Finite Group Databasebeta

← Group #13041362

Character table — Group #13041362

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222244444444444555588888881010101010101010101010101010101010101010161616161616161616202020202020202020202020202020202020203232404040404040404040
order12224444444588881010102222444202020204444444444448888888820202020204040404044444444444888888882020444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1
χ31111111111111111111-1-1-1-11111111-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i111111111-1-1-1ii−i−iii−i−i-1-1-1-1ii−i−i11-1-1-1i−iii−i−i
χ41111111111111111111-1-1-1-11111111-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111111111-1-1-1−i−iii−i−iii-1-1-1-1−i−iii11-1-1-1−ii−i−iii
χ5111111111111-1-1-1-111111111-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ6111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11-1-111-1-1-1-1
χ7111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii11111-1-1-1-1-1-1-1−i−iiiii−i−i1111−i−iii-1-1-111−iiii−i−i
χ8111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i11111-1-1-1-1-1-1-1ii−i−i−i−iii1111ii−i−i-1-1-111i−i−i−iii
χ9111111111-1-1111111111111-1-1-11111111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1
χ10111111111-1-1111111111111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111
χ11111111111-1-111111111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i1-1-1-1-11111-111−i−iiiii−i−i-1-1-1-1ii−i−i-1-1111−ii−i−iii
χ12111111111-1-111111111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii1-1-1-1-11111-111ii−i−i−i−iii-1-1-1-1−i−iii-1-1111i−iii−i−i
χ13111111111-1-11-1-1-1-11111111-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-111-11111-1-1-1-1
χ14111111111-1-11-1-1-1-11111111-111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-11111
χ15111111111-1-11-1-1-1-1111-1-1-1-1-1111111-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii1-1-1-1-1-1-1-1-1-111ii−i−iii−i−i1111−i−iii111-1-1i−i−i−iii
χ16111111111-1-11-1-1-1-1111-1-1-1-1-1111111-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i1-1-1-1-1-1-1-1-1-111−i−iii−i−iii1111ii−i−i111-1-1−iiii−i−i
χ1711111-1-11-111111-1-11111111-11-11-1-11-1-111-1-111-1-11111111111-111-1-111-1-1-11111111-11-111-1-1-1-1-1-11-1-11-1-1-11-11-1
χ1811111-1-11-111111-1-11111111-11-11-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-1-1-1-11-1111-1-111111-1-11-111-11-11
χ1911111-1-11-111111-1-1111-1-1-1-1-11-11-1-1111ii−i−i−i−iii-1-1iiii−i−i−i−i-111-1-111-1-11-1-1ii−i−ii−i−ii-1-111−i−iii1-11-11−iii−i−ii
χ2011111-1-11-111111-1-1111-1-1-1-1-11-11-1-1111−i−iiiii−i−i-1-1−i−i−i−iiiii-111-1-111-1-11-1-1−i−iii−iii−i-1-111ii−i−i1-11-11i−i−iii−i
χ2111111-1-11-1111-1-1111111111-1-111-1-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-111-1-1-1-11-11-1-1-1111111-11-1-11111-11-1
χ2211111-1-11-1111-1-1111111111-1-111-1-11-1-1-1-111-1-1111111111111-111-1-1-1-111-1111111-11-11-1-111-1-1-1-1-11-1-11-1-1-11-11
χ2311111-1-11-1111-1-111111-1-1-1-1-1-111-1-1111ii−i−i−i−iii-1-1−i−i−i−iiiii-111-1-1-1-1111-1-1−i−iiii−i−ii11-1-1ii−i−i-1111-1i−ii−i−ii
χ2411111-1-11-1111-1-111111-1-1-1-1-1-111-1-1111−i−iiiii−i−i-1-1iiii−i−i−i−i-111-1-1-1-1111-1-1ii−i−i−iii−i11-1-1−i−iii-1111-1−ii−iii−i
χ2511111-1-11-1-1-1111-1-111111111-111-1-11-1-111-1-111-1-11111111111-1-1-11111-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-111-1111-11-11
χ2611111-1-11-1-1-1111-1-111111111-111-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-11-1111-1-11111-111-11-1-11-11-1
χ2711111-1-11-1-1-1111-1-1111-1-1-1-11-111-1-1111ii−i−i−i−iii-1-1iiii−i−i−i−i-1-1-11111-1-1111−i−iiii−i−ii-1-111−i−iii-11-11-1i−i−iii−i
χ2811111-1-11-1-1-1111-1-1111-1-1-1-11-111-1-1111−i−iiiii−i−i-1-1−i−i−i−iiiii-1-1-11111-1-1111ii−i−i−iii−i-1-111ii−i−i-11-11-1−iii−i−ii
