Finite Group Databasebeta

← Group #13020755

Character table — Group #13020755

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122224444455558888888810101010161616161616161616162020202020202020203232404040404040404040404040808080
order12224444451010104444888820202020224442040404040404040404444444442020888888888888488
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111-1-111111111-111111-1-1-1-1111111111-1-111-1-1-1-1-1-11111-1-1-1
χ41111111111111111111-1-111111111-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111
χ511111111111111111-1-11111111111-11-1-1-1-11111111111111-1-1-1-1111111-1-1-1-1-1-1-1
χ611111111111111111-1-11111111111-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111
χ711111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111
χ811111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1
χ91111111111111-1-1-1-111111111-1-1-1-11111111111-1iiii−i−i−i−i11-1-1-1-1ii−i−iii−i−i-1i−i
χ101111111111111-1-1-1-111111111-1-1-1-11111111111-1−i−i−i−iiiii11-1-1-1-1−i−iii−i−iii-1−ii
χ111111111111111-1-1-1-111-1-11111-1-1-1-1-111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-111−i−iiiii−i−i1−ii
χ121111111111111-1-1-1-111-1-11111-1-1-1-1-111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-111ii−i−i−i−iii1i−i
χ131111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1iiii−i−i−i−i-1-111-1-1ii−i−i−i−iii1−ii
χ141111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1−i−i−i−iiiii-1-111-1-1−i−iiiii−i−i1i−i
χ151111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111111−i−iii−i−iii-1i−i
χ161111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111111ii−i−iii−i−i-1−ii
χ1722222-2-22-22222222200002-22-222-2-20-200000000-222-2-222-2-200000000000000000
χ1822222-2-22-22222222200002-22-222-2-20-200000000-2-2-222-2-22200000000000000000
χ1922222-2-22-22222-2-2-2-200002-22-2-2-2220-20000000022i2i−2i−2i−2i−2i2i2i00000000000000000
χ2022222-2-22-22222-2-2-2-200002-22-2-2-2220-2000000002−2i−2i2i2i2i2i−2i−2i00000000000000000
χ212222-222-2-2222222220000-22-22-2-2220-200000000-2000000000000002-22-20000000
χ222222-222-2-2222222220000-22-22-2-2220-200000000-200000000000000-22-220000000
χ232222-222-2-22222-2-2-2-20000-22-2222-2-20-2000000002000000000000002i−2i−2i2i0000000
χ242222-222-2-22222-2-2-2-20000-22-2222-2-20-200000000200000000000000−2i2i2i−2i0000000
χ252222-2-2-2-2222222222002i−2i-2-2-2-2-2-2-2-20200002i2i−2i−2i20000000000002i−2i00000000000
χ262222-2-2-2-222222222200−2i2i-2-2-2-2-2-2-2-2020000−2i−2i2i2i2000000000000−2i2i00000000000
χ272222-2-2-2-222222-2-2-2-2002i−2i-2-2-2-222220200002i2i−2i−2i-2000000000000−2i2i00000000000
χ282222-2-2-2-222222-2-2-2-200−2i2i-2-2-2-22222020000−2i−2i2i2i-20000000000002i−2i00000000000
χ2922-2-2200-2022-2-222-2-22−20020-202-2000022−2−200000002-2002-2002−20000002−22−2000
χ3022-2-2200-2022-2-222-2-22−20020-202-2000022−2−20000000-2200-22002−2000000−22−22000
χ3122-2-2200-2022-2-222-2-2−220020-202-20000−2−22200000002-2002-200−22000000−22−22000
