Finite Group Databasebeta

← Group #13024597

Character table — Group #13024597

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112244444444448888101016161616161616161616161616161620202020202020404040404040404040408080808080
order12222244510101010101010444422210101010202020202020202020202444444448888888848888
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
χ5111111111111111111-1-111-1-1-1-1-111-1-1-1-111111111111-1-111111111-1-1-1-1-1
χ6111111111111111111-1-111-1-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111iiii−i−i−i−i1−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111−i−i−i−iiiii1ii−i−i
χ9111111-1-111111111-111111-1-1-1-1-1-1-1111111-1-1111-1-1-1-111ii−i−iii−i−i-1i−ii−i
χ10111111-1-111111111-111111-1-1-1-1-1-1-1111111-1-1111-1-1-1-111−i−iii−i−iii-1−ii−ii
χ11111111-1-111111111-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-111-1-1-1-11111-1-11
χ12111111-1-111111111-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11111-1-11-111-1
χ13111111-1-111111111-11-1-11111111-1-1-1-1-1-111-1-1111-1-1-1-1-1-1ii−i−iii−i−i1−ii−ii
χ14111111-1-111111111-11-1-11111111-1-1-1-1-1-111-1-1111-1-1-1-1-1-1−i−iii−i−iii1i−ii−i
χ15111111-1-111111111-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-111-1-111-1
χ16111111-1-111111111-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1111111-1-11111-1-1-11-1-11
χ172222222222222222-2-2002200000-2-20000-2-2222-2-2-2-222000000000000000
χ182222222222222222-2-200-2-200000-2-20000-2-222-22222-2-2000000000000000
χ19222222-2-2222222222-2002200000220000-2-2-2-22-2-222-2-2000000000000000
χ20222222-2-2222222222-200-2-200000220000-2-2-2-2-222-2-222000000000000000
χ2122-2-2-222i−2i222-22-2-2-200000000000000000002i−2i02i−2i2-20000i2−i22−22−2i2−i200000
χ2222-2-2-222i−2i222-22-2-2-200000000000000000002i−2i02i−2i2-20000−i2i2−22−22−i2i200000
χ2322-2-2-222i−2i222-22-2-2-200000000000000000002i−2i0−2i2i-2200002−2−i2i2i2−i2−2200000
χ2422-2-2-222i−2i222-22-2-2-200000000000000000002i−2i0−2i2i-220000−22i2−i2−i2i22−200000
χ2522-2-2-22−2i2i222-22-2-2-20000000000000000000−2i2i02i−2i-2200002−2i2−i2−i2i2−2200000
χ2622-2-2-22−2i2i222-22-2-2-20000000000000000000−2i2i02i−2i-220000−22−i2i2i2−i22−200000
χ2722-2-2-22−2i2i222-22-2-2-20000000000000000000−2i2i0−2i2i2-20000i2−i2−22−22i2−i200000
χ2822-2-2-22−2i2i222-22-2-2-20000000000000000000−2i2i0−2i2i2-20000−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
χ3044444444-1-1-1-1-1-1-1-144-4-400-41111-1-11111-1-1-1-10000000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-40000055−5−51155−5−511-1-10000000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-400000−5−55511−5−55511-1-10000000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-14-40000055−5−5-1-1−5−55511110000000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-400000−5−555-1-155−5−511110000000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-444400-4111111-1-1-1-1-1-1110000000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-44-4-4004-1-1-1-1111111-1-1110000000000000000000000
χ374444-4-4004-4-444-4-44000044000000000000000-4000000000000000000000
χ384444-4-4004-4-444-4-440000-4-40000000000000004000000000000000000000
χ3944-4-44-4004-4-4-4444-4000000000000000000000000004i−4i000000000000000
χ4044-4-44-4004-4-4-4444-400000000000000000000000000−4i4i000000000000000
χ414-44-400004004-400-4002i−2i4-400000002i−2i2i−2i000000000002i−2i0000000000000
χ424-44-400004004-400-4002i−2i-4400000002i−2i2i−2i00000000000−2i2i0000000000000
χ434-44-400004004-400-400−2i2i4-40000000−2i2i−2i2i00000000000−2i2i0000000000000
χ444-44-400004004-400-400−2i2i-440000000−2i2i−2i2i000000000002i−2i0000000000000
χ458888-8-800-222-2-222-20000000000000000025−25000000000000000000000000
χ468888-8-800-222-2-222-200000000000000000−2525000000000000000000000000
χ4788-8-88-800-2222-2-2-220000000000025−25000000000000000000000000000000
χ4888-8-88-800-2222-2-2-2200000000000−2525000000000000000000000000000000
χ4988-8-8-888i−8i-2-2-22-22220000000000000000000−2i2i0000000000000000000000
χ5088-8-8-88−8i8i-2-2-22-222200000000000000000002i−2i0000000000000000000000
χ518-88-80000-225−25-2225−252004i−4i000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000
χ528-88-80000-225−25-2225−25200−4i4i0000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000
χ538-88-80000-2−2525-22−25252004i−4i000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000
χ548-88-80000-2−2525-22−2525200−4i4i0000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000
χ558-8-880000800-8-80080000000000000000000000000000000000000000000
χ568-8-880000-225−2522−2525-20000000−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000000
χ578-8-880000-225−2522−2525-200000002ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000000
χ588-8-880000-2−25252225−25-200000002ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000000
χ598-8-880000-2−25252225−25-20000000−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000000

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