Finite Group Databasebeta

← Group #13024599

Character table — Group #13024599

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112244444444448888101016161616161616161616161616161620202020202020404040404040404040408080808080
order12222244510101010101010444422420202020202020202020202020202444444448888888828888
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
χ5111111111111111111-1-111-111-1-1-1-11111-1-1-1-11111111-1-111111111-1-1-1-1-1
χ6111111111111111111-1-111-111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1−i−iii
χ8111111111111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1ii−i−i
χ9111111-1-111111111-111111-1-1-1111111-1-1-1-1-1-1111-1-1-1-111ii−i−iii−i−i-1i−ii−i
χ10111111-1-111111111-111111-1-1-1111111-1-1-1-1-1-1111-1-1-1-111−i−iii−i−iii-1−ii−ii
χ11111111-1-111111111-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11
χ12111111-1-111111111-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-111-1
χ13111111-1-111111111-11-1-1111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1ii−i−iii−i−i1−ii−ii
χ14111111-1-111111111-11-1-1111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1−i−iii−i−iii1i−ii−i
χ15111111-1-111111111-11-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-111111111-1-1-1-111-1-111-1
χ16111111-1-111111111-11-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1111111-1-11111-1-1-11-1-11
χ172222222222222222-2-200220-2-20000-2-22200002-2-2-2-222000000000000000
χ182222222222222222-2-200-2-20-2-20000-2-2220000-22222-2-2000000000000000
χ19222222-2-2222222222-200220220000-2-2-2-200002-2-222-2-2000000000000000
χ20222222-2-2222222222-200-2-20220000-2-2-2-20000-222-2-222000000000000000
χ212-22-22-22i−2i2-2-2222-2-20000000000000002i−2i000002i−2i2-20000i2−i22−22−2i2−i200000
χ222-22-22-22i−2i2-2-2222-2-20000000000000002i−2i000002i−2i2-20000−i2i2−22−22−i2i200000
χ232-22-22-22i−2i2-2-2222-2-20000000000000002i−2i00000−2i2i-2200002−2−i2i2i2−i2−2200000
χ242-22-22-22i−2i2-2-2222-2-20000000000000002i−2i00000−2i2i-220000−22i2−i2−i2i22−200000
χ252-22-22-2−2i2i2-2-2222-2-2000000000000000−2i2i000002i−2i-2200002−2i2−i2−i2i2−2200000
χ262-22-22-2−2i2i2-2-2222-2-2000000000000000−2i2i000002i−2i-220000−22−i2i2i2−i22−200000
χ272-22-22-2−2i2i2-2-2222-2-2000000000000000−2i2i00000−2i2i2-20000i2−i2−22−22i2−i200000
χ282-22-22-2−2i2i2-2-2222-2-2000000000000000−2i2i00000−2i2i2-20000−i2i22−22−2−i2i200000
χ2944444444-1-1-1-1-1-1-1-14444004-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444-1-1-1-1-1-1-1-144-4-400-4-1-11111-1-1-1-111110000000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-4000001155−5−511-1-155−5−50000000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-40000011−5−55511-1-1−5−5550000000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-14-400000-1-155−5−51111−5−5550000000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-400000-1-1−5−555111155−5−50000000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-444400-411-1-1-1-1-1-11111110000000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-44-4-4004111111-1-111-1-1-1-10000000000000000000000
χ374444-4-4004-4-44-4-444000044000000000000000-4000000000000000000000
χ384444-4-4004-4-44-4-4440000-4-40000000000000004000000000000000000000
χ3944-4-40000400-4004-4002i−2i4-40002i−2i2i−2i0000000000000002i−2i0000000000000
χ4044-4-40000400-4004-4002i−2i-440002i−2i2i−2i000000000000000−2i2i0000000000000
χ4144-4-40000400-4004-400−2i2i4-4000−2i2i−2i2i000000000000000−2i2i0000000000000
χ4244-4-40000400-4004-400−2i2i-44000−2i2i−2i2i0000000000000002i−2i0000000000000
χ434-44-4-44004444-4-4-4-4000000000000000000000000004i−4i000000000000000
χ444-44-4-44004444-4-4-4-400000000000000000000000000−4i4i000000000000000
χ458888-8-800-222-222-2-2000000000000025−250000000000000000000000000000
χ468888-8-800-222-222-2-20000000000000−25250000000000000000000000000000
χ4788-8-80000-225−25225−25-22004i−4i00000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38000000000000000000000000000000
χ4888-8-80000-225−25225−25-2200−4i4i000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38000000000000000000000000000000
χ4988-8-80000-2−25252−2525-22004i−4i00000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000000000000000000000000000
χ5088-8-80000-2−25252−2525-2200−4i4i000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000000000000000000000000000
χ518-88-88-88i−8i-222-2-2-222000000000000000−2i2i00000000000000000000000000
χ528-88-88-8−8i8i-222-2-2-2220000000000000002i−2i00000000000000000000000000
χ538-88-8-8800-2-2-2-22222000000025−250000000000000000000000000000000000
χ548-88-8-8800-2-2-2-222220000000−25250000000000000000000000000000000000
χ558-8-880000800-800-880000000000000000000000000000000000000000000
χ568-8-880000-225−252−25252-200000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ140000000000000000000000
χ578-8-880000-225−252−25252-2000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ140000000000000000000000
χ588-8-880000-2−2525225−252-2000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ380000000000000000000000
χ598-8-880000-2−2525225−252-200000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ380000000000000000000000

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