Finite Group Databasebeta

← Group #13019807

Character table — Group #13019807

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444444810101010161616161616161616161616161616162020202040404040404040404040404040404040408080
order12222244445101010101010102444424101010101010202020202020202022444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111-1-111-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111-1-1-1-11111111111111111-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111-1-1-1-11111111111111111-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911111111-1-111111111-111111-1-1-1111111-1-1-1-1-1-1-1-111-111-1-111-1-111-1-111-1-11-1
χ1011111111-1-111111111-111111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-111-1-111-1-111-1-1111-1
χ1111111111-1-111111111-11111-11-1-1-1-1-1-111-1-11111-1-111-111-1-111-1-1-1-111-1-111-11
χ1211111111-1-111111111-11111-11-1-1-1-1-1-111-1-11111-1-111-1-1-111-1-11111-1-111-1-1-11
χ1311111111-1-111111111-1-1-1-1-11-1-1-1111111-1-1-1-1-1-111-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111111-1-111111111-1-1-1-1-11-1-1-1111111-1-1-1-1-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111111-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1111111-1-11ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111111-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1111111-1-11−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222-2-22222222222-2222200-2-20000-2-222000022-2-2-2000000000000000000
χ18222222-2-22222222222-2-2-2-2-200-2-20000-2-2220000-2-2222000000000000000000
χ19222222-2-2-2-2222222222222200220000-2-2-2-20000-2-2-2-22000000000000000000
χ20222222-2-2-2-2222222222-2-2-2-200220000-2-2-2-200002222-2000000000000000000
χ212222-2-22-20022-2-222-2-2022-2-2000000002-2000000002-20002i−2i002i−2i0000000000
χ222222-2-22-20022-2-222-2-2022-2-2000000002-2000000002-2000−2i2i00−2i2i0000000000
χ232222-2-22-20022-2-222-2-20-2-222000000002-200000000-220002-200-220000000000
χ242222-2-22-20022-2-222-2-20-2-222000000002-200000000-22000-22002-20000000000
χ252222-2-2-220022-2-222-2-2022-2-200000000-2200000000-2202i−2i002i−2i000000000000
χ262222-2-2-220022-2-222-2-2022-2-200000000-2200000000-220−2i2i00−2i2i000000000000
χ272222-2-2-220022-2-222-2-20-2-22200000000-22000000002-202-200-22000000000000
χ282222-2-2-220022-2-222-2-20-2-22200000000-22000000002-20-22002-2000000000000
χ2922-2-2-22002i−2i2222-2-2-2-202i−2i2i−2i00000000002i−2i00002-2000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00
χ3022-2-2-22002i−2i2222-2-2-2-202i−2i2i−2i00000000002i−2i00002-200000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00
χ3122-2-2-22002i−2i2222-2-2-2-20−2i2i−2i2i00000000002i−2i0000-22000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00
χ3222-2-2-22002i−2i2222-2-2-2-20−2i2i−2i2i00000000002i−2i0000-2200000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00
χ3322-2-2-2200−2i2i2222-2-2-2-202i−2i2i−2i0000000000−2i2i0000-22000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00
χ3422-2-2-2200−2i2i2222-2-2-2-202i−2i2i−2i0000000000−2i2i0000-2200000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00
χ3522-2-2-2200−2i2i2222-2-2-2-20−2i2i−2i2i0000000000−2i2i00002-2000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00
χ3622-2-2-2200−2i2i2222-2-2-2-20−2i2i−2i2i0000000000−2i2i00002-200000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00
χ374444444444-1-1-1-1-1-1-1-14000044-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ384444444444-1-1-1-1-1-1-1-140000-4-4-1-11111-1-1-1-1111100000000000000000000000
χ3944444444-4-4-1-1-1-1-1-1-1-1-400004-411-1-1-1-1-1-111111100000000000000000000000
χ4044444444-4-4-1-1-1-1-1-1-1-1-40000-44111111-1-111-1-1-1-100000000000000000000000
χ41444444-4-444-1-1-1-1-1-1-1-1-40000001155−5−511-1-155−5−500000000000000000000000
χ42444444-4-444-1-1-1-1-1-1-1-1-400000011−5−55511-1-1−5−55500000000000000000000000
χ43444444-4-4-4-4-1-1-1-1-1-1-1-14000000-1-155−5−51111−5−55500000000000000000000000
χ44444444-4-4-4-4-1-1-1-1-1-1-1-14000000-1-1−5−555111155−5−500000000000000000000000
χ4544-4-44-4000044-4-4-4-44404i−4i−4i4i000000000000000000000000000000000000000
χ4644-4-44-4000044-4-4-4-4440−4i4i4i−4i000000000000000000000000000000000000000
χ478888-8-88-800-2-222-2-2220000000000000-2200000000000000000000000000000
χ488888-8-8-8800-2-222-2-22200000000000002-200000000000000000000000000000
χ4988-8-88-80000-2-22222-2-2000000025−2500000000000000000000000000000000000
χ5088-8-88-80000-2-22222-2-20000000−252500000000000000000000000000000000000
χ5188-8-8-88008i−8i-2-2-2-22222000000000000000−2i2i000000000000000000000000000
χ5288-8-8-8800−8i8i-2-2-2-222220000000000000002i−2i000000000000000000000000000
χ538-88-80000008-8008-80000000000000000000000000000000000000000000000
χ548-88-8000000-2225−25-2225−250000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000000
χ558-88-8000000-2225−25-2225−25000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000000
χ568-88-8000000-22−2525-22−2525000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000000
χ578-88-8000000-22−2525-22−25250000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000000
χ588-8-880000008-800-880000000000000000000000000000000000000000000000
χ598-8-88000000-2225−252-2−2525000000000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000
χ608-8-88000000-2225−252-2−252500000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000
χ618-8-88000000-22−25252-225−2500000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000
χ628-8-88000000-22−25252-225−25000000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000

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