44-4-4444-4442220-2-2-22-2-2-2220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-44-4-4444-4442220-2-2-22-2-2-2220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000
χ1028-8-888-4-4-4-84-84448-4-42-40-42-444-244-2000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-48-4-44-84-844-482-4-402-4-44-244-24000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4-4444444-4-42220222-2-2-2-2-2-20000-1-111006i−6i0000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4-4444444-4-42220222-2-2-2-2-2-20000-1-11100−6i6i00003i−3i3i−3i00000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).