Finite Group Databasebeta

← Group #13026417

Character table — Group #13026417

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444488888888888888888816161616161616162020202020202020404040408080808080808080
order12222244510101010101010444444202020202020202020202020202020202020202044444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ91111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1i−ii−ii−ii−i
χ101111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1−ii−ii−ii−ii
χ111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1-11-11
χ121111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-111-11-1
χ131111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111i−i−iii−i−ii
χ141111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−iii−i−iii−i
χ151111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11-111-1
χ161111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-11-1-11
χ17222222-2-2222222222-20000-2-2-2-20000000022-2-2000022-2-22-22-2000000000000
χ18222222-2-2222222222-20000-2-2-2-20000000022-2-20000-2-222-22-22000000000000
χ19222222-2-222222222-220000-2-2-2-200000000-2-222000022-2-2-22-22000000000000
χ20222222-2-222222222-220000-2-2-2-200000000-2-2220000-2-2222-22-2000000000000
χ212-2-222-22-22-2-2222-2-200002-222-2-22222-2-2-2-200000000000022-2-22-20000000000
χ222-2-222-22-22-2-2222-2-200002-222-2-22222-2-2-2-2000000000000-2-222-220000000000
χ232-2-222-22-22-2-2222-2-20000-2222-2-2-2-2-2-2222200000000000022-2-2-220000000000
χ242-2-222-22-22-2-2222-2-20000-2222-2-2-2-2-2-22222000000000000-2-2222-20000000000
χ252-2-222-2-222-2-2222-2-2002i−2i00-2-2220000000000002i2i−2i−2i00002-2-22002i−2i00000000
χ262-2-222-2-222-2-2222-2-2002i−2i00-2-2220000000000002i2i−2i−2i0000-222-200−2i2i00000000
χ272-2-222-2-222-2-2222-2-200−2i2i00-2-222000000000000−2i−2i2i2i00002-2-2200−2i2i00000000
χ282-2-222-2-222-2-2222-2-200−2i2i00-2-222000000000000−2i−2i2i2i0000-222-2002i−2i00000000
χ2944444444-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ3044444444-1-1-1-1-1-1-1-144-4-4-4-4-1-1-1-111111111-1-1-1-1111100000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-1111111111111-1-1-1-100000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-14-40000111155−5−555−5−5-1-1115−55−500000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-400001111−5−555−5−555-1-111−55−5500000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-440000111155−5−555−5−511-1-1−55−5500000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-4400001111−5−555−5−55511-1-15−55−500000000000000000000
χ374444-4-4004-4-44-4-44400000000000000000000000000004-40000000000000000
χ384444-4-4004-4-44-4-4440000000000000000000000000000-440000000000000000
χ394-4-444-44-4-111-1-1-11100004-4-1-111-1-1-1-11111i5−i5i5−i5i5−i5−i5i500000000000000000000
χ404-4-444-44-4-111-1-1-11100004-4-1-111-1-1-1-11111−i5i5−i5i5−i5i5i5−i500000000000000000000
χ414-4-444-44-4-111-1-1-1110000-44-1-1111111-1-1-1-1i5−i5i5−i5−i5i5i5−i500000000000000000000
χ424-4-444-44-4-111-1-1-1110000-44-1-1111111-1-1-1-1−i5i5−i5i5i5−i5−i5i500000000000000000000
χ434-4-444-4-44-111-1-1-111004i−4i0011-1-155−5−5−5−555i5−i5−i5i5−i−iii00000000000000000000
χ444-4-444-4-44-111-1-1-111004i−4i0011-1-1−5−55555−5−5−i5i5i5−i5−i−iii00000000000000000000
χ454-4-444-4-44-111-1-1-11100−4i4i0011-1-155−5−5−5−555−i5i5i5−i5ii−i−i00000000000000000000
χ464-4-444-4-44-111-1-1-11100−4i4i0011-1-1−5−55555−5−5i5−i5−i5i5ii−i−i00000000000000000000
χ474-4-44-44004444-4-4-4-4000000000000000000000000004i−4i000000000000000000
χ484-4-44-44004444-4-4-4-400000000000000000000000000−4i4i000000000000000000
χ498888-8-800-222-222-2-200000025−2525−25000000000000000000000000000000000000
χ508888-8-800-222-222-2-2000000−2525−2525000000000000000000000000000000000000
χ5188-8-80000800-8008-80000000000000000000000000000000000000000000000
χ5288-8-80000-225−25225−25-2200000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000
χ5388-8-80000-225−25225−25-220000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000
χ5488-8-80000-2−25252−2525-220000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000
χ5588-8-80000-2−25252−2525-2200000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000
χ568-88-80000800-800-880000000000000000000000000000000000000000000000
χ578-88-80000-225−252−25252-20000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000
χ588-88-80000-225−252−25252-200000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000
χ598-88-80000-2−2525225−252-200000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000
χ608-88-80000-2−2525225−252-20000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000
χ618-8-88-8800-2-2-2-2222200000025−25−2525000000000000000000000000000000000000
χ628-8-88-8800-2-2-2-22222000000−252525−25000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.