Finite Group Databasebeta

← Group #13022347

Character table — Group #13022347

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222224444444444448888888888888888101010101010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12222244444444510101010101010224420202020202020202020202022224444101010102020202044448888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111−i−i−i−iiiii
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111iiii−i−i−i−i
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ131111111111-1-1-1-111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ141111111111-1-1-1-111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ151111111111-1-1-1-111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ161111111111-1-1-1-111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ171-11-11-111-1-1ii−i−i111-11-1-1-11-1i−i11-1-1iiii−i−i−i−i1-11-11-11-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ181-11-11-111-1-1ii−i−i111-11-1-1-11-1i−i11-1-1iiii−i−i−i−i1-11-11-11-111-1-1ii−i−iii−i−i-1-111−i−iii-1-111−i−iii1-1i−i-11−ii-11−ii
χ191-11-11-111-1-1ii−i−i111-11-1-1-11-1i−i11-1-1iiii−i−i−i−i-11-11-11-1111-1-1ii−i−i−i−iiiii−i−i-1-111−i−iii11-1-1-11−iii−i-11−ii1-1
χ201-11-11-111-1-1ii−i−i111-11-1-1-11-1i−i11-1-1iiii−i−i−i−i-11-11-11-1111-1-1ii−i−i−i−iii−i−iii11-1-1ii−i−i-1-111-11−ii−ii1-1i−i-11
χ211-11-11-111-1-1ii−i−i111-11-1-1-1-11−ii11-1-1−i−i−i−iiiii1-11-11-11-1-1-111ii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii
χ221-11-11-111-1-1ii−i−i111-11-1-1-1-11−ii11-1-1−i−i−i−iiiii1-11-11-11-1-1-111ii−i−iii−i−i-1-111−i−iii-1-111−i−iii-11−ii1-1i−i1-1i−i
χ231-11-11-111-1-1ii−i−i111-11-1-1-1-11−ii11-1-1−i−i−i−iiiii-11-11-11-11-1-111ii−i−i−i−iiiii−i−i-1-111−i−iii11-1-11-1i−i−ii1-1i−i-11
χ241-11-11-111-1-1ii−i−i111-11-1-1-1-11−ii11-1-1−i−i−i−iiiii-11-11-11-11-1-111ii−i−i−i−iii−i−iii11-1-1ii−i−i-1-1111-1i−ii−i-11−ii1-1
χ251-11-11-111-1-1−i−iii111-11-1-1-11-1−ii11-1-1−i−i−i−iiiii1-11-11-11-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ261-11-11-111-1-1−i−iii111-11-1-1-11-1−ii11-1-1−i−i−i−iiiii1-11-11-11-111-1-1−i−iii−i−iii-1-111ii−i−i-1-111ii−i−i1-1−ii-11i−i-11i−i
χ271-11-11-111-1-1−i−iii111-11-1-1-11-1−ii11-1-1−i−i−i−iiiii-11-11-11-1111-1-1−i−iiiii−i−iii−i−i11-1-1−i−iii-1-111-11i−ii−i1-1−ii-11
χ281-11-11-111-1-1−i−iii111-11-1-1-11-1−ii11-1-1−i−i−i−iiiii-11-11-11-1111-1-1−i−iiiii−i−i−i−iii-1-111ii−i−i11-1-1-11i−i−ii-11i−i1-1
χ291-11-11-111-1-1−i−iii111-11-1-1-1-11i−i11-1-1iiii−i−i−i−i1-11-11-11-1-1-111−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i
χ301-11-11-111-1-1−i−iii111-11-1-1-1-11i−i11-1-1iiii−i−i−i−i1-11-11-11-1-1-111−i−iii−i−iii-1-111ii−i−i-1-111ii−i−i-11i−i1-1−ii1-1−ii
χ311-11-11-111-1-1−i−iii111-11-1-1-1-11i−i11-1-1iiii−i−i−i−i-11-11-11-11-1-111−i−iiiii−i−iii−i−i11-1-1−i−iii-1-1111-1−ii−ii-11i−i1-1
χ321-11-11-111-1-1−i−iii111-11-1-1-1-11i−i11-1-1iiii−i−i−i−i-11-11-11-11-1-111−i−iiiii−i−i−i−iii-1-111ii−i−i11-1-11-1−iii−i1-1−ii-11
χ33222222-2-2-2-22-22-2222222220000-2-2-2-2000000002222-2-2-2-200002-22-22-22-20000000000000000000000000000
χ34222222-2-2-2-22-22-2222222220000-2-2-2-200000000-2-2-2-2222200002-22-2-22-220000000000000000000000000000
χ35222222-2-2-2-2-22-22222222220000-2-2-2-2000000002222-2-2-2-20000-22-22-22-220000000000000000000000000000
χ36222222-2-2-2-2-22-22222222220000-2-2-2-200000000-2-2-2-222220000-22-222-22-20000000000000000000000000000
χ372222-2-22-22-200002-2-222-2-2200002-22-2000000002-2-2222-2-20000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ382222-2-22-22-200002-2-222-2-2200002-22-2000000002-2-2222-2-2000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ392222-2-22-22-200002-2-222-2-2200002-22-200000000-222-2-2-2220000000000002-22-20000-22-220000000000000000
χ402222-2-22-22-200002-2-222-2-2200002-22-200000000-222-2-2-222000000000000-22-2200002-22-20000000000000000
χ412222-2-2-22-2200002-2-222-2-220000-22-22000000002-2-22-2-22200000000000000002-22-200002-22-2000000000000
χ422222-2-2-22-2200002-2-222-2-220000-22-22000000002-2-22-2-2220000000000000000-22-220000-22-22000000000000
χ432222-2-2-22-2200002-2-222-2-220000-22-2200000000-222-222-2-200000000000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ442222-2-2-22-2200002-2-222-2-220000-22-2200000000-222-222-2-20000000000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ452-22-22-2-2-2222i−2i−2i2i222-22-2-2-20000-2-222000000002-22-2-22-2200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ462-22-22-2-2-2222i−2i−2i2i222-22-2-2-20000-2-22200000000-22-222-22-200002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ472-22-22-2-2-222−2i2i2i−2i222-22-2-2-20000-2-222000000002-22-2-22-220000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ482-22-22-2-2-222−2i2i2i−2i222-22-2-2-20000-2-22200000000-22-222-22-20000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ492-22-2-222-2-2200002-2-2-2222-200002-2-220000000022-2-22-2-220000000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ502-22-2-222-2-2200002-2-2-2222-200002-2-220000000022-2-22-2-22000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ512-22-2-222-2-2200002-2-2-2222-200002-2-2200000000-2-222-222-20000000000002-2-220000-222-20000000000000000
