Finite Group Databasebeta

← Group #13014502

Character table — Group #13014502

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111224444444444888888888888881616161616161616161640404040404040408080808080808080
order12222244510101010101010442020202020202020202020204420202020202020202222888844444444
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ91-1-111-11-11-1-1111-1-11-1111111-1-1-1-1-1-1i−iiiii−i−i−i−i1-11-1ii−i−i1-1i−i1-1i−i
χ101-1-111-11-11-1-1111-1-11-1111111-1-1-1-1-1-1i−iiiii−i−i−i−i1-11-1ii−i−i-11−ii-11−ii
χ111-1-111-11-11-1-1111-1-11-1111111-1-1-1-1-1-1i−iiiii−i−i−i−i-11-11−i−iiii−i-11−ii1-1
χ121-1-111-11-11-1-1111-1-11-1111111-1-1-1-1-1-1i−iiiii−i−i−i−i-11-11−i−iii−ii1-1i−i-11
χ131-1-111-11-11-1-1111-1-11-1111111-1-1-1-1-1-1−ii−i−i−i−iiiii1-11-1−i−iii1-1−ii1-1−ii
χ141-1-111-11-11-1-1111-1-11-1111111-1-1-1-1-1-1−ii−i−i−i−iiiii1-11-1−i−iii-11i−i-11i−i
χ151-1-111-11-11-1-1111-1-11-1111111-1-1-1-1-1-1−ii−i−i−i−iiiii-11-11ii−i−ii−i1-1−ii-11
χ161-1-111-11-11-1-1111-1-11-1111111-1-1-1-1-1-1−ii−i−i−i−iiiii-11-11ii−i−i−ii-11i−i1-1
χ172222222222222222-2-222-2-2-2-222-2-2-2-200000000002-2-22000000000000
χ182222222222222222-2-222-2-2-2-222-2-2-2-20000000000-222-2000000000000
χ192-2-222-22-22-2-2222-2-2-2222-2-2-2-2-2-22222000000000022-2-2000000000000
χ202-2-222-22-22-2-2222-2-2-2222-2-2-2-2-2-222220000000000-2-222000000000000
χ2144444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-10000000000000000
χ2244444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-4-4111111110000000000000000
χ2344444444-1-1-1-1-1-1-1-1-4-4-1-11111-1-111110055−5−555−5−50000000000000000
χ2444444444-1-1-1-1-1-1-1-1-4-4-1-11111-1-1111100−5−555−5−5550000000000000000
χ25444444-4-44444444400-4-40000-4-4000000000000000000000000000000
χ26444444-4-4-1-1-1-1-1-1-1-1001155−5−51155−5−500−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−ζ180000000000000000
χ27444444-4-4-1-1-1-1-1-1-1-1001155−5−51155−5−500ζ2−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+ζ180000000000000000
χ28444444-4-4-1-1-1-1-1-1-1-10011−5−55511−5−55500−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+ζ180000000000000000
χ29444444-4-4-1-1-1-1-1-1-1-10011−5−55511−5−55500ζ2+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−ζ180000000000000000
χ304444-4-4004444-4-4-4-400000000000000000000000000002i−2i2i−2i00000000
χ314444-4-4004444-4-4-4-40000000000000000000000000000−2i2i−2i2i00000000
χ324-4-444-44-4-111-1-1-1114-4-1-1-1-1-1-11111114i−4i−i−i−i−iiiii0000000000000000
χ334-4-444-44-4-111-1-1-1114-4-1-1-1-1-1-1111111−4i4iiiii−i−i−i−i0000000000000000
χ344-4-444-44-4-111-1-1-111-44-1-1111111-1-1-1-100i5i5−i5−i5−i5−i5i5i50000000000000000
χ354-4-444-44-4-111-1-1-111-44-1-1111111-1-1-1-100−i5−i5i5i5i5i5−i5−i50000000000000000
χ364-4-444-4-444-4-4444-4-400-4-4000044000000000000000000000000000000
χ374-4-444-4-44-111-1-1-111001155−5−5-1-1−5−55500−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−ζ190000000000000000
χ384-4-444-4-44-111-1-1-111001155−5−5-1-1−5−55500ζ3−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+ζ190000000000000000
χ394-4-444-4-44-111-1-1-1110011−5−555-1-155−5−500ζ3−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+ζ190000000000000000
χ404-4-444-4-44-111-1-1-1110011−5−555-1-155−5−500−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−ζ190000000000000000
χ414-4-44-44004-4-44-4-44400000000000000000000000000002-2-2200000000
χ424-4-44-44004-4-44-4-4440000000000000000000000000000-222-200000000
χ438888-8-800-2-2-2-222220025−25000025−25000000000000000000000000000000
χ448888-8-800-2-2-2-2222200−25250000−2525000000000000000000000000000000
χ4588-8-8000088-8-800000000000000000000000000000000000000000000
χ4688-8-80000-2-22225−2525−2500002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000
χ4788-8-80000-2-22225−2525−250000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ1900−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000
χ4888-8-80000-2-222−2525−25250000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ700−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000
χ4988-8-80000-2-222−2525−252500002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000
χ508-88-800008-88-800000000000000000000000000000000000000000000
χ518-88-80000-22-2225−25−252500002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ1900−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000
χ528-88-80000-22-2225−25−25250000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000
χ538-88-80000-22-22−252525−250000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000
χ548-88-80000-22-22−252525−2500002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ700−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000
χ558-8-88-8800-222-222-2-20025−250000−2525000000000000000000000000000000
χ568-8-88-8800-222-222-2-200−2525000025−25000000000000000000000000000000

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