Finite Group Databasebeta

← Group #13019366

Character table — Group #13019366

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444445555888881010161616161616161616161616161620202020404040404040404040404040404040404040404040
order12222244445101010101010104444444444420202020202020202020202020204444222448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ7111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1111111111111-111-1-111-1-1-1-111-1-1-1-11111-1-111-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1111111111111-111-1-111-1-1-1-111-1-1-1-11111-1-111-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-111-1-111
χ1211111111-1-1111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-111-1-1
χ1311111111-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-111111111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-111111111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-222222222222222-20000220000-2-222-2-2000022-2-2-200000000000000000000
χ18222222-2-22222222222-2-2-2-2-20000-2-20000-2-222-2-20000-2-222200000000000000000000
χ19222222-2-2-2-222222222222220000220000-2-2-2-2220000-2-2-2-2200000000000000000000
χ20222222-2-2-2-222222222-2-2-2-220000-2-20000-2-2-2-22200002222-200000000000000000000
χ212222-2-22-20022-2-2-2-222222200000-2-200002-200000000002-200000002-2002-200000000
χ222222-2-22-20022-2-2-2-222222200000-2-200002-200000000002-20000000-2200-2200000000
χ232222-2-22-20022-2-2-2-222-2-2-2-2000002200002-20000000000-2200000002i−2i00−2i2i00000000
χ242222-2-22-20022-2-2-2-222-2-2-2-2000002200002-20000000000-220000000−2i2i002i−2i00000000
χ252222-2-2-220022-2-2-2-222222200000-2-20000-220000000000-22000002-2002-20000000000
χ262222-2-2-220022-2-2-2-222222200000-2-20000-220000000000-2200000-2200-220000000000
χ272222-2-2-220022-2-2-2-222-2-2-2-200000220000-2200000000002-2000002i−2i00−2i2i0000000000
χ282222-2-2-220022-2-2-2-222-2-2-2-200000220000-2200000000002-200000−2i2i002i−2i0000000000
χ292-22-22-2002i−2i2-222-2-2-2222-2-2000002-20000002i−2i0000002i−2i0000000000000002−2i2−i22−2i2−i2
χ302-22-22-2002i−2i2-222-2-2-2222-2-2000002-20000002i−2i0000002i−2i000000000000000−22−i2i2−22−i2i2
χ312-22-22-2002i−2i2-222-2-2-22-2-22200000-220000002i−2i000000−2i2i000000000000000i2−i2−22−i2i22−2
χ322-22-22-2002i−2i2-222-2-2-22-2-22200000-220000002i−2i000000−2i2i000000000000000−i2i22−2i2−i2−22
χ332-22-22-200−2i2i2-222-2-2-2222-2-2000002-2000000−2i2i000000−2i2i0000000000000002−2−i2i22−2−i2i2
χ342-22-22-200−2i2i2-222-2-2-2222-2-2000002-2000000−2i2i000000−2i2i000000000000000−22i2−i2−22i2−i2
χ352-22-22-200−2i2i2-222-2-2-22-2-22200000-22000000−2i2i0000002i−2i000000000000000i2−i22−2−i2i2−22
χ362-22-22-200−2i2i2-222-2-2-22-2-22200000-22000000−2i2i0000002i−2i000000000000000−i2i2−22i2−i22−2
χ374444444444-1-1-1-1-1-1-1-100004444400-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000
χ384444444444-1-1-1-1-1-1-1-100004-4-4-4-4001111-1-1-1-1-1-111110000000000000000000000000
χ3944444444-4-4-1-1-1-1-1-1-1-10000-444-4-4001111-1-11111-1-1-1-10000000000000000000000000
χ4044444444-4-4-1-1-1-1-1-1-1-10000-4-4-44400-1-1-1-1-1-1111111110000000000000000000000000
χ41444444-4-444-1-1-1-1-1-1-1-10000-400000055−5−511-1-11155−5−50000000000000000000000000
χ42444444-4-444-1-1-1-1-1-1-1-10000-4000000−5−55511-1-111−5−5550000000000000000000000000
χ43444444-4-4-4-4-1-1-1-1-1-1-1-10000400000055−5−51111-1-1−5−5550000000000000000000000000
χ44444444-4-4-4-4-1-1-1-1-1-1-1-100004000000−5−5551111-1-155−5−50000000000000000000000000
χ4544-4-40000004-400004-44i−4i4i−4i02i−2i000000000000002i−2i2i−2i000002-2000000000000000000
χ4644-4-40000004-400004-44i−4i4i−4i0−2i2i00000000000000−2i2i−2i2i00000-22000000000000000000
χ4744-4-40000004-400004-4−4i4i−4i4i02i−2i000000000000002i−2i2i−2i00000-22000000000000000000
χ4844-4-40000004-400004-4−4i4i−4i4i0−2i2i00000000000000−2i2i−2i2i000002-2000000000000000000
χ494-44-4-4400004-4-4-444-4444-4-400000-44000000000000000000000000000000000000000
χ504-44-4-4400004-4-4-444-44-4-444000004-4000000000000000000000000000000000000000
χ514-4-44000000440000-4-44i−4i−4i4i0002-2002-22-2000000000000000002i−2i0000000000000000
χ524-4-44000000440000-4-44i−4i−4i4i000-2200-22-2200000000000000000−2i2i0000000000000000
χ534-4-44000000440000-4-4−4i4i4i−4i0002-2002-22-200000000000000000−2i2i0000000000000000
χ544-4-44000000440000-4-4−4i4i4i−4i000-2200-22-22000000000000000002i−2i0000000000000000
χ558888-8-88-800-2-22222-2-2000000000000000-22000000000000000000000000000000000
χ568888-8-8-8800-2-22222-2-20000000000000002-2000000000000000000000000000000000
χ5788-8-8000000-2225−2525−25-22000004i−4i00000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000
χ5888-8-8000000-2225−2525−25-2200000−4i4i000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000000
χ5988-8-8000000-22−2525−2525-22000004i−4i00000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000
χ6088-8-8000000-22−2525−2525-2200000−4i4i000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000
χ618-88-88-8008i−8i-22-2-2222-200000000000000000−2i2i0000000000000000000000000000000
χ628-88-88-800−8i8i-22-2-2222-2000000000000000002i−2i0000000000000000000000000000000
χ638-88-8-880000-2222-2-22-2000000000000000000025−2500000000000000000000000000000
χ648-88-8-880000-2222-2-22-20000000000000000000−252500000000000000000000000000000
χ658-8-88000000-2-225−25−25252200000004-400−1+51−5−1−51+500000000000000000000000000000000000
χ668-8-88000000-2-225−25−2525220000000-44001−5−1+51+5−1−500000000000000000000000000000000000
χ678-8-88000000-2-2−252525−252200000004-400−1−51+5−1+51−500000000000000000000000000000000000
χ688-8-88000000-2-2−252525−25220000000-44001+5−1−51−5−1+500000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.