Finite Group Databasebeta

← Group #13022538

Character table — Group #13022538

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444455558888888888881010101010101616161616161616161616162020202020202020404040404040404040404040404040404040
order12222244445101010444422448810102020202022224410101010202020204040404044444444444444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ5111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1
χ8111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ911111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111iiii−i−i−i−i-1-1-1-1ii−i−iii−i−i-1-1ii−i−i
χ1011111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1−i−iii−i−iii-1-1−i−iii
χ1111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1−i−iii−i−iii11ii−i−i
χ1211111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1ii−i−iii−i−i11−i−iii
χ1311111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-111−i−iiiii−i−i11−i−iii
χ1411111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i−i−iii11ii−i−i
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1111ii−i−i−i−iii-1-1−i−iii
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1111−i−iiiii−i−i-1-1ii−i−i
χ17222222-2-2-2-22222222200000022-2-2-2-2-2-2-2-22200000000000000000000000000002i−2i2i−2i000000
χ18222222-2-2-2-22222222200000022-2-2-2-2-2-2-2-2220000000000000000000000000000−2i2i−2i2i000000
χ19222222-2-2-2-22222-2-2-2-200000022-2-2-2-22222-2-200000000000000000000000000002-2-22000000
χ20222222-2-2-2-22222-2-2-2-200000022-2-2-2-22222-2-20000000000000000000000000000-222-2000000
χ212222-2-222-2-222222222000000-2-222-2-22-2-22-2-200000000000022-2-222-2-2000000000000000000
χ222222-2-222-2-222222222000000-2-222-2-22-2-22-2-2000000000000-2-222-2-222000000000000000000
χ232222-2-222-2-22222-2-2-2-2000000-2-222-2-2-222-2220000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ242222-2-222-2-22222-2-2-2-2000000-2-222-2-2-222-222000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ252222-2-2-2-22222222222002-200-2-2-2-222-222-2-2-2000022-2-20000000000002-20000000000000000
χ262222-2-2-2-2222222222200-2200-2-2-2-222-222-2-2-20000-2-222000000000000-220000000000000000
χ272222-2-2-2-2222222-2-2-2-2002-200-2-2-2-2222-2-2222000022-2-2000000000000-220000000000000000
χ282222-2-2-2-2222222-2-2-2-200-2200-2-2-2-2222-2-22220000-2-2220000000000002-20000000000000000
χ292-2-222-22-22-222-2-222-2-200002i−2i2-22-22-2-22-222-2000000002i2i−2i−2i000000000000000000002i−2i0000
χ302-2-222-22-22-222-2-222-2-20000−2i2i2-22-22-2-22-222-200000000−2i−2i2i2i00000000000000000000−2i2i0000
χ312-2-222-22-22-222-2-2-2-22200002i−2i2-22-22-22-22-2-22000000002i2i−2i−2i00000000000000000000−2i2i0000
χ322-2-222-22-22-222-2-2-2-2220000−2i2i2-22-22-22-22-2-2200000000−2i−2i2i2i000000000000000000002i−2i0000
χ332-2-222-2-22-2222-2-222-2-20000002-2-22-222-22-22-200000000000000000000000000000000002i−2i2i−2i
χ342-2-222-2-22-2222-2-222-2-20000002-2-22-222-22-22-20000000000000000000000000000000000−2i2i−2i2i
χ352-2-222-2-22-2222-2-2-2-2220000002-2-22-22-22-22-2200000000000000000000000000000000002-2-22
χ362-2-222-2-22-2222-2-2-2-2220000002-2-22-22-22-22-220000000000000000000000000000000000-222-2
χ372-2-22-222-2-2222-2-222-2-2000000-222-2-22-2-222-220000000000000000000000002-22-20000000000
χ382-2-22-222-2-2222-2-222-2-2000000-222-2-22-2-222-22000000000000000000000000-22-220000000000
χ392-2-22-222-2-2222-2-2-2-222000000-222-2-2222-2-22-20000000000000000000000002i−2i−2i2i0000000000
