Finite Group Databasebeta

← Group #13020725

Character table — Group #13020725

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222244444444455558888881010101010101010101010101616161616161616161620202020202020202020202020202020203232404040404040808080
order12224444458888101010222288202020204444888888884204040404040404040444444444888888882020888888444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1
χ3111111111111111111111-1-11111111111111111-111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111
χ511111111111111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i1111111111-1iiii−i−i−i−i-1-1-1-1ii−i−i11-1-1ii−i−i-1i−i
χ611111111111111111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii1111111111-1−i−i−i−iiiii-1-1-1-1−i−iii11-1-1−i−iii-1−ii
χ711111111111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−i-1-111−i−iii1−ii
χ811111111111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii-1-111ii−i−i1i−i
χ91111111111-1-1-1-11111111111111111111111111-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1
χ101111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111
χ111111111111-1-1-1-11111111-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111
χ121111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111111-1-1
χ131111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i-11-1-1-1-11111-1−i−i−i−iiiii1111ii−i−i-1-1-1-1ii−i−i1−ii
χ141111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii-11-1-1-1-11111-1iiii−i−i−i−i1111−i−iii-1-1-1-1−i−iii1i−i
χ151111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111ii−i−i1111−i−iii-1i−i
χ161111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−iii1111ii−i−i-1−ii
χ1722222-22-2-2200002222222002-22-22-2-22000000000-200000000-222-2-222-2-20000000000000000000
χ1822222-22-2-2200002222222002-22-22-2-22000000000-200000000-2-2-222-2-2220000000000000000000
χ1922222-22-2-220000222-2-2-2-2002-22-2-222-2000000000-20000000022i2i−2i−2i−2i−2i2i2i0000000000000000000
χ2022222-22-2-220000222-2-2-2-2002-22-2-222-2000000000-2000000002−2i−2i2i2i2i2i−2i−2i0000000000000000000
χ212222-22-22-220000222222200-22-22-222-2222222220-200000000-2000000000000-2-2-2-200000000000
χ222222-22-22-220000222222200-22-22-222-2-2-2-2-2-2-2-2-20-200000000-2000000000000222200000000000
χ232222-22-22-220000222-2-2-2-200-22-222-2-222i2i2i2i−2i−2i−2i−2i0-2000000002000000000000−2i−2i2i2i00000000000
χ242222-22-22-220000222-2-2-2-200-22-222-2-22−2i−2i−2i−2i2i2i2i2i0-20000000020000000000002i2i−2i−2i00000000000
χ252222-2-2-2-2222i2i−2i−2i222222200-2-2-2-2-2-2-2-200000000022i2i−2i−2i00002000000002i2i−2i−2i000000000000000
χ262222-2-2-2-2222i2i−2i−2i222-2-2-2-200-2-2-2-2222200000000022i2i−2i−2i0000-200000000−2i−2i2i2i000000000000000
χ272222-2-2-2-222−2i−2i2i2i222222200-2-2-2-2-2-2-2-20000000002−2i−2i2i2i0000200000000−2i−2i2i2i000000000000000
χ282222-2-2-2-222−2i−2i2i2i222-2-2-2-200-2-2-2-222220000000002−2i−2i2i2i0000-2000000002i2i−2i−2i000000000000000
χ2922-2-220-20022−22−22-2-222-2-20020-20200-222−2−222−2−2002−22−200000002-2002-22−22−22−22−200000000000
χ3022-2-220-20022−22−22-2-222-2-20020-20200-2−2−222−2−222002−22−20000000-2200-222−22−2−22−2200000000000
χ3122-2-220-20022−22−22-2-2-2-2220020-20-2002i2i2−i2−i2−i2−i2i2i2002−22−200000002i−2i00−2i2i−22−22i2−i2−i2i200000000000
χ3222-2-220-20022−22−22-2-2-2-2220020-20-2002−i2−i2i2i2i2i2−i2−i2002−22−20000000−2i2i002i−2i−22−22−i2i2i2−i200000000000
χ3322-2-220-2002−22−222-2-222-2-20020-20200-222−2−222−2−200−22−220000000-2200-22−22−222−22−200000000000
χ3422-2-220-2002−22−222-2-222-2-20020-20200-2−2−222−2−22200−22−2200000002-2002-2−22−22−22−2200000000000
χ3522-2-220-2002−22−222-2-2-2-2220020-20-2002i2i2−i2−i2−i2−i2i2i200−22−220000000−2i2i002i−2i2−22−2i2−i2−i2i200000000000
χ3622-2-220-2002−22−222-2-2-2-2220020-20-2002−i2−i2i2i2i2i2−i2−i200−22−2200000002i−2i00−2i2i2−22−2−i2i2i2−i200000000000
χ3722-2-2-202002i2−i2−i2i22-2-222-2-200-2020-200222−2−222−2−200i2−i2−i2i2000002i−2i002i−2i00i2−i2−i2i2−22−2200000000000
χ3822-2-2-202002i2−i2−i2i22-2-222-2-200-2020-2002−2−222−2−22200i2−i2−i2i200000−2i2i00−2i2i00i2−i2−i2i22−22−200000000000
