Finite Group Databasebeta

← Group #13026542

Character table — Group #13026542

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444488888888888888888816161616161616162020202020202020404040408080808080808080
order12222244510101010101010444444202020202020202020202020202020202020202022222244444444444444
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
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ91111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1i−ii−ii−ii−i
χ101111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1−ii−ii−ii−ii
χ111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111-11-1-11-11
χ121111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-11-111-11-1
χ131111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111i−i−iii−i−ii
χ141111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−iii−i−iii−i
χ151111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1-11-111-1
χ161111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-11-1-11
χ17222222-2-2222222222-2000000000000-2-2-2-2000022-2-22222-2-2-2-2000000000000
χ18222222-2-2222222222-2000000000000-2-2-2-2000022-2-2-2-2-2-22222000000000000
χ19222222-2-222222222-22000000000000-2-2-2-20000-2-22222-2-222-2-2000000000000
χ20222222-2-222222222-22000000000000-2-2-2-20000-2-222-2-222-2-222000000000000
χ212-22-22-22-2222-2-2-2-2200002i−2i2i2i2i2i−2i−2i−2i−2i22-2-200000000002-22-2002i−2i0000000000
χ222-22-22-22-2222-2-2-2-2200002i−2i2i2i2i2i−2i−2i−2i−2i22-2-20000000000-22-2200−2i2i0000000000
χ232-22-22-22-2222-2-2-2-220000−2i2i−2i−2i−2i−2i2i2i2i2i22-2-200000000002-22-200−2i2i0000000000
χ242-22-22-22-2222-2-2-2-220000−2i2i−2i−2i−2i−2i2i2i2i2i22-2-20000000000-22-22002i−2i0000000000
χ252-22-22-2-22222-2-2-2-22002i−2i0000000000-2-2222i2i−2i−2i0000002-2-2200002i−2i00000000
χ262-22-22-2-22222-2-2-2-22002i−2i0000000000-2-2222i2i−2i−2i000000-222-20000−2i2i00000000
χ272-22-22-2-22222-2-2-2-2200−2i2i0000000000-2-222−2i−2i2i2i0000002-2-220000−2i2i00000000
χ282-22-22-2-22222-2-2-2-2200−2i2i0000000000-2-222−2i−2i2i2i000000-222-200002i−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
χ3044444444-1-1-1-1-1-1-1-144-4-4-4-411111111-1-1-1-11111-1-1-1-100000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-444-4-411111111-1-1-1-1-1-1-1-1111100000000000000000000
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
χ33444444-4-4-1-1-1-1-1-1-1-14-4000055−5−555−5−511115−55−5-1-11100000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-40000−5−555−5−5551111−55−55-1-11100000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-44000055−5−555−5−51111−55−5511-1-100000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-440000−5−555−5−55511115−55−511-1-100000000000000000000
χ374444-4-4004-4-44-4-444000000000000000000000000000000004-4000000000000
χ384444-4-4004-4-44-4-44400000000000000000000000000000000-44000000000000
χ394-44-44-44-4-1-1-11111-100004i−4i−i−i−i−iiiii-1-111i5−i5−i5i55−55−500000000000000000000
χ404-44-44-44-4-1-1-11111-100004i−4i−i−i−i−iiiii-1-111−i5i5i5−i5−55−5500000000000000000000
χ414-44-44-44-4-1-1-11111-10000−4i4iiiii−i−i−i−i-1-111i5−i5−i5i5−55−5500000000000000000000
χ424-44-44-44-4-1-1-11111-10000−4i4iiiii−i−i−i−i-1-111−i5i5i5−i55−55−500000000000000000000
χ434-44-44-4-44-1-1-11111-1004i−4i00i5i5−i5−i5−i5−i5i5i511-1-1−i−iii5−5−5500000000000000000000
χ444-44-44-4-44-1-1-11111-1004i−4i00−i5−i5i5i5i5i5−i5−i511-1-1−i−iii−555−500000000000000000000
χ454-44-44-4-44-1-1-11111-100−4i4i00i5i5−i5−i5−i5−i5i5i511-1-1ii−i−i−555−500000000000000000000
χ464-44-44-4-44-1-1-11111-100−4i4i00−i5−i5i5i5i5i5−i5−i511-1-1ii−i−i5−5−5500000000000000000000
χ474-44-4-44004-4-4-444-44000000000000000000000000004-4000000000000000000
χ484-44-4-44004-4-4-444-4400000000000000000000000000-44000000000000000000
χ498888-8-800-222-222-2-20000000000000025−2525−250000000000000000000000000000
χ508888-8-800-222-222-2-200000000000000−2525−25250000000000000000000000000000
χ5188-8-80000800800-8-80000000000000000000000000000000000000000000000
χ5288-8-80000-225−25-225−25220000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000
χ5388-8-80000-225−25-225−2522000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000
χ5488-8-80000-2−2525-2−252522000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000
χ5588-8-80000-2−2525-2−2525220000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000
χ568-88-8-8800-2222-2-22-20000000000000025−25−25250000000000000000000000000000
χ578-88-8-8800-2222-2-22-200000000000000−252525−250000000000000000000000000000
χ588-8-880000800-8008-80000000000000000000000000000000000000000000000
χ598-8-880000-225−252−2525-22000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000000000
χ608-8-880000-225−252−2525-220000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000000000
χ618-8-880000-2−2525225−25-220000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000000000
χ628-8-880000-2−2525225−25-22000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000000000

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