Finite Group Databasebeta

← Group #13019332

Character table — Group #13019332

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444445555888881010161616161616161616161616161620202020404040404040404040404040404040404040404040
order12222222445101010101010102222444442210102020202020202020202020202244444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ7111111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111-1-111111111111111-111-1-111-1-111-1-1-1-1-1-11111-1-111-111-1-111-1-111-1-111-1-111-1-1
χ10111111-1-111111111111111-111-1-111-1-111-1-1-1-1-1-11111-1-111-111-1-1-1-111-1-111-1-111-1-111
χ11111111-1-111111111111111-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-111-1-111
χ12111111-1-111111111111111-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-111-1-1
χ13111111-1-11111111111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-11111111111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-11111111111-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-11111111111-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222-2-2222222222222-200002222-2-2-2-20000000022-2-2-200000000000000000000
χ1822222222-2-222222222-2-2-2-2-20000-2-222-2-2-2-200000000-2-222200000000000000000000
χ19222222-2-2-2-22222222222222000022-2-2-2-22200000000-2-2-2-2200000000000000000000
χ20222222-2-2-2-222222222-2-2-2-220000-2-2-2-2-2-222000000002222-200000000000000000000
χ212222-2-2002-22-2-222-2-22222200000-2-2002-20000000000002-200000002-2002-200000000
χ222222-2-2002-22-2-222-2-22222200000-2-2002-20000000000002-20000000-2200-2200000000
χ232222-2-2002-22-2-222-2-22-2-2-2-20000022002-2000000000000-2200000002i−2i00−2i2i00000000
χ242222-2-2002-22-2-222-2-22-2-2-2-20000022002-2000000000000-220000000−2i2i002i−2i00000000
χ252222-2-200-222-2-222-2-22222200000-2-200-22000000000000-22000002-2002-20000000000
χ262222-2-200-222-2-222-2-22222200000-2-200-22000000000000-2200000-2200-220000000000
χ272222-2-200-222-2-222-2-22-2-2-2-2000002200-220000000000002-2000002i−2i00−2i2i0000000000
χ282222-2-200-222-2-222-2-22-2-2-2-2000002200-220000000000002-200000−2i2i002i−2i0000000000
χ292-2-22-222-2002-2-2-2-222222-2-2000002-22-20000000000002-2000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-2-22-222-2002-2-2-2-222222-2-2000002-22-20000000000002-2000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-2-22-222-2002-2-2-2-2222-2-22200000-222-2000000000000-220000000000000002−22−2−22−22
χ322-2-22-222-2002-2-2-2-2222-2-22200000-222-2000000000000-22000000000000000−22−222−22−2
χ332-2-22-22-22002-2-2-2-222222-2-2000002-2-22000000000000-22000000000000000i2−i2−i2i2i2−i2−i2i2
χ342-2-22-22-22002-2-2-2-222222-2-2000002-2-22000000000000-22000000000000000−i2i2i2−i2−i2i2i2−i2
χ352-2-22-22-22002-2-2-2-2222-2-22200000-22-220000000000002-20000000000000002−2−22−222−2
χ362-2-22-22-22002-2-2-2-2222-2-22200000-22-220000000000002-2000000000000000−222−22−2−22
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
χ3944444444-4-4-1-1-1-1-1-1-1-10000-4000000-1-1111155−5−555−5−50000000000000000000000000
χ4044444444-4-4-1-1-1-1-1-1-1-10000-4000000-1-11111−5−555−5−5550000000000000000000000000
χ41444444-4-444-1-1-1-1-1-1-1-10000-444-4-40011-1-1111111-1-1-1-10000000000000000000000000
χ42444444-4-444-1-1-1-1-1-1-1-10000-4-4-4440011-1-111-1-1-1-111110000000000000000000000000
χ43444444-4-4-4-4-1-1-1-1-1-1-1-1000040000001111-1-155−5−5−5−5550000000000000000000000000
χ44444444-4-4-4-4-1-1-1-1-1-1-1-1000040000001111-1-1−5−55555−5−50000000000000000000000000
χ4544-4-40000004004-400-44-44-402i−2i000000000000002i−2i2i−2i000002i−2i000000000000000000
χ4644-4-40000004004-400-44-44-40−2i2i00000000000000−2i2i−2i2i00000−2i2i000000000000000000
χ4744-4-40000004004-400-4-44-4402i−2i000000000000002i−2i2i−2i00000−2i2i000000000000000000
χ4844-4-40000004004-400-4-44-440−2i2i00000000000000−2i2i−2i2i000002i−2i000000000000000000
χ494-44-4000000400-4400-44-4-440002i−2i000000002i−2i2i−2i000000000002i−2i0000000000000000
χ504-44-4000000400-4400-44-4-44000−2i2i00000000−2i2i−2i2i00000000000−2i2i0000000000000000
χ514-44-4000000400-4400-4-444-40002i−2i000000002i−2i2i−2i00000000000−2i2i0000000000000000
χ524-44-4000000400-4400-4-444-4000−2i2i00000000−2i2i−2i2i000000000002i−2i0000000000000000
χ534-4-444-40000444-4-4-4-4444-4-400000-44000000000000000000000000000000000000000
χ544-4-444-40000444-4-4-4-44-4-444000004-4000000000000000000000000000000000000000
χ558888-8-8008-8-222-2-222-20000000000000-2200000000000000000000000000000000000
χ568888-8-800-88-222-2-222-200000000000002-200000000000000000000000000000000000
χ5788-8-8000000-225−25-2225−252000004i−4i00000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000
χ5888-8-8000000-225−25-2225−25200000−4i4i000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000000
χ5988-8-8000000-2−2525-22−25252000004i−4i00000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000
χ6088-8-8000000-2−2525-22−2525200000−4i4i000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000
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
χ658-8-888-80000-2-2-22222-20000000000000002i5−2i5000000000000000000000000000000000
χ668-8-888-80000-2-2-22222-2000000000000000−2i52i5000000000000000000000000000000000
χ678-8-88-888-800-22222-2-2-200000000000-220000000000000000000000000000000000000
χ688-8-88-88-8800-22222-2-2-2000000000002-20000000000000000000000000000000000000

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