Finite Group Databasebeta

← Group #13019367

Character table — Group #13019367

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444445555888881010161616161616161616161616161620202020404040404040404040404040404040404040404040
order12222244445101010101010104444244444410102020202020202020202020204444224448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-111111111
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
χ7111111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1111111111111-111-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1111111111111-111-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1111111111111-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-111-1-111
χ1211111111-1-1111111111111-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-111-1-1
χ1311111111-1-111111111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-111111111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-111111111-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-111111111-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-222222222222222-2000022-2-2-2-2220000000022-2-200-2000000000000000000
χ18222222-2-22222222222-2-2-2-2-20000-2-2-2-2-2-22200000000-2-222002000000000000000000
χ19222222-2-2-2-2222222222222200002222-2-2-2-200000000-2-2-2-2002000000000000000000
χ20222222-2-2-2-222222222-2-2-2-220000-2-222-2-2-2-200000000222200-2000000000000000000
χ212222-2-22-2002-2-222-2-22222200000-2-2002-20000000000002-200000002-2002-200000000
χ222222-2-22-2002-2-222-2-22222200000-2-2002-20000000000002-20000000-2200-2200000000
χ232222-2-22-2002-2-222-2-22-2-2-2-20000022002-2000000000000-2200000002i−2i00−2i2i00000000
χ242222-2-22-2002-2-222-2-22-2-2-2-20000022002-2000000000000-220000000−2i2i002i−2i00000000
χ252222-2-2-22002-2-222-2-22222200000-2-200-22000000000000-22000002-2002-20000000000
χ262222-2-2-22002-2-222-2-22222200000-2-200-22000000000000-2200000-2200-220000000000
χ272222-2-2-22002-2-222-2-22-2-2-2-2000002200-220000000000002-2000002i−2i00−2i2i0000000000
χ282222-2-2-22002-2-222-2-22-2-2-2-2000002200-220000000000002-200000−2i2i002i−2i0000000000
χ292-2-222-2002i−2i222-2-2-2-2222-2-2000002-200002i−2i000000002i−2i0000000000000002−2i2−i22−2i2−i2
χ302-2-222-2002i−2i222-2-2-2-2222-2-2000002-200002i−2i000000002i−2i000000000000000−22−i2i2−22−i2i2
χ312-2-222-2002i−2i222-2-2-2-22-2-22200000-2200002i−2i00000000−2i2i000000000000000i2−i2−22−i2i22−2
χ322-2-222-2002i−2i222-2-2-2-22-2-22200000-2200002i−2i00000000−2i2i000000000000000−i2i22−2i2−i2−22
χ332-2-222-200−2i2i222-2-2-2-2222-2-2000002-20000−2i2i00000000−2i2i0000000000000002−2−i2i22−2−i2i2
χ342-2-222-200−2i2i222-2-2-2-2222-2-2000002-20000−2i2i00000000−2i2i000000000000000−22i2−i2−22i2−i2
χ352-2-222-200−2i2i222-2-2-2-22-2-22200000-220000−2i2i000000002i−2i000000000000000i2−i22−2−i2i2−22
χ362-2-222-200−2i2i222-2-2-2-22-2-22200000-220000−2i2i000000002i−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
χ384444444444-1-1-1-1-1-1-1-100004-4-4-4-400-1-1-1-1-1-1111111110000000000000000000000000
χ3944444444-4-4-1-1-1-1-1-1-1-10000-444-4-40011-1-1111111-1-1-1-10000000000000000000000000
χ4044444444-4-4-1-1-1-1-1-1-1-10000-4-4-4440011-1-111-1-1-1-111110000000000000000000000000
χ41444444-4-444-1-1-1-1-1-1-1-10000-40000001111-1-155−5−555−5−50000000000000000000000000
χ42444444-4-444-1-1-1-1-1-1-1-10000-40000001111-1-1−5−555−5−5550000000000000000000000000
χ43444444-4-4-4-4-1-1-1-1-1-1-1-100004000000-1-1111155−5−5−5−5550000000000000000000000000
χ44444444-4-4-4-4-1-1-1-1-1-1-1-100004000000-1-11111−5−55555−5−50000000000000000000000000
χ4544-4-40000004004-400-44i−4i4i−4i02i−2i000000000000002i−2i2i−2i00002-20000000000000000000
χ4644-4-40000004004-400-44i−4i4i−4i0−2i2i00000000000000−2i2i−2i2i0000-220000000000000000000
χ4744-4-40000004004-400-4−4i4i−4i4i02i−2i000000000000002i−2i2i−2i0000-220000000000000000000
χ4844-4-40000004004-400-4−4i4i−4i4i0−2i2i00000000000000−2i2i−2i2i00002-20000000000000000000
χ494-44-4000000400-4400-44i−4i−4i4i0002i−2i000000002i−2i2i−2i000000000002-20000000000000000
χ504-44-4000000400-4400-44i−4i−4i4i000−2i2i00000000−2i2i−2i2i00000000000-220000000000000000
χ514-44-4000000400-4400-4−4i4i4i−4i0002i−2i000000002i−2i2i−2i00000000000-220000000000000000
χ524-44-4000000400-4400-4−4i4i4i−4i000−2i2i00000000−2i2i−2i2i000000000002-20000000000000000
χ534-4-44-4400004-4-4-4-444444-4-400000-44000000000000000000000000000000000000000
χ544-4-44-4400004-4-4-4-4444-4-444000004-4000000000000000000000000000000000000000
χ558888-8-88-800-222-2-222-20000000000000-2200000000000000000000000000000000000
χ568888-8-8-8800-222-2-222-200000000000002-200000000000000000000000000000000000
χ5788-8-8000000-225−25-2225−252000004i−4i00000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000
χ5888-8-8000000-225−25-2225−25200000−4i4i000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000
χ5988-8-8000000-2−2525-22−25252000004i−4i00000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000
χ6088-8-8000000-2−2525-22−2525200000−4i4i000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000000
χ618-88-8000000-225−252-2−2525200000004i−4i00000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000000
χ628-88-8000000-225−252-2−252520000000−4i4i000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000000
χ638-88-8000000-2−25252-225−25200000004i−4i00000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000000
χ648-88-8000000-2−25252-225−2520000000−4i4i000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000000
χ658-8-888-8008i−8i-2-2-22222-2000000000000000−2i2i000000000000000000000000000000000
χ668-8-888-800−8i8i-2-2-22222-20000000000000002i−2i000000000000000000000000000000000
χ678-8-88-880000-22222-2-2-20000000000025−250000000000000000000000000000000000000
χ688-8-88-880000-22222-2-2-200000000000−25250000000000000000000000000000000000000

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