Finite Group Databasebeta

← Group #13172723

Character table — Group #13172723

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order12223336666666662333666666666664436666666666666662244412121212121212122222224466666666121212121212121212121212246666661212226124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1-11-1-1-1-1-1-1-111-1-11-1-1
χ311111111111111111111111111111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-111-1-111-1-1-111111-1-11111-1111-1-1-1-1-1-1-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ51111111111111111111111111111111-1-11111111111111111-11111-1-111-1-111-1-11111-1-1-1-111-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-111-1-1-1-1-1111-1-1-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-111111-11
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
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-11-1111-1-111-1-111-1-111-1-1-1-1-1-1111
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-1111-1-1111111-1-111-1-1-1-111-1-111-1-11-111-1-1-1-1111-111-1-111-1-1111-1-1
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11111111-1-1-11-1-1-1-1111111-11-1
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-11111111111111-1-111-1-1-1-1-1-1-1-11-11-11111-1-111-1-11111-1-111-1-1-1-11
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-1-1-1-1-1-1-1-11111-1-11111111111-11-11-1-1-1-111-1-1-1-11111-1-11111-1-1-1
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-1-1-1-1-1-111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-111-11-1-1-1-11111-1-1-111
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-1-111-1-1-1-111-1-111-1-111-1-111-1-111-11-1-11111-1-11-111-1-111-1-1-1-11-11
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-111-1-111-1-111-1-1-1-111-1-111-1-11-11-1-1-111-1-11111-1-111-1-1-1-11111-1
χ17222222-1222-1-1-12222-12-1-1-1-122-1-1-1-12-100-122-1-122-1-1-1-1-1-1-1-1-1022220022002200222200002-100-1-1-1-1-1200-1-1-1-1-1-10000-1-1-1-10000000
χ18222222-1222-1-1-12222-12-1-1-1-122-1-1-1-12-100-122-1-122-1-1-1-1-1-1-1-1-1022-2-2002200-2-200-2-2-2-200002-100-1-1-111-200-1-11111000011110000000
χ19222222-1222-1-1-12222-12-1-1-1-122-1-1-1-12-100-122-1-122-1-1-1-1-1-1-1-1-10-2-22200-2-2002200-2-2-2-20000-2100111-1-120011-1-1-1-1000011110000000
χ20222222-1222-1-1-12222-12-1-1-1-122-1-1-1-12-100-122-1-122-1-1-1-1-1-1-1-1-10-2-2-2-200-2-200-2-20022220000-210011111-2001111110000-1-1-1-10000000
χ21222222-1222-1-1-1222-2-12-111-122-1-1-1-12-100-1-2-211-2-211-1-1-1111102-22-200-2-200-2-20022-2-200002-100-1-11-1120011-1-1110000-1-1110000000
χ22222222-1222-1-1-1222-2-12-111-122-1-1-1-12-100-1-2-211-2-211-1-1-1111102-2-2200-2-2002200-2-22200002-100-1-111-1-2001111-1-1000011-1-10000000
χ23222222-1222-1-1-1222-2-12-111-122-1-1-1-12-100-1-2-211-2-211-1-1-111110-222-2002200-2-200-2-2220000-210011-1-11200-1-1-1-111000011-1-10000000
χ24222222-1222-1-1-1222-2-12-111-122-1-1-1-12-100-1-2-211-2-211-1-1-111110-22-22002200220022-2-20000-210011-11-1-200-1-111-1-10000-1-1110000000
χ2522222-122-1-12222-1222-1-1222-1-1-1-122-1-122-12-122-1-1-1-1-1-1-1-1-1-1-122200-1-1-1-12200000000222-1-12-1-1-1-12000-1-1-1-1000020000000-1-100-100
χ2622222-122-1-12222-1222-1-1222-1-1-1-122-1-122-12-122-1-1-1-1-1-1-1-1-1-1-12-2-200-1-1112200000000-2-22-11-2-1-111-2000-1-1110000-200000001100100
χ2722222-122-1-12222-1222-1-1222-1-1-1-122-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-2220011-1-1-2-200000000-2-2-21-1211-1-1200011-1-10000-200000001100100
