Finite Group Databasebeta

← Group #13024563

Character table — Group #13024563

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112244444444448888101016161616161616161616161616161620202020202020404040404040404040408080808080
order12222244510101010101010244422410102020202020202020202020202224444448888888824444
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
χ5111111111111111111-1-111-11111-1-1-1-111-1-1-1-11111111-1-111111111-1-1-1-1-1
χ6111111111111111111-1-111-11111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1−i−iii
χ8111111111111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1ii−i−i
χ9111111-1-111111111-111111-1-1-1111111-1-1-1-1-1-11-1-111-1-111ii−i−iii−i−i-1i−ii−i
χ10111111-1-111111111-111111-1-1-1111111-1-1-1-1-1-11-1-111-1-111−i−iii−i−iii-1−ii−ii
χ11111111-1-111111111-1111-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-11
χ12111111-1-111111111-1111-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-111-1
χ13111111-1-111111111-11-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-1ii−i−iii−i−i1−ii−ii
χ14111111-1-111111111-11-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-1−i−iii−i−iii1i−ii−i
χ15111111-1-111111111-11-1-1-1-11-1-111-1-1-1-1-1-11111-111-1-1111111-1-1-1-111-1-111-1
χ16111111-1-111111111-11-1-1-1-11-1-111-1-1-1-1-1-11111-111-1-11111-1-11111-1-1-11-1-11
χ172222222222222222-2-200220-2-2-2-200002200002-2-2-2-222000000000000000
χ182222222222222222-2-200-2-20-2-2-2-20000220000-22222-2-2000000000000000
χ19222222-2-2222222222-20022022-2-20000-2-20000222-2-2-2-2000000000000000
χ20222222-2-2222222222-200-2-2022-2-20000-2-20000-2-2-22222000000000000000
χ2122-2-22-22i−2i22-2-222-2-20000000000000002i−2i000002-22i−2i0000i2−i22−22−2i2−i200000
χ2222-2-22-22i−2i22-2-222-2-20000000000000002i−2i000002-22i−2i0000−i2i2−22−22−i2i200000
χ2322-2-22-22i−2i22-2-222-2-20000000000000002i−2i00000-22−2i2i00002−2−i2i2i2−i2−2200000
χ2422-2-22-22i−2i22-2-222-2-20000000000000002i−2i00000-22−2i2i0000−22i2−i2−i2i22−200000
χ2522-2-22-2−2i2i22-2-222-2-2000000000000000−2i2i000002-2−2i2i0000i2−i2−22−22i2−i200000
χ2622-2-22-2−2i2i22-2-222-2-2000000000000000−2i2i000002-2−2i2i0000−i2i22−22−2−i2i200000
χ2722-2-22-2−2i2i22-2-222-2-2000000000000000−2i2i00000-222i−2i00002−2i2−i2−i2i2−2200000
χ2822-2-22-2−2i2i22-2-222-2-2000000000000000−2i2i00000-222i−2i0000−22−i2i2i2−i22−200000
χ2944444444-1-1-1-1-1-1-1-14444004-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444-1-1-1-1-1-1-1-144-4-400-4-1-1-1-11111-1-111110000000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-400000111155−5−5-1-155−5−50000000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4000001111−5−555-1-1−5−5550000000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-14-400000-1-11155−5−511−5−5550000000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-400000-1-111−5−5551155−5−50000000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-444400-411-1-1-1-1-1-11111110000000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-44-4-400411-1-1111111-1-1-1-10000000000000000000000
χ374444-4-40044-4-4-4-444000044000000000000000-4000000000000000000000
χ384444-4-40044-4-4-4-4440000-4-40000000000000004000000000000000000000
χ3944-4-4-44004444-4-4-4-4000000000000000000000000004i−4i000000000000000
χ4044-4-4-44004444-4-4-4-400000000000000000000000000−4i4i000000000000000
χ414-4-4400004-40000-44002-24-4000002-22-200000000000002-20000000000000
χ424-4-4400004-40000-44002-2-44000002-22-20000000000000-220000000000000
χ434-4-4400004-40000-4400-224-400000-22-220000000000000-220000000000000
χ444-4-4400004-40000-4400-22-4400000-22-2200000000000002-20000000000000
χ458888-8-800-2-22222-2-200000000025−2500000000000000000000000000000000
χ468888-8-800-2-22222-2-2000000000−252500000000000000000000000000000000
χ4788-8-88-88i−8i-2-222-2-222000000000000000−2i2i00000000000000000000000000
χ4888-8-88-8−8i8i-2-222-2-2220000000000000002i−2i00000000000000000000000000
χ4988-8-8-8800-2-2-2-22222000000025−250000000000000000000000000000000000
χ5088-8-8-8800-2-2-2-222220000000−25250000000000000000000000000000000000
χ518-88-800008-800008-80000000000000000000000000000000000000000000
χ528-88-80000-2225−2525−25-22000000000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ380000000000000000000000
χ538-88-80000-2225−2525−25-2200000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ380000000000000000000000
χ548-88-80000-22−2525−2525-2200000000000000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ140000000000000000000000
χ558-88-80000-22−2525−2525-22000000000000000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ140000000000000000000000
χ568-8-880000-2225−25−25252-2004-40000000−1+51−5−1−51+50000000000000000000000000000
χ578-8-880000-2225−25−25252-200-4400000001−5−1+51+5−1−50000000000000000000000000000
χ588-8-880000-22−252525−252-2004-40000000−1−51+5−1+51−50000000000000000000000000000
χ598-8-880000-22−252525−252-200-4400000001+5−1−51−5−1+50000000000000000000000000000

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