χ2911111-1-11-1-1-11-1-111111111111-11-1-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111111-11-1-1-11111111-111-1-1-1-11-11
χ3011111-1-11-1-1-11-1-111111111111-11-1-11-1-1-1-111-1-1111111111111-1-1-111-1-111-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11-111-1111-11-1
χ3111111-1-11-1-1-11-1-111111-1-1-1-111-11-1-1111ii−i−i−i−iii-1-1−i−i−i−iiiii-1-1-111-1-111111ii−i−ii−i−ii11-1-1ii−i−i1-1-1-11−ii−iii−i
χ3211111-1-11-1-1-11-1-111111-1-1-1-111-11-1-1111−i−iiiii−i−i-1-1iiii−i−i−i−i-1-1-111-1-111111−i−iii−iii−i11-1-1−i−iii1-1-1-11i−ii−i−ii
χ332222-222-2-200200002222222000-222-22222222222-2-200000000-200000000-2000000-2-2-2-20000000000000000000
χ342222-222-2-200200002222222000-222-222-2-2-2-2-2-2-2-2-2-200000000-200000000-200000022220000000000000000000
χ352222-222-2-20020000222-2-2-2-2000-222-2-2-22i2i2i2i−2i−2i−2i−2i2200000000-2000000002000000−2i−2i2i2i0000000000000000000
χ362222-222-2-20020000222-2-2-2-2000-222-2-2-2−2i−2i−2i−2i2i2i2i2i2200000000-20000000020000002i2i−2i−2i0000000000000000000
χ372222-2-2-2-2200200002222222000-2-2-2-2-2-222-2-222-2-2-2-2000000002000000002000000-22-220000000000000000000
χ382222-2-2-2-2200200002222222000-2-2-2-2-2-2-2-222-2-222-2-20000000020000000020000002-22-20000000000000000000
χ392222-2-2-2-220020000222-2-2-2-2000-2-2-2-2222i2i−2i−2i−2i−2i2i2i2200000000200000000-2000000−2i2i2i−2i0000000000000000000
χ402222-2-2-2-220020000222-2-2-2-2000-2-2-2-222−2i−2i2i2i2i2i−2i−2i2200000000200000000-20000002i−2i−2i2i0000000000000000000
χ4122-2-2200-202-2200002-2-222-2-2000200-200000000002-222-2-222-2-202-200000002-22-22-200000000000000000000000
χ4222-2-2200-202-2200002-2-222-2-2000200-200000000002-2-2-222-2-22202-200000002-2-22-2200000000000000000000000
χ4322-2-2200-202-2200002-2-2-2-222000200-20000000000-222i2i−2i−2i−2i−2i2i2i02-20000000-222i−2i−2i2i00000000000000000000000
χ4422-2-2200-202-2200002-2-2-2-222000200-20000000000-22−2i−2i2i2i2i2i−2i−2i02-20000000-22−2i2i2i−2i00000000000000000000000
χ4522-2-2200-20-22200002-2-222-2-2000200-200000000002-222-2-222-2-20-220000000-22-22-2200000000000000000000000
χ4622-2-2200-20-22200002-2-222-2-2000200-200000000002-2-2-222-2-2220-220000000-222-22-200000000000000000000000
χ4722-2-2200-20-22200002-2-2-2-222000200-20000000000-222i2i−2i−2i−2i−2i2i2i0-2200000002-2−2i2i2i−2i00000000000000000000000
χ4822-2-2200-20-22200002-2-2-2-222000200-20000000000-22−2i−2i2i2i2i2i−2i−2i0-2200000002-22i−2i−2i2i00000000000000000000000
χ492-2-2202-200002i2−i2i2−i2-2-222-2-2200002-202-22i−2i2i−2i2i−2i2i−2i002−22−22−22−200000i2−i2i2−i200000000000i2−i2i2−i22−22−200000000000
χ502-2-2202-200002i2−i2i2−i2-2-222-2-2200002-202-2−2i2i−2i2i−2i2i−2i2i00−22−22−22−2200000i2−i2i2−i200000000000i2−i2i2−i2−22−2200000000000
χ512-2-2202-200002i2−i2i2−i2-2-22-222-200002-20-222-22-2-22-2200−i2i2−i2i2i2−i2i2−i200000i2−i2i2−i200000000000−i2i2−i2i2−i2i2i2−i200000000000
χ522-2-2202-200002i2−i2i2−i2-2-22-222-200002-20-22-22-222-22-200i2−i2i2−i2−i2i2−i2i200000i2−i2i2−i200000000000−i2i2−i2i2i2−i2−i2i200000000000
χ532-2-2202-200002−i2i2−i2i2-2-222-2-2200002-202-22i−2i2i−2i2i−2i2i−2i00−22−22−22−2200000−i2i2−i2i200000000000−i2i2−i2i2−22−2200000000000
χ542-2-2202-200002−i2i2−i2i2-2-222-2-2200002-202-2−2i2i−2i2i−2i2i−2i2i002−22−22−22−200000−i2i2−i2i200000000000−i2i2−i2i22−22−200000000000
χ552-2-2202-200002−i2i2−i2i2-2-22-222-200002-20-222-22-2-22-2200i2−i2i2−i2−i2i2−i2i200000−i2i2−i2i200000000000i2−i2i2−i2i2−i2−i2i200000000000
χ562-2-2202-200002−i2i2−i2i2-2-22-222-200002-20-22-22-222-22-200−i2i2−i2i2i2−i2i2−i200000−i2i2−i2i200000000000i2−i2i2−i2−i2i2i2−i200000000000
χ572-2-220-2200002i2−i2−i2i2-2-222-2-220000-220-222i−2i−2i2i2i−2i−2i2i002−22−22−22−200000i2−i2−i2i200000000000i2−i2−i2i2−22−2200000000000
