Finite Group Databasebeta

← Group #13024677

Character table — Group #13024677

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112244444444448888101016161616161616161616161616161620202020202020404040404040404040408080808080
order12222222510101010101010444444410102020202020202020202020202244444228888888844444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1ii−i−i
χ411111111111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1−i−iii
χ511111111111111111-1-1111-1111111-1-1-1-1-1-1-1-11111111-1-111111111-1-1-1-1-1
χ611111111111111111-1-1111-1111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1−i−iii
χ811111111111111111-1-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1ii−i−i
χ9111111-1-111111111111-111-1-1-111-1-1-1-1-1-11111-1-1111-1-111ii−i−iii−i−i-1i−ii−i
χ10111111-1-111111111111-111-1-1-111-1-1-1-1-1-11111-1-1111-1-111−i−iii−i−iii-1−ii−ii
χ11111111-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-11111-1-11
χ12111111-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-11-111-1
χ13111111-1-1111111111-1-1-1111-1-111-1-11111-1-1-1-1-1-1111-1-1-1-1ii−i−iii−i−i1−ii−ii
χ14111111-1-1111111111-1-1-1111-1-111-1-11111-1-1-1-1-1-1111-1-1-1-1−i−iii−i−iii1i−ii−i
χ15111111-1-1111111111-1-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-1111111-1-1-1-111-1-111-1
χ16111111-1-1111111111-1-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-11111-1-11111-1-1-11-1-11
χ172222222222222222-200-222022-2-2-2-200000000-2-2-2-2222000000000000000
χ182222222222222222-200-2-2-2022-2-2-2-2000000002222-2-2-2000000000000000
χ19222222-2-222222222-2002220-2-2-2-2220000000022-2-22-2-2000000000000000
χ20222222-2-222222222-2002-2-20-2-2-2-22200000000-2-222-222000000000000000
χ212-22-2-222-22-2-222-2-2200000002-20000000000002-22-200000i2−i2i2−i2i2−i2i2−i200000
χ222-22-2-222-22-2-222-2-2200000002-20000000000002-22-200000−i2i2−i2i2−i2i2−i2i200000
χ232-22-2-222-22-2-222-2-2200000002-2000000000000-22-22000002−22−2−22−2200000
χ242-22-2-222-22-2-222-2-2200000002-2000000000000-22-2200000−22−222−22−200000
χ252-22-2-22-222-2-222-2-220000000-220000000000002-2-2200000i2−i2−i2i2−i2i2i2−i200000
χ262-22-2-22-222-2-222-2-220000000-220000000000002-2-2200000−i2i2i2−i2i2−i2−i2i200000
χ272-22-2-22-222-2-222-2-220000000-22000000000000-222-2000002−2−222−2−2200000
χ282-22-2-22-222-2-222-2-220000000-22000000000000-222-200000−222−2−222−200000
χ2944444444-1-1-1-1-1-1-1-14444004-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444-1-1-1-1-1-1-1-14-4-4400-4-1-1-1-1-1-1111111110000000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-400-4000-1-1111155−5−555−5−50000000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-400-4000-1-11111−5−555−5−5550000000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-1444-400-411-1-1111111-1-1-1-10000000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-4-4-400411-1-111-1-1-1-111110000000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-40040001111-1-155−5−5−5−5550000000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-40040001111-1-1−5−55555−5−50000000000000000000000
χ374444-4-4004-4-4-4-44440000440000000000000000000-400000000000000000
χ384444-4-4004-4-4-4-44440000-4-40000000000000000000400000000000000000
χ3944-4-40000400004-4-402i−2i04i−4i000000000002i−2i2i−2i00000002-20000000000000
χ4044-4-40000400004-4-402i−2i0−4i4i000000000002i−2i2i−2i0000000-220000000000000
χ4144-4-40000400004-4-40−2i2i04i−4i00000000000−2i2i−2i2i0000000-220000000000000
χ4244-4-40000400004-4-40−2i2i0−4i4i00000000000−2i2i−2i2i00000002-20000000000000
χ434-44-44-400444-4-4-4-44000000000000000000000000004i−4i000000000000000
χ444-44-44-400444-4-4-4-4400000000000000000000000000−4i4i000000000000000
χ458888-8-800-22222-2-2-200000000025−2500000000000000000000000000000000
χ468888-8-800-22222-2-2-2000000000−252500000000000000000000000000000000
χ4788-8-80000-225−2525−25-22204i−4i00000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000
χ4888-8-80000-225−2525−25-2220−4i4i000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000
χ4988-8-80000-2−2525−2525-22204i−4i00000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000
χ5088-8-80000-2−2525−2525-2220−4i4i000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000
χ518-88-88-800-2-2-22222-2000000000002i5−2i5000000000000000000000000000000
χ528-88-88-800-2-2-22222-200000000000−2i52i5000000000000000000000000000000
χ538-88-8-888-8-222-2-222-20000000-220000000000000000000000000000000000
χ548-88-8-88-88-222-2-222-200000002-20000000000000000000000000000000000
χ558-8-88000080000-88-80000000000000000000000000000000000000000000
χ568-8-880000-225−25−25252-2200000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000000
χ578-8-880000-225−25−25252-220000000000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000000
χ588-8-880000-2−252525−252-220000000000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000
χ598-8-880000-2−252525−252-2200000000000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000

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