χ3922-2-2-202002i2−i2−i2i22-2-2-2-22200-2020200-2i2i2−i2−i2−i2−i2i2i200i2−i2−i2i200000-22002-200−i2i2i2−i2−i2i2i2−i200000000000
χ4022-2-2-202002i2−i2−i2i22-2-2-2-22200-2020200-2−i2−i2i2i2i2i2−i2−i200i2−i2−i2i2000002-200-2200−i2i2i2−i2i2−i2−i2i200000000000
χ4122-2-2-202002−i2i2i2−i22-2-222-2-200-2020-200222−2−222−2−200−i2i2i2−i200000−2i2i00−2i2i00−i2i2i2−i2−22−2200000000000
χ4222-2-2-202002−i2i2i2−i22-2-222-2-200-2020-2002−2−222−2−22200−i2i2i2−i2000002i−2i002i−2i00−i2i2i2−i22−22−200000000000
χ4322-2-2-202002−i2i2i2−i22-2-2-2-22200-2020200-2i2i2−i2−i2−i2−i2i2i200−i2i2i2−i2000002-200-2200i2−i2−i2i2−i2i2i2−i200000000000
χ4422-2-2-202002−i2i2i2−i22-2-2-2-22200-2020200-2−i2−i2i2i2i2i2−i2−i200−i2i2i2−i200000-22002-200i2−i2−i2i2i2−i2−i2i200000000000
χ452-2-22020-2020000-2-222-2-22i2−i2020-202-202-22-22-22-2000000i2i2−i2−i20000000000000000000i2−i2i2−i2i2−i2000
χ462-2-22020-2020000-2-222-2-22i2−i2020-202-20-22-22-22-22000000i2i2−i2−i20000000000000000000i2−i2−i2i2−i2i2000
χ472-2-22020-2020000-2-222-2-22−i2i2020-202-202-22-22-22-2000000−i2−i2i2i20000000000000000000−i2i2−i2i2−i2i2000
χ482-2-22020-2020000-2-222-2-22−i2i2020-202-20-22-22-22-22000000−i2−i2i2i20000000000000000000−i2i2i2−i2i2−i2000
χ492-2-22020-2020000-2-22-222-2i2−i2020-20-2202i−2i2i−2i−2i2i−2i2i000000i2i2−i2−i20000000000000000000−i2i2−222−2000
χ502-2-22020-2020000-2-22-222-2i2−i2020-20-220−2i2i−2i2i2i−2i2i−2i000000i2i2−i2−i20000000000000000000−i2i22−2−22000
χ512-2-22020-2020000-2-22-222-2−i2i2020-20-2202i−2i2i−2i−2i2i−2i2i000000−i2−i2i2i20000000000000000000i2−i22−2−22000
χ522-2-22020-2020000-2-22-222-2−i2i2020-20-220−2i2i−2i2i2i−2i2i−2i000000−i2−i2i2i20000000000000000000i2−i2−222−2000
χ53444444444-14444-1-1-1000044-1-1-1-10000000000004-1-1-1-1-1-1-1-1-100000000000000000-1-1000000000
χ54444444444-14444-1-1-10000-4-4-1-1-1-1000000000000-4-1-1-1-1-111110000000000000000011000000000
χ55444444444-1-4-4-4-4-1-1-1000044-1-1-1-1000000000000-4-11111-1-1-1-10000000000000000011000000000
χ56444444444-1-4-4-4-4-1-1-10000-4-4-1-1-1-10000000000004-11111111100000000000000000-1-1000000000
χ574444-4-4-4-44-14i4i−4i−4i-1-1-100000011110000000000000-1−i−iiii5−i5i5−i5000000000000000005−5000000000
χ584444-4-4-4-44-14i4i−4i−4i-1-1-100000011110000000000000-1−i−iii−i5i5−i5i500000000000000000−55000000000
χ594444-4-4-4-44-1−4i−4i4i4i-1-1-100000011110000000000000-1ii−i−ii5−i5i5−i500000000000000000−55000000000
χ604444-4-4-4-44-1−4i−4i4i4i-1-1-100000011110000000000000-1ii−i−i−i5i5−i5i5000000000000000005−5000000000
χ614-44-40000040000-44-44-44-4000000000022−22−222222−22−222200000000000000000000000000000000000000
χ624-44-40000040000-44-44-44-40000000000−222222−22−222222−2200000000000000000000000000000000000000
χ634-44-40000040000-44-4-44-4400000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ644-44-40000040000-44-4-44-440000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ654-4-440-404040000-4-444-4-44000-4040-4400000000000000000000000000000000000000000000000
χ664-4-440-404040000-4-44-444-4000-40404-400000000000000000000000000000000000000000000000
χ6788888-88-8-8-20000-2-2-2000000-22-2200000000000002000000000000000000000000000000000000
χ688888-88-88-8-20000-2-2-20000002-22-200000000000002000000000000000000000000000000000000
χ6988-8-880-800-242−4242−42-222000000-202000000000000000−22−2200000000000000000000000000000000
χ7088-8-880-800-2−4242−4242-222000000-2020000000000000002−22−200000000000000000000000000000000
χ7188-8-8-80800-24i2−4i2−4i24i2-22200000020-2000000000000000−i2i2i2−i200000000000000000000000000000000
χ7288-8-8-80800-2−4i24i24i2−4i2-22200000020-2000000000000000i2−i2−i2i200000000000000000000000000000000
χ738-8-88080-80-2000022-200004i2−4i20-202000000000000000000−i2−i2i2i20000000000000000000000000000
χ748-8-88080-80-2000022-20000−4i24i20-202000000000000000000i2i2−i2−i20000000000000000000000000000
χ758-8-880-8080-2000022-2000000020-200000000000000000010−10−10100000000000000000000000000000
χ768-8-880-8080-2000022-2000000020-2000000000000000000−101010−100000000000000000000000000000
χ7716-1616-1600000-400004-44000000000000000000000000000000000000000000000000000000000000

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