Finite Group Databasebeta

← Group #13019830

Character table — Group #13019830

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444444810101010161616161616161616161616161616162020202040404040404040404040404040404040408080
order12222244445101010101010102444444101020202020202020202020202044444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111-1-1111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1
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
χ71111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911111111-1-111111111-111111-1-1-111-1-1-1-1-1-11111-1-111-111-1-111-1-111-1-111-1-11-1
χ1011111111-1-111111111-111111-1-1-111-1-1-1-1-1-11111-1-111-1-1-111-1-111-1-111-1-1111-1
χ1111111111-1-111111111-11111-11-1-111-1-11111-1-1-1-1-1-111-111-1-111-1-1-1-111-1-111-11
χ1211111111-1-111111111-11111-11-1-111-1-11111-1-1-1-1-1-111-1-1-111-1-11111-1-111-1-1-11
χ1311111111-1-111111111-1-1-1-1-11-1-1-111-1-1-1-1-1-1111111-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111111-1-111111111-1-1-1-1-11-1-1-111-1-1-1-1-1-1111111-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111111-1-111111111-1-1-1-1-1-11-1-111-1-11111-1-1-1-111-1-11ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111111-1-111111111-1-1-1-1-1-11-1-111-1-11111-1-1-1-111-1-11−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222-2-22222222222-2222200-2-2-2-2220000000022-2-2-2000000000000000000
χ18222222-2-22222222222-2-2-2-2-200-2-2-2-22200000000-2-2222000000000000000000
χ19222222-2-2-2-222222222222220022-2-2-2-200000000-2-2-2-22000000000000000000
χ20222222-2-2-2-2222222222-2-2-2-20022-2-2-2-2000000002222-2000000000000000000
χ212222-2-22-2002-2-222-2-22022-2-200002-20000000000002-20002i−2i002i−2i0000000000
χ222222-2-22-2002-2-222-2-22022-2-200002-20000000000002-2000−2i2i00−2i2i0000000000
χ232222-2-22-2002-2-222-2-220-2-22200002-2000000000000-220002-200-220000000000
χ242222-2-22-2002-2-222-2-220-2-22200002-2000000000000-22000-22002-20000000000
χ252222-2-2-22002-2-222-2-22022-2-20000-22000000000000-2202i−2i002i−2i000000000000
χ262222-2-2-22002-2-222-2-22022-2-20000-22000000000000-220−2i2i00−2i2i000000000000
χ272222-2-2-22002-2-222-2-220-2-2220000-220000000000002-202-200-22000000000000
χ282222-2-2-22002-2-222-2-220-2-2220000-220000000000002-20-22002-2000000000000
χ292-2-222-2002i−2i222-2-2-2-2202-22-20000002i−2i000000002i−2i000000000002−2i2−i22−2i2−i200
χ302-2-222-2002i−2i222-2-2-2-2202-22-20000002i−2i000000002i−2i00000000000−22−i2i2−22−i2i200
χ312-2-222-2002i−2i222-2-2-2-220-22-220000002i−2i00000000−2i2i00000000000i2−i2−22−i2i22−200
χ322-2-222-2002i−2i222-2-2-2-220-22-220000002i−2i00000000−2i2i00000000000−i2i22−2i2−i2−2200
χ332-2-222-200−2i2i222-2-2-2-2202-22-2000000−2i2i00000000−2i2i000000000002−2−i2i22−2−i2i200
χ342-2-222-200−2i2i222-2-2-2-2202-22-2000000−2i2i00000000−2i2i00000000000−22i2−i2−22i2−i200
χ352-2-222-200−2i2i222-2-2-2-220-22-22000000−2i2i000000002i−2i00000000000i2−i22−2−i2i2−2200
χ362-2-222-200−2i2i222-2-2-2-220-22-22000000−2i2i000000002i−2i00000000000−i2i2−22i2−i22−200
χ374444444444-1-1-1-1-1-1-1-14000044-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ384444444444-1-1-1-1-1-1-1-140000-4-4-1-1-1-1-1-11111111100000000000000000000000
χ3944444444-4-4-1-1-1-1-1-1-1-1-400004-411-1-1111111-1-1-1-100000000000000000000000
χ4044444444-4-4-1-1-1-1-1-1-1-1-40000-4411-1-111-1-1-1-1111100000000000000000000000
χ41444444-4-444-1-1-1-1-1-1-1-1-40000001111-1-155−5−555−5−500000000000000000000000
χ42444444-4-444-1-1-1-1-1-1-1-1-40000001111-1-1−5−555−5−55500000000000000000000000
χ43444444-4-4-4-4-1-1-1-1-1-1-1-14000000-1-1111155−5−5−5−55500000000000000000000000
χ44444444-4-4-4-4-1-1-1-1-1-1-1-14000000-1-11111−5−55555−5−500000000000000000000000
χ454-4-44-4400004-4-4-4-444404-4-44000000000000000000000000000000000000000
χ464-4-44-4400004-4-4-4-44440-444-4000000000000000000000000000000000000000
χ478888-8-88-800-222-2-222-2000000000-22000000000000000000000000000000000
χ488888-8-8-8800-222-2-222-20000000002-2000000000000000000000000000000000
χ4988-8-80000008008-800-800000000000000000000000000000000000000000000
χ5088-8-8000000-225−25-2225−252000000000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000
χ5188-8-8000000-225−25-2225−25200000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000
χ5288-8-8000000-2−2525-22−2525200000000000000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000
χ5388-8-8000000-2−2525-22−25252000000000000000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000
χ548-88-8000000800-8800-800000000000000000000000000000000000000000000
χ558-88-8000000-225−252-2−2525200000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000
χ568-88-8000000-225−252-2−252520000000000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000
χ578-88-8000000-2−25252-225−2520000000000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000
χ588-88-8000000-2−25252-225−25200000000000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000
χ598-8-888-8008i−8i-2-2-22222-200000000000−2i2i0000000000000000000000000000000
χ608-8-888-800−8i8i-2-2-22222-2000000000002i−2i0000000000000000000000000000000
χ618-8-88-880000-22222-2-2-2000000025−2500000000000000000000000000000000000
χ628-8-88-880000-22222-2-2-20000000−252500000000000000000000000000000000000

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