Finite Group Databasebeta

← Group #13024567

Character table — Group #13024567

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112244444444448888101016161616161616161616161616161620202020202020404040404040404040408080808080
order12222244510101010101010444444420202020202020202020202020202244444448888888824444
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
χ9111111-1-1111111111-11111-1-1-1111111-1-1-1-1-1-1-1-1111-1-111ii−i−iii−i−i-1i−ii−i
χ10111111-1-1111111111-11111-1-1-1111111-1-1-1-1-1-1-1-1111-1-111−i−iii−i−iii-1−ii−ii
χ11111111-1-1111111111-111-1-1-1-1-1111111-1-1-1-1-1-111-1-1-111-1-111-1-1-1-11111-1-11
χ12111111-1-1111111111-111-1-1-1-1-1111111-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-11-111-1
χ13111111-1-1111111111-1-1-1111-1-1-1-1-1-111-1-11111-1-1111-1-1-1-1ii−i−iii−i−i1−ii−ii
χ14111111-1-1111111111-1-1-1111-1-1-1-1-1-111-1-11111-1-1111-1-1-1-1−i−iii−i−iii1i−ii−i
χ15111111-1-1111111111-1-1-1-1-11-1-1-1-1-1-111-1-1111111-1-1-1111111-1-1-1-111-1-111-1
χ16111111-1-1111111111-1-1-1-1-11-1-1-1-1-1-111-1-1111111-1-1-11111-1-11111-1-1-11-1-11
χ172222222222222222-2-200220-2-20000-2-2220000-2-22-2-222000000000000000
χ182222222222222222-2-200-2-20-2-20000-2-222000022-222-2-2000000000000000
χ19222222-2-222222222-2200220220000-2-2-2-20000222-2-2-2-2000000000000000
χ20222222-2-222222222-2200-2-20220000-2-2-2-20000-2-2-22222000000000000000
χ212-22-22-22i−2i2-2-2-2222-20000000000000002i−2i00002-202i−2i0000i2−i22−22−2i2−i200000
χ222-22-22-22i−2i2-2-2-2222-20000000000000002i−2i00002-202i−2i0000−i2i2−22−22−i2i200000
χ232-22-22-22i−2i2-2-2-2222-20000000000000002i−2i0000-220−2i2i00002−2−i2i2i2−i2−2200000
χ242-22-22-22i−2i2-2-2-2222-20000000000000002i−2i0000-220−2i2i0000−22i2−i2−i2i22−200000
χ252-22-22-2−2i2i2-2-2-2222-2000000000000000−2i2i00002-20−2i2i0000i2−i2−22−22i2−i200000
χ262-22-22-2−2i2i2-2-2-2222-2000000000000000−2i2i00002-20−2i2i0000−i2i22−22−2−i2i200000
χ272-22-22-2−2i2i2-2-2-2222-2000000000000000−2i2i0000-2202i−2i00002−2i2−i2−i2i2−2200000
χ282-22-22-2−2i2i2-2-2-2222-2000000000000000−2i2i0000-2202i−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
χ3044444444-1-1-1-1-1-1-1-144-4-400-4-1-11111-1-1-1-111110000000000000000000000
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
χ33444444-4-4-1-1-1-1-1-1-1-14-44400-411-1-1-1-1-1-11111110000000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-4-4-4004111111-1-111-1-1-1-10000000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-4400000-1-155−5−51111−5−5550000000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-4400000-1-1−5−555111155−5−50000000000000000000000
χ374444-4-40044-4-44-4-4400004400000000000000000-40000000000000000000
χ384444-4-40044-4-44-4-440000-4-40000000000000000040000000000000000000
χ394-44-4-44004-4444-4-4-4000000000000000000000000004i−4i000000000000000
χ404-44-4-44004-4444-4-4-400000000000000000000000000−4i4i000000000000000
χ414-4-4400004400-400-4002-24i−4i0002-22-20000000000000002i−2i0000000000000
χ424-4-4400004400-400-4002-2−4i4i0002-22-2000000000000000−2i2i0000000000000
χ434-4-4400004400-400-400-224i−4i000-22-22000000000000000−2i2i0000000000000
χ444-4-4400004400-400-400-22−4i4i000-22-220000000000000002i−2i0000000000000
χ458888-8-800-2-222-222-2000000000000025−250000000000000000000000000000
χ468888-8-800-2-222-222-20000000000000−25250000000000000000000000000000
χ4788-8-800008-800-80080000000000000000000000000000000000000000000
χ4888-8-80000-2225−25225−25-200000000000000000−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000
χ4988-8-80000-2225−25225−25-2000000000000000002ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000
χ5088-8-80000-22−25252−2525-2000000000000000002ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000
χ5188-8-80000-22−25252−2525-200000000000000000−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000
χ528-88-88-88i−8i-2222-2-2-22000000000000000−2i2i00000000000000000000000000
χ538-88-88-8−8i8i-2222-2-2-220000000000000002i−2i00000000000000000000000000
χ548-88-8-8800-22-2-2-2222000000025−250000000000000000000000000000000000
χ558-88-8-8800-22-2-2-22220000000−25250000000000000000000000000000000000
χ568-8-880000-2-225−252−25252004-400000−1+51−5−1−51+5000000000000000000000000000000
χ578-8-880000-2-225−252−2525200-44000001−5−1+51+5−1−5000000000000000000000000000000
χ588-8-880000-2-2−2525225−252004-400000−1−51+5−1+51−5000000000000000000000000000000
χ598-8-880000-2-2−2525225−25200-44000001+5−1−51−5−1+5000000000000000000000000000000

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