χ2822222-122-1-12222-1222-1-1222-1-1-1-122-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2001111-2-20000000022-211-21111-20001111000020000000-1-100-100
χ2922222-122-1-12222-12-22-1-1-2-22-1-1-1-122-1-122-1-21-2-21111-1-1-11111-22-200-1-1112200000000-2-2-21-1211-1-1-2000-1-1110000200000001100-100
χ3022222-122-1-12222-12-22-1-1-2-22-1-1-1-122-1-122-1-21-2-21111-1-1-11111-2-2200-1-1-1-1220000000022-211-211112000-1-1-1-10000-20000000-1-100100
χ3122222-122-1-12222-12-22-1-1-2-22-1-1-1-122-1-1-2-2-1-21-2-21111-1-1-1111122-2001111-2-200000000222-1-12-1-1-1-1-200011110000-20000000-1-100100
χ3222222-122-1-12222-12-22-1-1-2-22-1-1-1-122-1-1-2-2-1-21-2-21111-1-1-111112-220011-1-1-2-200000000-2-22-11-2-1-111200011-1-10000200000001100-100
χ332222-122-122222-12-12-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1200222200-1-1-1-122000000-1200-1-100022-1-1-100-1-1-1-102-1-1000000000-10
χ342222-122-122222-12-12-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1200-2-22200-1-111-2-2000000-1200-1-1000-2-21-1-10011110-21100000000010
χ352222-122-122222-12-12-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-20022-2-20011-1-1-2-20000001-2001100022-11100-1-1-1-10-21100000000010
χ362222-122-122222-12-12-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-200-2-2-2-2001111220000001-20011000-2-211100111102-1-1000000000-10
χ372222-122-122222-12-1-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-11111-2002-22200-1-111-2-20000001-200110002-2-1-1-100-1-1110211000000000-10
χ382222-122-122222-12-1-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-11111-200-222200-1-1-1-1220000001-20011000-221-1-10011-1-10-2-1-100000000010
χ392222-122-122222-12-1-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-111112002-2-2-200111122000000-1200-1-10002-2-11100-1-1110-2-1-100000000010
χ402222-122-122222-12-1-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-11111200-22-2-20011-1-1-2-2000000-1200-1-1000-221110011-1-10211000000000-10
χ412-22-2222-2-2-22-2-2-222022200-22-22-22-2-2-2002000000002-2-2000000000000000002-22-2002-200000000000000000000002-22-2002-200000
χ422-22-2222-2-2-22-2-2-222022200-22-22-22-2-2-2002000000002-2-2000000000000000002-2-2200-2200000000000000000000002-2-2200-2200000
χ432-22-2222-2-2-22-2-2-222022200-22-22-22-2-2-2002000000002-2-200000000000000000-222-200-220000000000000000000000-222-200-2200000
χ442-22-2222-2-2-22-2-2-222022200-22-22-22-2-2-2002000000002-2-200000000000000000-22-22002-20000000000000000000000-22-22002-200000
χ452-2-22222-22-2-22-22-2-2022200-2-2-2-22-222-22-2200000000-22-20000000002-2002-20000002-2000000000000002-20000000000002-2002-2000
χ462-2-22222-22-2-22-22-2-2022200-2-2-2-22-222-22-2200000000-22-20000000002-2002-2000000-22000000000000002-2000000000000-2200-22000
χ472-2-22222-22-2-22-22-2-2022200-2-2-2-22-222-2-22200000000-22-2000000000-2200-220000002-200000000000000-220000000000002-200-22000
χ482-2-22222-22-2-22-22-2-2022200-2-2-2-22-222-2-22200000000-22-2000000000-2200-22000000-2200000000000000-22000000000000-22002-2000
χ4944444-2-24-2-2-2-2-24-244-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-21111111110440000-2-200000000000000-2-20011-200000110000000000000000000
χ5044444-2-24-2-2-2-2-24-244-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-21111111110-4-4000022000000000000002200-1-1200000-1-10000000000000000000
χ5144444-2-24-2-2-2-2-24-24-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-104-400002200000000000000-2-20011200000-1-10000000000000000000
χ5244444-2-24-2-2-2-2-24-24-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-10-440000-2-2000000000000002200-1-1-200000110000000000000000000