χ402-2-22-222-2-2222-2-2-2-222000000-222-2-2222-2-22-2000000000000000000000000−2i2i2i−2i0000000000
χ412-2-22-22-222-222-2-222-2-22-20000-22-222-222-2-2-2222-2-20000000000000000002-200000000000000
χ422-2-22-22-222-222-2-222-2-2-220000-22-222-222-2-2-22-2-222000000000000000000-2200000000000000
χ432-2-22-22-222-222-2-2-2-2222-20000-22-222-2-2-2222-222-2-2000000000000000000-2200000000000000
χ442-2-22-22-222-222-2-2-2-222-220000-22-222-2-2-2222-2-2-2220000000000000000002-200000000000000
χ454444444444-1-1-1-10000444444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-1-1-1-1000044-4-4-4-4-1-1-1-1-1-1000000-1-1-1-11111111100000000000000000000000000
χ474444444444-1-1-1-10000-4-444-4-4-1-1-1-1-1-10000001111-1-1-1-1111100000000000000000000000000
χ484444444444-1-1-1-10000-4-4-4-444-1-1-1-1-1-100000011111111-1-1-1-100000000000000000000000000
χ494444-4-4-4-444-1-1-1-10000004-4001111-1-10000005−55−5-1-1115−55−500000000000000000000000000
χ504444-4-4-4-444-1-1-1-10000004-4001111-1-1000000−55−55-1-111−55−5500000000000000000000000000
χ514444-4-4-4-444-1-1-1-1000000-44001111-1-10000005−55−511-1-1−55−5500000000000000000000000000
χ524444-4-4-4-444-1-1-1-1000000-44001111-1-1000000−55−5511-1-15−55−500000000000000000000000000
χ5344-4-40000004-44-44i−4i4i−4i000000000000000000000000000000002+2i−2−2i002−2i−2+2i000000000000000000
χ5444-4-40000004-44-44i−4i4i−4i00000000000000000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000
χ5544-4-40000004-44-4−4i4i−4i4i000000000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000
χ5644-4-40000004-44-4−4i4i−4i4i00000000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000
χ574-44-40000004-4-444i−4i−4i4i0000000000000000000000000000002−2i−2+2i002+2i−2−2i00000000000000000000
χ584-44-40000004-4-444i−4i−4i4i000000000000000000000000000000−2+2i2−2i00−2−2i2+2i00000000000000000000
χ594-44-40000004-4-44−4i4i4i−4i0000000000000000000000000000002+2i−2−2i002−2i−2+2i00000000000000000000
χ604-44-40000004-4-44−4i4i4i−4i000000000000000000000000000000−2−2i2+2i00−2+2i2−2i00000000000000000000
χ614-4-444-44-44-4-1-111000000004i−4i-11-11-110000005−5−55i5−i5i5−i5−i−iii00000000000000000000000000
χ624-4-444-44-44-4-1-111000000004i−4i-11-11-11000000−555−5−i5i5−i5i5−i−iii00000000000000000000000000
χ634-4-444-44-44-4-1-11100000000−4i4i-11-11-110000005−5−55−i5i5−i5i5ii−i−i00000000000000000000000000
χ644-4-444-44-44-4-1-11100000000−4i4i-11-11-11000000−555−5i5−i5i5−i5ii−i−i00000000000000000000000000
χ654-4-44-44-444-4-1-11100004-400001-11-1-11000000-1-111i5−i5−i5i5i5−i5−i5i500000000000000000000000000
χ664-4-44-44-444-4-1-11100004-400001-11-1-11000000-1-111−i5i5i5−i5−i5i5i5−i500000000000000000000000000
χ674-4-44-44-444-4-1-1110000-4400001-11-1-1100000011-1-1i5−i5−i5i5−i5i5i5−i500000000000000000000000000
χ684-4-44-44-444-4-1-1110000-4400001-11-1-1100000011-1-1−i5i5i5−i5i5−i5−i5i500000000000000000000000000
χ69888888-8-8-8-8-2-2-2-20000000000-2-2222200000000000000000000000000000000000000000000
χ708888-8-888-8-8-2-2-2-2000000000022-2-22200000000000000000000000000000000000000000000
χ718-8-888-8-88-88-2-2220000000000-222-22-200000000000000000000000000000000000000000000
χ728-8-88-888-8-88-2-22200000000002-2-222-200000000000000000000000000000000000000000000
χ731616-16-16000000-44-44000000000000000000000000000000000000000000000000000000000000
χ7416-1616-16000000-444-4000000000000000000000000000000000000000000000000000000000000

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