Finite Group Databasebeta

← Group #13014008

Character table — Group #13014008

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112244444488888888101010101616161616161616161616161616202040404040404040404040808080808080
order12222222510101024101010101010222244101020202020202020202020222444444444444444
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-111111111111111-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ611111111111111111111-1-1-1-111111111111111-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ711111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-11111-1111-1-1-1-11111i−i-1-111iiii−i−i−i−i-1-1-1111-1-111-1-1i−ii−ii−i
χ10111111-1-11111-1111-1-1-1-11111i−i-1-111iiii−i−i−i−i-1-1-11-1-111-1-111i−i−ii−ii
χ11111111-1-11111-1111-1-1-1-11111−ii-1-111−i−i−i−iiiii-1-1-1111-1-111-1-1−ii−ii−ii
χ12111111-1-11111-1111-1-1-1-11111−ii-1-111−i−i−i−iiiii-1-1-11-1-111-1-111−iii−ii−i
χ13111111-1-11111-1111-1-1-1-1-1-1-1-1i−i-1-111iiii−i−i−i−i111-1ii−i−i−i−iii−ii-111-1
χ14111111-1-11111-1111-1-1-1-1-1-1-1-1i−i-1-111iiii−i−i−i−i111-1−i−iiiii−i−i−ii1-1-11
χ15111111-1-11111-1111-1-1-1-1-1-1-1-1−ii-1-111−i−i−i−iiiii111-1ii−i−i−i−iiii−i1-1-11
χ16111111-1-11111-1111-1-1-1-1-1-1-1-1−ii-1-111−i−i−i−iiiii111-1−i−iiiii−i−ii−i-111-1
χ17222222222222-2-2222222222200-2-2-2-200000000-2-22-200000000000000
χ18222222222222-2-2222222-2-2-2-200-2-2-2-20000000022-2200000000000000
χ19222222-2-222222-222-2-2-2-222220022-2-20000000022-2-200000000000000
χ20222222-2-222222-222-2-2-2-2-2-2-2-20022-2-200000000-2-22200000000000000
χ2144444444-1-1-1-144-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2244444444-1-1-1-144-1-1-1-1-1-10000-4-4-1-1-1-111111111000000000000000000
χ2344444444-1-1-1-1-4-4-1-1-1-1-1-1000000111155−5−555−5−5000000000000000000
χ2444444444-1-1-1-1-4-4-1-1-1-1-1-10000001111−5−555−5−555000000000000000000
χ25444444-4-4-1-1-1-14-4-1-11111000000-1-111i5i5−i5−i5−i5−i5i5i5000000000000000000
χ26444444-4-4-1-1-1-14-4-1-11111000000-1-111−i5−i5i5i5i5i5−i5−i5000000000000000000
χ27444444-4-4-1-1-1-1-44-1-1111100004i−4i11-1-1−i−i−i−iiiii000000000000000000
χ28444444-4-4-1-1-1-1-44-1-111110000−4i4i11-1-1iiii−i−i−i−i000000000000000000
χ294444-4-400444400-4-400004-44-400000000000000000000000000000000
χ304444-4-400444400-4-40000-44-4400000000000000000000000000000000
χ3144-4-4000044-4-400000000040-40000000000000000002i−2i002i−2i00000000
χ3244-4-4000044-4-400000000040-4000000000000000000−2i2i00−2i2i00000000
χ3344-4-4000044-4-4000000000-4040000000000000000002-200-2200000000
χ3444-4-4000044-4-4000000000-404000000000000000000-22002-200000000
χ354-44-400004-44-40000000040-40000000000000000000002i−2i002i−2i000000
χ364-44-400004-44-40000000040-4000000000000000000000−2i2i00−2i2i000000
χ374-44-400004-44-400000000-4040000000000000000000002-200-22000000
χ384-44-400004-44-400000000-404000000000000000000000-22002-2000000
χ394-4-444-4004-4-44004-400000000000000000000004-40000000000000000
χ404-4-444-4004-4-44004-40000000000000000000000-440000000000000000
χ414-4-44-444-44-4-4400-44-4-444000000000000000000000000000000000000
χ424-4-44-444-4-111-1001-111-1-10000005−55−5−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18000000000000000000
χ434-4-44-444-4-111-1001-111-1-10000005−55−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18000000000000000000
χ444-4-44-444-4-111-1001-111-1-1000000−55−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18000000000000000000
χ454-4-44-444-4-111-1001-111-1-1000000−55−55ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18000000000000000000
χ464-4-44-44-444-4-4400-4444-4-4000000000000000000000000000000000000
χ474-4-44-44-44-111-1001-1-1-1110000005−5−55ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19000000000000000000
χ484-4-44-44-44-111-1001-1-1-1110000005−5−55−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19000000000000000000
χ494-4-44-44-44-111-1001-1-1-111000000−555−5−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19000000000000000000
χ504-4-44-44-44-111-1001-1-1-111000000−555−5ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19000000000000000000
χ518888-8-800-2-2-2-2002225−2525−25000000000000000000000000000000000000
χ528888-8-800-2-2-2-20022−2525−2525000000000000000000000000000000000000
χ538-8-888-800-222-200-2225−25−2525000000000000000000000000000000000000
χ548-8-888-800-222-200-22−252525−25000000000000000000000000000000000000
χ551616-16-160000-4-44400000000000000000000000000000000000000000000
χ5616-1616-160000-44-4400000000000000000000000000000000000000000000

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