χ582-2-220-2200002i2−i2−i2i2-2-222-2-220000-220-22−2i2i2i−2i−2i2i2i−2i00−22−22−22−2200000i2−i2−i2i200000000000i2−i2−i2i22−22−200000000000
χ592-2-220-2200002i2−i2−i2i2-2-22-222-20000-2202-22-2-22-222-200−i2i2−i2i2i2−i2i2−i200000i2−i2−i2i200000000000−i2i2i2−i2i2−i2−i2i200000000000
χ602-2-220-2200002i2−i2−i2i2-2-22-222-20000-2202-2-222-22-2-2200i2−i2i2−i2−i2i2−i2i200000i2−i2−i2i200000000000−i2i2i2−i2−i2i2i2−i200000000000
χ612-2-220-2200002−i2i2i2−i2-2-222-2-220000-220-222i−2i−2i2i2i−2i−2i2i00−22−22−22−2200000−i2i2i2−i200000000000−i2i2i2−i22−22−200000000000
χ622-2-220-2200002−i2i2i2−i2-2-222-2-220000-220-22−2i2i2i−2i−2i2i2i−2i002−22−22−22−200000−i2i2i2−i200000000000−i2i2i2−i2−22−2200000000000
χ632-2-220-2200002−i2i2i2−i2-2-22-222-20000-2202-22-2-22-222-200i2−i2i2−i2−i2i2−i2i200000−i2i2i2−i200000000000i2−i2−i2i2−i2i2i2−i200000000000
χ642-2-220-2200002−i2i2i2−i2-2-22-222-20000-2202-2-222-22-2-2200−i2i2−i2i2i2−i2i2−i200000−i2i2i2−i200000000000i2−i2−i2i2i2−i2−i2i200000000000
χ6544444444444-14444-1-1-10000444-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1-10000000000000000000-1-1000000000
χ6644444444444-1-4-4-4-4-1-1-100004-4-4-1-1-1-100000000000000000000-1-1-1-1-11111000000000000000000011000000000
χ67444444444-4-4-14444-1-1-10000-4-4-4-1-1-1-100000000000000000000-11111-1-1-1-1000000000000000000011000000000
χ68444444444-4-4-1-4-4-4-4-1-1-10000-444-1-1-1-100000000000000000000-1111111110000000000000000000-1-1000000000
χ6944444-4-44-444-144-4-4-1-1-10000-44-4-111-1000000000000000000001-1-111-1-1110000000000000000000-11000000000
χ7044444-4-44-444-1-4-444-1-1-10000-4-44-111-1000000000000000000001-1-11111-1-100000000000000000001-1000000000
χ7144444-4-44-4-4-4-144-4-4-1-1-100004-44-111-100000000000000000000111-1-1-1-11100000000000000000001-1000000000
χ7244444-4-44-4-4-4-1-4-444-1-1-1000044-4-111-100000000000000000000111-1-111-1-10000000000000000000-11000000000
χ7344-4-4-4004000400004-4-444-4-4000-40040000000000-4400000000000000000000000000000000000000000000000
χ7444-4-4-4004000400004-4-4-4-444000-400400000000004-400000000000000000000000000000000000000000000000
χ754-44-4000000040000-44-44-44-4000000000000000000022−22−222222−22−2222000000000000000000000000000000000000000
χ764-44-4000000040000-44-44-44-40000000000000000000−222222−22−222222−22000000000000000000000000000000000000000
χ774-44-4000000040000-44-4-44-4400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ784-44-4000000040000-44-4-44-440000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ798888-888-8-800-20000-2-2-200000002-2-2200000000000000000000200000000000000000000000000000000000000
χ808888-8-8-8-8800-20000-2-2-20000000222200000000000000000000-200000000000000000000000000000000000000
χ8188-8-8800-808-8-20000-2220000000-2002000000000000000000000-22000000000000000000000000000000000000
χ8288-8-8800-80-88-20000-2220000000-20020000000000000000000002-2000000000000000000000000000000000000
χ8388-8-8-8008000-20000-2220000000200-2000000000000000000000002i5−2i50000000000000000000000000000000000
χ8488-8-8-8008000-20000-2220000000200-200000000000000000000000−2i52i50000000000000000000000000000000000
χ858-8-8808-80000-24i2−4i24i2−4i222-200000000-2200000000000000000000000000−i2i2−i2i2000000000000000000000000000000
χ868-8-8808-80000-2−4i24i2−4i24i222-200000000-2200000000000000000000000000i2−i2i2−i2000000000000000000000000000000
χ878-8-880-880000-24i2−4i2−4i24i222-2000000002-200000000000000000000000000−i2i2i2−i2000000000000000000000000000000
χ888-8-880-880000-2−4i24i24i2−4i222-2000000002-200000000000000000000000000i2−i2−i2i2000000000000000000000000000000
χ8916-1616-160000000-400004-440000000000000000000000000000000000000000000000000000000000000000000000

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