Finite Group Databasebeta

← Group #13026527

Character table — Group #13026527

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444488888888888888888816161616161616162020202020202020404040408080808080808080
order12222222510101010101010244444101010102020202020202020101020202020202022222244444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ611111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ711111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ811111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ91111111111111111-111-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1i−ii−ii−ii−i
χ101111111111111111-111-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−ii−ii−ii−ii
χ111111111111111111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-11
χ121111111111111111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-111-1
χ131111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111i−ii−i−ii−ii
χ141111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111−ii−iii−ii−i
χ151111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-11-111-1
χ161111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-11-1-11
χ17222222-2-222222222200-200-2-2-2-20000000022-2-2000022-2-222-2-2000000000000
χ18222222-2-222222222200-200-2-2-2-20000000022-2-20000-2-222-2-222000000000000
χ19222222-2-222222222-200200-2-2-2-200000000-2-222000022-2-2-2-222000000000000
χ20222222-2-222222222-200200-2-2-2-200000000-2-2220000-2-22222-2-2000000000000
χ212-22-22-22-2222-22-2-2-200002i−2i22-2-20000000000002i2i−2i−2i00002-22-22i−2i0000000000
χ222-22-22-22-2222-22-2-2-200002i−2i22-2-20000000000002i2i−2i−2i0000-22-22−2i2i0000000000
χ232-22-22-22-2222-22-2-2-20000−2i2i22-2-2000000000000−2i−2i2i2i00002-22-2−2i2i0000000000
χ242-22-22-22-2222-22-2-2-20000−2i2i22-2-2000000000000−2i−2i2i2i0000-22-222i−2i0000000000
χ252-22-22-2-22222-22-2-2-202i−2i000-2-2222i2i2i2i−2i−2i−2i−2i0000000000002-2-22002i−2i00000000
χ262-22-22-2-22222-22-2-2-202i−2i000-2-2222i2i2i2i−2i−2i−2i−2i000000000000-222-200−2i2i00000000
χ272-22-22-2-22222-22-2-2-20−2i2i000-2-222−2i−2i−2i−2i2i2i2i2i0000000000002-2-2200−2i2i00000000
χ282-22-22-2-22222-22-2-2-20−2i2i000-2-222−2i−2i−2i−2i2i2i2i2i000000000000-222-2002i−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
χ3044444444-1-1-1-1-1-1-1-14-4-44-4-4-1-1-1-111111111-1-1-1-1111100000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-444-4-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-1111111111111-1-1-1-100000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-1400-400111155−5−555−5−5-1-1115−55−500000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-1400-4001111−5−555−5−555-1-111−55−5500000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-400400111155−5−555−5−511-1-1−55−5500000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-4004001111−5−555−5−55511-1-15−55−500000000000000000000
χ374444-4-4004-4-444-4-44000000000000000000000000004-4000000000000000000
χ384444-4-4004-4-444-4-4400000000000000000000000000-44000000000000000000
χ394-44-44-44-4-1-1-11-111100004i−4i-1-111i5i5−i5−i5−i5−i5i5i55−55−5−i−iii00000000000000000000
χ404-44-44-44-4-1-1-11-111100004i−4i-1-111−i5−i5i5i5i5i5−i5−i5−55−55−i−iii00000000000000000000
χ414-44-44-44-4-1-1-11-11110000−4i4i-1-111i5i5−i5−i5−i5−i5i5i5−55−55ii−i−i00000000000000000000
χ424-44-44-44-4-1-1-11-11110000−4i4i-1-111−i5−i5i5i5i5i5−i5−i55−55−5ii−i−i00000000000000000000
χ434-44-44-4-44-1-1-11-111104i−4i00011-1-1−i−i−i−iiiii5−5−55i5−i5−i5i500000000000000000000
χ444-44-44-4-44-1-1-11-111104i−4i00011-1-1−i−i−i−iiiii−555−5−i5i5i5−i500000000000000000000
χ454-44-44-4-44-1-1-11-11110−4i4i00011-1-1iiii−i−i−i−i5−5−55−i5i5i5−i500000000000000000000
χ464-44-44-4-44-1-1-11-11110−4i4i00011-1-1iiii−i−i−i−i−555−5i5−i5−i5i500000000000000000000
χ474-44-4-44004-4-4-4444-400000000000000000000000000004-40000000000000000
χ484-44-4-44004-4-4-4444-40000000000000000000000000000-440000000000000000
χ498888-8-800-222-2-222-200000025−2525−25000000000000000000000000000000000000
χ508888-8-800-222-2-222-2000000−2525−2525000000000000000000000000000000000000
χ5188-8-80000800-8-80080000000000000000000000000000000000000000000000
χ5288-8-80000-225−252225−25-200000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000
χ5388-8-80000-225−252225−25-20000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000
χ5488-8-80000-2−252522−2525-20000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000
χ5588-8-80000-2−252522−2525-200000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000
χ568-88-8-8800-2222-2-2-2200000025−25−2525000000000000000000000000000000000000
χ578-88-8-8800-2222-2-2-22000000−252525−25000000000000000000000000000000000000
χ588-8-8800008008-800-80000000000000000000000000000000000000000000000
χ598-8-880000-225−25-22−252520000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000
χ608-8-880000-225−25-22−2525200000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000
χ618-8-880000-2−2525-2225−25200000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000
χ628-8-880000-2−2525-2225−2520000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000

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