χ534444-24-2-244-2-2-2-24-241-2-2-2-21-2-2-2-211-2-2001-2411-2-2-2-2111111100044000000-2-200000000000000000-2-2-200001111000000000000000
χ544444-24-2-244-2-2-2-24-241-2-2-2-21-2-2-2-211-2-2001-2411-2-2-2-21111111000-4-400000022000000000000000002220000-1-1-1-1000000000000000
χ554444-24-2-244-2-2-2-24-2-41-2-2221-2-2-2-211-2-20012-4-1-12222111-1-1-1-10004-40000002200000000000000000-22-2000011-1-1000000000000000
χ564444-24-2-244-2-2-2-24-2-41-2-2221-2-2-2-211-2-20012-4-1-12222111-1-1-1-1000-44000000-2-2000000000000000002-220000-1-111000000000000000
χ574444-2-24-2-2-2444-2-2-24-21-244-211-2-2-2-21-2441-2-2-2-211-2-2111111140000-2-200-2-20000000000-2-2001100000011000000000000000000000
χ584444-2-24-2-2-2444-2-2-24-21-244-211-2-2-2-21-2-4-41-2-2-2-211-2-21111111-4000022002200000000002200-1-1000000-1-1000000000000000000000
χ594444-2-24-2-2-2444-2-2-2-4-21-2-4-4-211-2-2-2-21-24412222-1-122111-1-1-1-1-40000-2-200-2-200000000002200-1-100000011000000000000000000000
χ604444-2-24-2-2-2444-2-2-2-4-21-2-4-4-211-2-2-2-21-2-4-412222-1-122111-1-1-1-1400002200220000000000-2-20011000000-1-1000000000000000000000
χ6144-4-44444-44-4-44-4-4-40444004-44-4-4-4-4-4400400000000-4-44000000000000000000000000000000000000000000000000000000000000
χ6244-4-444-24-4422-2-4-4-40-24-2−2i32i3-2-442222-4-200-200−2i32i300−2i32i322-2−2i3−2i32i32i300000000000000000000000000000000000000000000000000000000
χ6344-4-444-24-4422-2-4-4-40-24-22i3−2i3-2-442222-4-200-2002i3−2i3002i3−2i322-22i32i3−2i3−2i300000000000000000000000000000000000000000000000000000000
χ6444-4-44-2442-2-4-44-42-404-2-20042-222-4-42-200-20000000022-200000000000−2i32i300000000000000000000000000−2i32i30000000000000000000
χ6544-4-44-2442-2-4-44-42-404-2-20042-222-4-42-200-20000000022-2000000000002i3−2i3000000000000000000000000002i3−2i30000000000000000000
χ6644-4-44-2-242-222-2-42-40-2-21−2i32i3-22-2-1-1222100100−2i32i300i3−i3-1-11i3i3−i3−i30000000−2i32i30000000000000000003-3000000i3−i30000000000000000000
χ6744-4-44-2-242-222-2-42-40-2-21−2i32i3-22-2-1-1222100100−2i32i300i3−i3-1-11i3i3−i3−i300000002i3−2i3000000000000000000-33000000−i3i30000000000000000000
χ6844-4-44-2-242-222-2-42-40-2-212i3−2i3-22-2-1-12221001002i3−2i300−i3i3-1-11−i3−i3i3i30000000−2i32i3000000000000000000-33000000i3−i30000000000000000000
χ6944-4-44-2-242-222-2-42-40-2-212i3−2i3-22-2-1-12221001002i3−2i300−i3i3-1-11−i3−i3i3i300000002i3−2i30000000000000000003-3000000−i3i30000000000000000000
χ7044-4-4-244-2-44-4-442-420-2-2400-22-2-4-4222400-20000000022-200000000000000023−230000000000000000000000000023−23000000000000000
χ7144-4-4-244-2-44-4-442-420-2-2400-22-2-4-4222400-20000000022-2000000000000000−232300000000000000000000000000−2323000000000000000
χ7244-4-4-24-2-2-4422-22-4201-2-2−2i32i312-222-1-12-200100i3−i300−2i32i3-1-11i3i3−i3−i30000000000023−230000000000000000000000003i−3i−33000000000000000
χ7344-4-4-24-2-2-4422-22-4201-2-2−2i32i312-222-1-12-200100i3−i300−2i32i3-1-11i3i3−i3−i300000000000−2323000000000000000000000000−3i3i3−3000000000000000
χ7444-4-4-24-2-2-4422-22-4201-2-22i3−2i312-222-1-12-200100−i3i3002i3−2i3-1-11−i3−i3i3i30000000000023−23000000000000000000000000−3i3i−33000000000000000
χ7544-4-4-24-2-2-4422-22-4201-2-22i3−2i312-222-1-12-200100−i3i3002i3−2i3-1-11−i3−i3i3i300000000000−23230000000000000000000000003i−3i3−3000000000000000
χ764-44-444-2-4-4-4-222-4440-24-20024-4-22-22-4200-200000000-22200000000000000000004-40000000000000000000000000000-22000000000
