Finite Group Databasebeta

← Group #13020235

Character table — Group #13020235

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444444488888881010101016161616161616161616161616162020202020202020404040404040404040404080808080
order12224424445101010210102020202022442810101010101020204040404024444444244444444444888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111-1-111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-11111-1-111
χ5111111111111111111111-1-1-1-111111111111111-1-1-1-1ii−i−i-1iii−i−i−iii−i−i-1-1i−i
χ6111111111111111111111-1-1-1-111111111111111-1-1-1-1−i−iii-1−i−i−iiii−i−iii-1-1−ii
χ7111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1ii−i−i-1iii−i−i−i−i−iii11−ii
χ8111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1−i−iii-1−i−i−iiiiii−i−i11i−i
χ911111111-1-11111-111111111111-1-1-11111-1-1-1-1-1-111-1-11111-11-1-11-1-1-1-1-1-11-111
χ1011111111-1-11111-111111111111-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11111111-1-1-1
χ1111111111-1-11111-11111111111-11-1-1-1-1-1-1-1-1111111-1-11111-11-1-11-1-11111-11-1-1
χ1211111111-1-11111-11111111111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1111
χ1311111111-1-11111-1111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-111ii−i−i1i−i−i−iii−i−iii-11i−i
χ1411111111-1-11111-1111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-111−i−iii1−iiii−i−iii−i−i-11−ii
χ1511111111-1-11111-1111111-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-111ii−i−i1i−i−i−iiiii−i−i1-1−ii
χ1611111111-1-11111-1111111-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-111−i−iii1−iiii−i−i−i−iii1-1i−i
χ17222222-2-2222222-2-2-22-2-2222-2-200-2-20000220000-22220000-200000000000000
χ18222222-2-2222222-2-2-22-2-22-2-22200-2-200002200002-2-2-20000200000000000000
χ19222222-2-2-2-222222-2-22-2-2222-2-200220000-2-20000-22-2-20000200000000000000
χ20222222-2-2-2-222222-2-22-2-22-2-22200220000-2-200002-2220000-200000000000000
χ212222-2-22-2002222022-2-2-2-222-2-2000000000000002-2000000002-202-200000000
χ222222-2-22-2002222022-2-2-2-222-2-2000000000000002-200000000-220-2200000000
χ232222-2-22-2002222022-2-2-2-2-2-22200000000000000-22000000002i−2i0−2i2i00000000
χ242222-2-22-2002222022-2-2-2-2-2-22200000000000000-2200000000−2i2i02i−2i00000000
χ252222-2-2-220022220-2-2-222-2222200000000000000-2-20022220-200-20000000000
χ262222-2-2-220022220-2-2-222-2222200000000000000-2-200-2-2-2-2020020000000000
χ272222-2-2-220022220-2-2-222-2-2-2-2-20000000000000022002i2i−2i−2i0−2i002i0000000000
χ282222-2-2-220022220-2-2-222-2-2-2-2-2000000000000002200−2i−2i2i2i02i00−2i0000000000
χ294444444444-1-1-1-14-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ304444444444-1-1-1-14-1-1-1-1-1-10000-4-4-1-11111-1-1111100000000000000000000000
χ3144444444-4-4-1-1-1-1-4-1-1-1-1-1-100004-411-1-1-1-111111100000000000000000000000
χ3244444444-4-4-1-1-1-1-4-1-1-1-1-1-10000-4411111111-1-1-1-100000000000000000000000
χ33444444-4-444-1-1-1-1-411-111-10000001155−5−5-1-155−5−500000000000000000000000
χ34444444-4-444-1-1-1-1-411-111-100000011−5−555-1-1−5−55500000000000000000000000
χ35444444-4-4-4-4-1-1-1-1411-111-1000000-1-155−5−511−5−55500000000000000000000000
χ36444444-4-4-4-4-1-1-1-1411-111-1000000-1-1−5−5551155−5−500000000000000000000000
χ3744-4-400000044-4-40000000004i−4i0000000000000000002+2i−2−2i2−2i−2+2i000000000000000
χ3844-4-400000044-4-40000000004i−4i000000000000000000−2−2i2+2i−2+2i2−2i000000000000000
χ3944-4-400000044-4-4000000000−4i4i0000000000000000002−2i−2+2i2+2i−2−2i000000000000000
χ4044-4-400000044-4-4000000000−4i4i000000000000000000−2+2i2−2i−2−2i2+2i000000000000000
χ414-44-40000004-44-400000004-400000000000000000000000000000002i−2i2i−2i0000
χ424-44-40000004-44-400000004-40000000000000000000000000000000−2i2i−2i2i0000
χ434-44-40000004-44-40000000-4400000000000000000000000000000002-2-220000
χ444-44-40000004-44-40000000-440000000000000000000000000000000-222-20000
χ454-4-444-4004-44-4-44000-40040000000000004-4000000000000000000000000000
χ464-4-444-4004-4-111-105−515−5-10000005−5−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18-11−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ1800000000000000000000000
χ474-4-444-4004-4-111-105−515−5-10000005−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18-11ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ1800000000000000000000000
χ484-4-444-4004-4-111-10−551−55-1000000−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18-11−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ1800000000000000000000000
χ494-4-444-4004-4-111-10−551−55-1000000−55ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18-11ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ1800000000000000000000000
χ504-4-444-400-444-4-44000-4004000000000000-44000000000000000000000000000
χ514-4-444-400-44-111-105−515−5-1000000−55−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ181-1ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ1800000000000000000000000
χ524-4-444-400-44-111-105−515−5-1000000−55ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ181-1−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ1800000000000000000000000
χ534-4-444-400-44-111-10−551−55-10000005−5−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ181-1ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ1800000000000000000000000
χ544-4-444-400-44-111-10−551−55-10000005−5ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ181-1−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ1800000000000000000000000
χ554-4-44-4400004-4-44000400-4000000000000000000004-40000000000000000000
χ564-4-44-4400004-4-44000400-400000000000000000000-440000000000000000000
χ578888-8-88-800-2-2-2-20-2-2222200000000000000000000000000000000000000000
χ588888-8-8-8800-2-2-2-20222-2-2200000000000000000000000000000000000000000
χ598-8-88-880000-222-2025−25-2−2525200000000000000000000000000000000000000000
χ608-8-88-880000-222-20−2525-225−25200000000000000000000000000000000000000000
χ611616-16-16000000-4-444000000000000000000000000000000000000000000000000
χ6216-1616-16000000-44-44000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.