Finite Group Databasebeta

← Group #13019349

Character table — Group #13019349

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444445555888881010161616161616161616161616161620202020404040404040404040404040404040404040404040
order12222244445101010101010104444224444410101010202020202020202020204444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-11-1-111-1-1-1-111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-11-1-111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111111-1-111111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111-1-1-1-111111-1-111111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-111111111111111-1-1-1111111-1-1-1-1-1-111-1-1-1-111-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-111111111111111-1-1-1111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1111111111111-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-11111-1-111-1-1-1-111-1-111
χ1211111111-1-1111111111111-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-1-111-1-11111-1-111-1-1
χ1311111111-1-111111111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-111111111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-22222222222222200-200220000220000-2-2-2-222-2-2-200000000000000000000
χ18222222-2-22222222222-2-2-2-200-200-2-20000220000-2-2-2-2-2-222200000000000000000000
χ19222222-2-2-2-222222222222200200220000-2-20000-2-222-2-2-2-2200000000000000000000
χ20222222-2-2-2-222222222-2-2-2-200200-2-20000-2-20000-2-2222222-200000000000000000000
χ212222-2-22-20022-2-22-2-22222200000-2-200000000002-200002-200000002-2002-200000000
χ222222-2-22-20022-2-22-2-22222200000-2-200000000002-200002-20000000-2200-2200000000
χ232222-2-22-20022-2-22-2-22-2-2-2-2000002200000000002-20000-2200000002i−2i00−2i2i00000000
χ242222-2-22-20022-2-22-2-22-2-2-2-2000002200000000002-20000-220000000−2i2i002i−2i00000000
χ252222-2-2-220022-2-22-2-22222200000-2-20000000000-220000-22000002-2002-20000000000
χ262222-2-2-220022-2-22-2-22222200000-2-20000000000-220000-2200000-2200-220000000000
χ272222-2-2-220022-2-22-2-22-2-2-2-200000220000000000-2200002-2000002i−2i00−2i2i0000000000
χ282222-2-2-220022-2-22-2-22-2-2-2-200000220000000000-2200002-200000−2i2i002i−2i0000000000
χ292-22-22-2002-22-2-2-2222-22i2i−2i−2i000002i−2i00002-2000000002i−2i0000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ302-22-22-2002-22-2-2-2222-22i2i−2i−2i000002i−2i00002-2000000002i−2i000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ312-22-22-2002-22-2-2-2222-2−2i−2i2i2i00000−2i2i00002-200000000−2i2i0000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ322-22-22-2002-22-2-2-2222-2−2i−2i2i2i00000−2i2i00002-200000000−2i2i000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ332-22-22-200-222-2-2-2222-22i2i−2i−2i000002i−2i0000-2200000000−2i2i0000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ342-22-22-200-222-2-2-2222-22i2i−2i−2i000002i−2i0000-2200000000−2i2i000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ352-22-22-200-222-2-2-2222-2−2i−2i2i2i00000−2i2i0000-22000000002i−2i0000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ362-22-22-200-222-2-2-2222-2−2i−2i2i2i00000−2i2i0000-22000000002i−2i000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ374444444444-1-1-1-1-1-1-1-100004444400-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000
χ384444444444-1-1-1-1-1-1-1-10000-4-44-4-4001111-1-11111-1-1-1-10000000000000000000000000
χ3944444444-4-4-1-1-1-1-1-1-1-1000044-4-4-400-1-1-1-1111111-1-1110000000000000000000000000
χ4044444444-4-4-1-1-1-1-1-1-1-10000-4-4-44400111111-1-1-1-1-1-1110000000000000000000000000
χ41444444-4-444-1-1-1-1-1-1-1-1000000-4000055−5−5-1-155−5−511110000000000000000000000000
χ42444444-4-444-1-1-1-1-1-1-1-1000000-40000−5−555-1-1−5−55511110000000000000000000000000
χ43444444-4-4-4-4-1-1-1-1-1-1-1-10000004000055−5−511−5−55511-1-10000000000000000000000000
χ44444444-4-4-4-4-1-1-1-1-1-1-1-100000040000−5−5551155−5−511-1-10000000000000000000000000
χ4544-4-40000004-400-40044i−4i4i−4i2-2000002-22-20000000000000002i−2i000000000000000000
χ4644-4-40000004-400-40044i−4i4i−4i-2200000-22-22000000000000000−2i2i000000000000000000
χ4744-4-40000004-400-4004−4i4i−4i4i2-2000002-22-2000000000000000−2i2i000000000000000000
χ4844-4-40000004-400-4004−4i4i−4i4i-2200000-22-220000000000000002i−2i000000000000000000
χ494-44-4-4400004-4444-4-4-44i4i−4i−4i00000−4i4i000000000000000000000000000000000000000
χ504-44-4-4400004-4444-4-4-4−4i−4i4i4i000004i−4i000000000000000000000000000000000000000
χ514-4-440000004400-400-44-4-440002i−2i000000002i−2i2i−2i000000000002i−2i0000000000000000
χ524-4-440000004400-400-44-4-44000−2i2i00000000−2i2i−2i2i00000000000−2i2i0000000000000000
χ534-4-440000004400-400-4-444-40002i−2i000000002i−2i2i−2i00000000000−2i2i0000000000000000
χ544-4-440000004400-400-4-444-4000−2i2i00000000−2i2i−2i2i000000000002i−2i0000000000000000
χ558888-8-88-800-2-222-222-2000000000000000000000-22000000000000000000000000000
χ568888-8-8-8800-2-222-222-20000000000000000000002-2000000000000000000000000000
χ5788-8-8000000-2225−25225−25-200004-400000−1+51−5−1−51+500000000000000000000000000000000000
χ5888-8-8000000-2225−25225−25-20000-44000001−5−1+51+5−1−500000000000000000000000000000000000
χ5988-8-8000000-22−25252−2525-200004-400000−1−51+5−1+51−500000000000000000000000000000000000
χ6088-8-8000000-22−25252−2525-20000-44000001+5−1−51−5−1+500000000000000000000000000000000000
χ618-88-88-8008-8-2222-2-2-22000000000000000-22000000000000000000000000000000000
χ628-88-88-800-88-2222-2-2-220000000000000002-2000000000000000000000000000000000
χ638-88-8-880000-22-2-2-2222000000000000000000000002i5−2i50000000000000000000000000
χ648-88-8-880000-22-2-2-222200000000000000000000000−2i52i50000000000000000000000000
χ658-8-88000000-2-225−252−2525200000004i−4i00000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000
χ668-8-88000000-2-225−252−252520000000−4i4i000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000
χ678-8-88000000-2-2−2525225−25200000004i−4i00000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000
χ688-8-88000000-2-2−2525225−2520000000−4i4i000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000

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