χ3222-2-2200-2022-2-222-2-2−220020-202-20000−2−2220000000-2200-2200−220000002−22−2000
χ3322-2-2200-2022-2-2-2-2222−20020-20-22000022−2−200000002i−2i00−2i2i00−22000000i2−i2−i2i2000
χ3422-2-2200-2022-2-2-2-2222−20020-20-22000022−2−20000000−2i2i002i−2i00−22000000−i2i2i2−i2000
χ3522-2-2200-2022-2-2-2-222−220020-20-220000−2−22200000002i−2i00−2i2i002−2000000−i2i2i2−i2000
χ3622-2-2200-2022-2-2-2-222−220020-20-220000−2−2220000000−2i2i002i−2i002−2000000i2−i2−i2i2000
χ37444444444-1-1-1-100004444-1-1-1-100004-1-1-1-1-1-1-1-1-1000000000-1-1000000000000000
χ38444444444-1-1-1-1000044-4-4-1-1-1-10000-4-1-1-1-1-1111100000000011000000000000000
χ39444444444-1-1-1-10000-4-444-1-1-1-10000-4-11111-1-1-1-100000000011000000000000000
χ40444444444-1-1-1-10000-4-4-4-4-1-1-1-100004-111111111000000000-1-1000000000000000
χ414444-4-4-4-44-1-1-1-10000004i−4i111100000-1i5−i5i5−i5−i−iii0000000005−5000000000000000
χ424444-4-4-4-44-1-1-1-10000004i−4i111100000-1−i5i5−i5i5−i−iii000000000−55000000000000000
χ434444-4-4-4-44-1-1-1-1000000−4i4i111100000-1i5−i5i5−i5ii−i−i000000000−55000000000000000
χ444444-4-4-4-44-1-1-1-1000000−4i4i111100000-1−i5i5−i5i5ii−i−i0000000005−5000000000000000
χ4544-4-4-4004044-4-444-4-40000-4040-4400000000000000000000000000000000000000
χ4644-4-4-4004044-4-4-4-4440000-40404-400000000000000000000000000000000000000
χ474-44-4000004-4-444i−4i4i−4i000000000000000000000002+2i−2−2i002−2i−2+2i0000000000000000000
χ484-44-4000004-4-444i−4i4i−4i00000000000000000000000−2−2i2+2i00−2+2i2−2i0000000000000000000
χ494-44-4000004-4-44−4i4i−4i4i000000000000000000000002−2i−2+2i002+2i−2−2i0000000000000000000
χ504-44-4000004-4-44−4i4i−4i4i00000000000000000000000−2+2i2−2i00−2−2i2+2i0000000000000000000
χ514-4-4404-4004-44-44i−4i−4i4i00000-404004i−4i000000000000000000000000000000000000
χ524-4-4404-4004-44-4−4i4i4i−4i00000-40400−4i4i000000000000000000000000000000000000
χ534-4-440-44004-44-44i−4i−4i4i0000040-400−4i4i000000000000000000000000000000000000
χ544-4-440-44004-44-4−4i4i4i−4i0000040-4004i−4i000000000000000000000000000000000000
χ5588888-8-88-8-2-2-2-200000000-22-220000020000000000000000000000000000000000
χ568888-888-8-8-2-2-2-2000000002-22-20000020000000000000000000000000000000000
χ5788-8-8800-80-2-222000042−4200-2020000000−2−222000000000000000000000000000000
χ5888-8-8800-80-2-2220000−424200-202000000022−2−2000000000000000000000000000000
χ5988-8-8-80080-2-2220000000020-20000000i10−i10−i10i10000000000000000000000000000000
χ6088-8-8-80080-2-2220000000020-20000000−i10i10i10−i10000000000000000000000000000000
χ618-8-8808-800-22-2200000000020-20000000000i10−i10i10−i1000000000000000000000000000
χ628-8-8808-800-22-2200000000020-20000000000−i10i10−i10i1000000000000000000000000000
χ638-8-880-8800-22-22000000000-202000000000010−10−101000000000000000000000000000
χ648-8-880-8800-22-22000000000-2020000000000−101010−1000000000000000000000000000
χ6516-1616-1600000-444-40000000000000000000000000000000000000000000000000000

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