Finite Group Databasebeta

← Group #13022575

Character table — Group #13022575

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122222224444558888888888881010101010101016161616161616161616161640404040404040404040404040404040404040404040
order12222222251010104424444410101010101044444441010202020202020202020202444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111-1-111-1-11111111111111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111-1-111-1-11111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ91111111111111-1-1111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111-1-1111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ121111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ131111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ141111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ151111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222-2-2-2-22222222-2000022-2-2-2-2222-2-2-2-222-2-200000000-2200000000000000000000
χ1822222-2-2-2-2222222-22000022-2-2-2-2222-2-2-2-2-2-222000000002-200000000000000000000
χ1922222-2-2-2-22222-2-22-2000022-2-2-2-2-2-2-2222222-2-2000000002-200000000000000000000
χ2022222-2-2-2-22222-2-2-22000022-2-2-2-2-2-2-22222-2-22200000000-2200000000000000000000
χ21222-2-222-2-22-2-222200002i−2i2-222-2-22-2-2-222-2000000002i2i−2i−2i00002i−2i0000000000000000
χ22222-2-222-2-22-2-22220000−2i2i2-222-2-22-2-2-222-200000000−2i−2i2i2i0000−2i2i0000000000000000
χ23222-2-222-2-22-2-22-2-200002i−2i2-222-2-2-2222-2-22000000002i2i−2i−2i0000−2i2i0000000000000000
χ24222-2-222-2-22-2-22-2-20000−2i2i2-222-2-2-2222-2-2200000000−2i−2i2i2i00002i−2i0000000000000000
χ25222-2-2-2-2222-2-2222002-2002-2-2-2222-2-22-2-22000022-2-20000002-2000000000000000000
χ26222-2-2-2-2222-2-222200-22002-2-2-2222-2-22-2-220000-2-222000000-22000000000000000000
χ27222-2-2-2-2222-2-22-2-2002-2002-2-2-222-222-222-2000022-2-2000000-22000000000000000000
χ28222-2-2-2-2222-2-22-2-200-22002-2-2-222-222-222-20000-2-2220000002-2000000000000000000
χ2922-22-22-22-2222222000000-2-22-22-2-22-2-22-22000000000000000000000000002-22-20000
χ3022-22-22-22-2222222000000-2-22-22-2-22-2-22-2200000000000000000000000000-22-220000
χ3122-22-22-22-22222-2-2000000-2-22-22-22-222-22-2000000000000000000000000002i−2i−2i2i0000
χ3222-22-22-22-22222-2-2000000-2-22-22-22-222-22-200000000000000000000000000−2i2i2i−2i0000
χ3322-22-2-22-22222222000000-2-2-22-22-22-22-22-20000000000000000002i−2i2i−2i000000000000
χ3422-22-2-22-22222222000000-2-2-22-22-22-22-22-2000000000000000000−2i2i−2i2i000000000000
χ3522-22-2-22-222222-2-2000000-2-2-22-222-22-22-220000000000000000002-2-22000000000000
χ3622-22-2-22-222222-2-2000000-2-2-22-222-22-22-22000000000000000000-222-2000000000000
χ3722-2-222-2-222-2-2222000000-222-2-22-2-2222-2-200000000000000000000002i−2i2i−2i00000000
χ3822-2-222-2-222-2-2222000000-222-2-22-2-2222-2-20000000000000000000000−2i2i−2i2i00000000
χ3922-2-222-2-222-2-22-2-2000000-222-2-2222-2-2-22200000000000000000000002-2-2200000000
χ4022-2-222-2-222-2-22-2-2000000-222-2-2222-2-2-2220000000000000000000000-222-200000000
χ4122-2-22-222-22-2-2222000000-22-222-2-2-22-2-2220000000000000000000000000000002-22-2
χ4222-2-22-222-22-2-2222000000-22-222-2-2-22-2-222000000000000000000000000000000-22-22
χ4322-2-22-222-22-2-22-2-2000000-22-222-222-222-2-20000000000000000000000000000002i−2i−2i2i
χ4422-2-22-222-22-2-22-2-2000000-22-222-222-222-2-2000000000000000000000000000000−2i2i2i−2i
χ45444444444-1-1-1-100444444-1-1-1-1-1-10000000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ46444444444-1-1-1-10044-4-4-4-4-1-1-1-1-1-10000000-1-1-1-1111111110000000000000000000000
χ47444444444-1-1-1-100-4-444-4-4-1-1-1-1-1-100000001111-1-1-1-111110000000000000000000000
χ48444444444-1-1-1-100-4-4-4-444-1-1-1-1-1-1000000011111111-1-1-1-10000000000000000000000
χ4944444-4-4-4-4-1-1-1-1004-40000-1-111110000000-1-111i5−i5i5−i5i5−i5i5−i50000000000000000000000
χ5044444-4-4-4-4-1-1-1-1004-40000-1-111110000000-1-111−i5i5−i5i5−i5i5−i5i50000000000000000000000
χ5144444-4-4-4-4-1-1-1-100-440000-1-11111000000011-1-1i5−i5i5−i5−i5i5−i5i50000000000000000000000
χ5244444-4-4-4-4-1-1-1-100-440000-1-11111000000011-1-1−i5i5−i5i5i5−i5i5−i50000000000000000000000
χ53444-4-444-4-4-111-10000004i−4i-11-1-11100000005−55−5i5−i5−i5i5−i−iii0000000000000000000000
χ54444-4-444-4-4-111-10000004i−4i-11-1-1110000000−55−55−i5i5i5−i5−i−iii0000000000000000000000
χ55444-4-444-4-4-111-1000000−4i4i-11-1-11100000005−55−5−i5i5i5−i5ii−i−i0000000000000000000000
χ56444-4-444-4-4-111-1000000−4i4i-11-1-1110000000−55−55i5−i5−i5i5ii−i−i0000000000000000000000
χ57444-4-4-4-444-111-100004-400-1111-1-100000005−5−55-1-1115−5−550000000000000000000000
χ58444-4-4-4-444-111-100004-400-1111-1-10000000−555−5-1-111−555−50000000000000000000000
χ59444-4-4-4-444-111-10000-4400-1111-1-100000005−5−5511-1-1−555−50000000000000000000000
χ60444-4-4-4-444-111-10000-4400-1111-1-10000000−555−511-1-15−5−550000000000000000000000
χ6188-88-88-88-8-2-2-2-20000000022-22-2200000000000000000000000000000000000000000
χ6288-88-8-88-88-2-2-2-200000000222-22-200000000000000000000000000000000000000000
χ6388-8-888-8-88-222-2000000002-2-222-200000000000000000000000000000000000000000
χ6488-8-88-888-8-222-2000000002-22-2-2200000000000000000000000000000000000000000
χ658-80000000800-88i−8i00000000000000000000000000000000000000000000000000000
χ668-80000000800-8−8i8i00000000000000000000000000000000000000000000000000000
χ6716-160000000-445−4540000000000000000000000000000000000000000000000000000000
χ6816-160000000-4−454540000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).