χ774-44-444-2-4-4-4-222-4440-24-20024-4-22-22-4200-200000000-2220000000000000000000-4400000000000000000000000000002-2000000000
χ784-44-44-24-4224-4-4-4-2404-2-200-4-22-224-42200-200000000-222000000000000000000000004-40000000000000000000000000000-2200000
χ794-44-44-24-4224-4-4-4-2404-2-200-4-22-224-42200-200000000-22200000000000000000000000-4400000000000000000000000000002-200000
χ804-44-4-2442-4-44-4-424-20-2-24002-224-4-222-400-200000000-222000000000000000004-40000000000000000000000000000-2200000000000
χ814-44-4-2442-4-44-4-424-20-2-24002-224-4-222-400-200000000-22200000000000000000-4400000000000000000000000000002-200000000000
χ824-4-4444-2-44-42-224-4-40-24-2002-4-42-22-24200-2000000002-220000000000000000000004-40000000000000000000000000000-220000000
χ834-4-4444-2-44-42-224-4-40-24-2002-4-42-22-24200-2000000002-22000000000000000000000-4400000000000000000000000000002-20000000
χ844-4-444-24-4-22-44-442-404-2-200-4222-2-44-224-4-2000000002-22000000000-22004-40000000000000000000000-22000000000000000000000
χ854-4-444-24-4-22-44-442-404-2-200-4222-2-44-22-44-2000000002-220000000002-200-4400000000000000000000002-2000000000000000000000
χ864-4-44-24424-4-44-4-2-420-2-2400222-442-2-2-44-4-2000000002-220000000004-400-220000000000000000000000-22000000000000000000000
χ874-4-44-24424-4-44-4-2-420-2-2400222-442-2-2-4-44-2000000002-22000000000-44002-200000000000000000000002-2000000000000000000000
χ884-4-44-2-242-22-44-4-2220-21-2002-1-12-22-2124-4100003-300-11-13-33-300000-2200-22000000000000003-30000001-1000000000000000000000
χ894-4-44-2-242-22-44-4-2220-21-2002-1-12-22-2124-410000-3300-11-1-33-3300000-2200-2200000000000000-330000001-1000000000000000000000
χ904-4-44-2-242-22-44-4-2220-21-2002-1-12-22-212-44100003-300-11-13-33-3000002-2002-200000000000000-33000000-11000000000000000000000
χ914-4-44-2-242-22-44-4-2220-21-2002-1-12-22-212-4410000-3300-11-1-33-33000002-2002-2000000000000003-3000000-11000000000000000000000
χ928888-4-4-4-4-4-4-4-4-4-4-4-48222-4-422222222200-1-4-4222222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-4-4-4-4-4-4-4-4-4-82224422222222200-144-2-2-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-48-44-4-8-884440-42-400-4-224444-2-400200000000-2-22000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-44-444-44440222−4i34i32-22-2-2-2-2-2200-1002i3−2i3002i3−2i311-1−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-4-44-444-444402224i3−4i32-22-2-2-2-2-2200-100−2i32i300−2i32i311-1i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ978-88-88-4-4-844-444-8-480-4-42004-442-2-444-2002000000002-2-2000000000000000000000000000000000000000000000000000000000000
χ988-88-8-48-44-8-8-44448-402-4-400-2-44-442-244002000000002-2-2000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-484448-8-84-4-40-42-40042-2-44-44-24002000000002-2-2000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4444-4444-4-4022200-22-22-22-2-2-200-100000000-111−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4444-4444-4-4022200-22-22-22-2-2-200-100000000-1113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000
χ1028-8-888-4-4-8-444-4484-80-4-4200444-224-4-4-200200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-48-448-84-44-4-8402-4-400-2444-4-22-4400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-44-444-44-444022200-2-2-2-22-222-200-100006-6001-11-33-3300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44-444-44-444022200-2-2-2-22-222-200-10000-66001-113-33-300000000000000000000000000000000000000000000000000000000

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