χ522-22-2-222-2-2200002-2-2-2222-200002-2-2200000000-2-222-222-2000000000000-222-200002-2-220000000000000000
χ532-22-2-22-222-200002-2-2-2222-20000-222-20000000022-2-2-222-200000000000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ542-22-2-22-222-200002-2-2-2222-20000-222-20000000022-2-2-222-20000000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ552-22-2-22-222-200002-2-2-2222-20000-222-200000000-2-2222-2-2200000000000000002-2-220000-222-2000000000000
χ562-22-2-22-222-200002-2-2-2222-20000-222-200000000-2-2222-2-220000000000000000-222-200002-2-22000000000000
χ5744444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ5844444444444444-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-111111111000000001111-1-1-1-100000000000000000000000000000000
χ594444444444-4-4-4-4-1-1-1-1-1-1-1-144-4-4-1-1-1-11111111100000000-1-1-1-1111100000000000000000000000000000000
χ604444444444-4-4-4-4-1-1-1-1-1-1-1-1-4-444-1-1-1-1-1-1-1-1-1-1-1-1000000001111111100000000000000000000000000000000
χ61444444-4-4-4-44-44-4-1-1-1-1-1-1-1-10000111155−5−555−5−5000000005−55−5-11-1100000000000000000000000000000000
χ62444444-4-4-4-44-44-4-1-1-1-1-1-1-1-100001111−5−555−5−55500000000−55−55-11-1100000000000000000000000000000000
χ63444444-4-4-4-4-44-44-1-1-1-1-1-1-1-10000111155−5−555−5−500000000−55−551-11-100000000000000000000000000000000
χ64444444-4-4-4-4-44-44-1-1-1-1-1-1-1-100001111−5−555−5−555000000005−55−51-11-100000000000000000000000000000000
χ654-44-44-444-4-44i4i−4i−4i-1-1-11-11114-44i−4i-1-111−i−i−i−iiiii00000000-1-111−i−iii00000000000000000000000000000000
χ664-44-44-444-4-44i4i−4i−4i-1-1-11-1111-44−4i4i-1-111iiii−i−i−i−i0000000011-1-1−i−iii00000000000000000000000000000000
χ674-44-44-444-4-4−4i−4i4i4i-1-1-11-11114-4−4i4i-1-111iiii−i−i−i−i00000000-1-111ii−i−i00000000000000000000000000000000
χ684-44-44-444-4-4−4i−4i4i4i-1-1-11-1111-444i−4i-1-111−i−i−i−iiiii0000000011-1-1ii−i−i00000000000000000000000000000000
χ694-44-44-4-4-4444i−4i−4i4i-1-1-11-1111000011-1-1i5i5−i5−i5−i5−i5i5i5000000005−5−55−iii−i00000000000000000000000000000000
χ704-44-44-4-4-4444i−4i−4i4i-1-1-11-1111000011-1-1−i5−i5i5i5i5i5−i5−i500000000−555−5−iii−i00000000000000000000000000000000
χ714-44-44-4-4-444−4i4i4i−4i-1-1-11-1111000011-1-1i5i5−i5−i5−i5−i5i5i500000000−555−5i−i−ii00000000000000000000000000000000
χ724-44-44-4-4-444−4i4i4i−4i-1-1-11-1111000011-1-1−i5−i5i5i5i5i5−i5−i5000000005−5−55i−i−ii00000000000000000000000000000000
χ738888-8-88-88-80000-222-2-222-20000-22-2200000000000000000000000000000000000000000000000000000000
χ748888-8-8-88-880000-222-2-222-200002-22-200000000000000000000000000000000000000000000000000000000
χ7588-8-80000000000800-8-80080000000000000000000000000000000000000000000000000000000000000000
χ7688-8-80000000000-225−252225−25-2000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18000000000000000000000000000000000000000000000000
χ7788-8-80000000000-225−252225−25-200000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18000000000000000000000000000000000000000000000000
χ7888-8-80000000000-2−252522−2525-200000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000000000000000000000000
χ7988-8-80000000000-2−252522−2525-2000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000000000000000000000000
χ808-88-8-888-8-880000-2222-2-2-220000-222-200000000000000000000000000000000000000000000000000000000
χ818-88-8-88-888-80000-2222-2-2-2200002-2-2200000000000000000000000000000000000000000000000000000000
χ828-8-8800000000008008-800-80000000000000000000000000000000000000000000000000000000000000000
χ838-8-880000000000-225−25-22−2525200000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7000000000000000000000000000000000000000000000000
χ848-8-880000000000-225−25-22−25252000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7000000000000000000000000000000000000000000000000
χ858-8-880000000000-2−2525-2225−252000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19000000000000000000000000000000000000000000000000
χ868-8-880000000000-2−2525-2225−25200000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19000000000000000000000000000000000000000000000000

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