Finite Group Databasebeta

← Group #13022624

Character table — Group #13022624

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122222224444558888888888881010101010101016161616161616161616161640404040404040404040404040404040404040404040
order12222444451010104422448810102020202022224441010101020202020404040404444444444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111-1-111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111-1-111-1-11111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ7111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ8111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ91111111111111-1-1111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1ii−i−iii−i−iii−i−i-1-1ii−i−i
χ101111111111111-1-1111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1−i−iii−i−iii−i−iii-1-1−i−iii
χ111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111ii−i−iii−i−i−i−iii11−i−iii
χ121111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111−i−iii−i−iiiii−i−i11ii−i−i
χ131111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−i−i−iiiii−i−i11−i−iii
χ141111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iiiii−i−i−i−iii11ii−i−i
χ151111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii−i−iii-1-1ii−i−i
χ161111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−iii−i−i-1-1−i−iii
χ1722222-2-2-2-222222200000022-2-2-2-2-2-2-2-222200000000000000002i−2i2i−2i00000000000000
χ1822222-2-2-2-222222200000022-2-2-2-2-2-2-2-22220000000000000000−2i2i−2i2i00000000000000
χ1922222-2-2-2-22222-2-200000022-2-2-2-22222-2-2-200000000000000002-2-2200000000000000
χ2022222-2-2-2-22222-2-200000022-2-2-2-22222-2-2-20000000000000000-222-200000000000000
χ21222-2-222-2-222-2-222002i−2i002-222-2-22-2-222-2-200002i2i−2i−2i0000002i−2i000000000000000000
χ22222-2-222-2-222-2-22200−2i2i002-222-2-22-2-222-2-20000−2i−2i2i2i000000−2i2i000000000000000000
χ23222-2-222-2-222-2-2-2-2002i−2i002-222-2-2-222-2-22200002i2i−2i−2i000000−2i2i000000000000000000
χ24222-2-222-2-222-2-2-2-200−2i2i002-222-2-2-222-2-2220000−2i−2i2i2i0000002i−2i000000000000000000
χ25222-2-2-2-22222-2-2220000002-2-2-222-222-22-2-20000000000000000000000002i−2i2i−2i000000
χ26222-2-2-2-22222-2-2220000002-2-2-222-222-22-2-2000000000000000000000000−2i2i−2i2i000000
χ27222-2-2-2-22222-2-2-2-20000002-2-2-2222-2-22-2220000000000000000000000002-2-22000000
χ28222-2-2-2-22222-2-2-2-20000002-2-2-2222-2-22-222000000000000000000000000-222-2000000
χ2922-22-22-22-222-2-2222-20000-222-22-2-2-222-2-2222-2-2000000002-200000000000000000000
χ3022-22-22-22-222-2-222-220000-222-22-2-2-222-2-22-2-22200000000-2200000000000000000000
χ3122-22-22-22-222-2-2-2-22-20000-222-22-222-2-222-222-2-200000000-2200000000000000000000
χ3222-22-22-22-222-2-2-2-2-220000-222-22-222-2-222-2-2-222000000002-200000000000000000000
χ3322-22-2-22-2222-2-222000000-22-22-2222-2-2-2-22000000000000000000002i−2i2i−2i0000000000
χ3422-22-2-22-2222-2-222000000-22-22-2222-2-2-2-2200000000000000000000−2i2i−2i2i0000000000
χ3522-22-2-22-2222-2-2-2-2000000-22-22-22-2-22222-2000000000000000000002-2-220000000000
χ3622-22-2-22-2222-2-2-2-2000000-22-22-22-2-22222-200000000000000000000-222-20000000000
χ3722-2-222-2-2222222200002-2-2-22-2-22-22-22-22-20000000022-2-200000000000000002-20000
χ3822-2-222-2-222222220000-22-2-22-2-22-22-22-22-200000000-2-2220000000000000000-220000
χ3922-2-222-2-222222-2-200002-2-2-22-2-222-22-22-220000000022-2-20000000000000000-220000
χ4022-2-222-2-222222-2-20000-22-2-22-2-222-22-22-2200000000-2-22200000000000000002-20000
χ4122-2-22-222-2222222000000-2-2-222-22-22-2-22-20000000000000000000000000000002i−2i2i−2i
χ4222-2-22-222-2222222000000-2-2-222-22-22-2-22-2000000000000000000000000000000−2i2i−2i2i
χ4322-2-22-222-22222-2-2000000-2-2-222-2-22-222-220000000000000000000000000000002-2-22
χ4422-2-22-222-22222-2-2000000-2-2-222-2-22-222-22000000000000000000000000000000-222-2
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
χ49444-4-444-4-4-1-11100004i−4i00-11-1-11100000005−55−5−i−iiii5−i5i5−i50000000000000000000000
χ50444-4-444-4-4-1-11100004i−4i00-11-1-1110000000−55−55−i−iii−i5i5−i5i50000000000000000000000
χ51444-4-444-4-4-1-1110000−4i4i00-11-1-11100000005−55−5ii−i−i−i5i5−i5i50000000000000000000000
χ52444-4-444-4-4-1-1110000−4i4i00-11-1-1110000000−55−55ii−i−ii5−i5i5−i50000000000000000000000
χ5344-44-44-44-4-1-111004-400001-1-11-110000000-1-111i5−i5i5−i5i5−i5−i5i50000000000000000000000
χ5444-44-44-44-4-1-111004-400001-1-11-110000000-1-111−i5i5−i5i5−i5i5i5−i50000000000000000000000
χ5544-44-44-44-4-1-11100-4400001-1-11-11000000011-1-1i5−i5i5−i5−i5i5i5−i50000000000000000000000
χ5644-44-44-44-4-1-11100-4400001-1-11-11000000011-1-1−i5i5−i5i5i5−i5−i5i50000000000000000000000
χ5744-4-444-4-44-1-1-1-10000004-411-111-100000005−5−555−5−55-1-1110000000000000000000000
χ5844-4-444-4-44-1-1-1-10000004-411-111-10000000−555−5−555−5-1-1110000000000000000000000
χ5944-4-444-4-44-1-1-1-1000000-4411-111-100000005−5−55−555−511-1-10000000000000000000000
χ6044-4-444-4-44-1-1-1-1000000-4411-111-10000000−555−55−5−5511-1-10000000000000000000000
χ6188888-8-8-8-8-2-2-2-200000000-2-2222200000000000000000000000000000000000000000
χ62888-8-8-8-888-2-22200000000-2222-2-200000000000000000000000000000000000000000
χ6388-88-8-88-88-2-222000000002-22-22-200000000000000000000000000000000000000000
χ6488-8-88-888-8-2-2-2-200000000222-2-2200000000000000000000000000000000000000000
χ658-800000008-8008i−8i00000000000000000000000000000000000000000000000000000
χ668-800000008-800−8i8i00000000000000000000000000000000000000000000000000000
χ6716-160000000-4445−450000000000000000000000000000000000000000000000000000000
χ6816-160000000-44−45450000000000000000000000000000000000000000000000000000000

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