Finite Group Databasebeta

← Group #13022800

Character table — Group #13022800

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444444444555588888888888888881010101010101616161616161616202020204040404040404040404040404040404040404040
order12222244445888810101020202020222288881010202040404040404040402244444040404040404040888844444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1ii−i−i
χ61111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1−i−iii
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−i−i−iiiii1111ii−i−i
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiiiii−i−i−i−i1111−i−iii
χ911111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1
χ1011111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111
χ1111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-1-1-1
χ1211111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111
χ1311111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii-1-111−i−iii
χ1411111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−i-1-111ii−i−i
χ1511111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i11-1-1−i−iii
χ1611111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iii11-1-1ii−i−i
χ17222222-2-2-2-220000222-2-2-2-22222000022-2-20000000022-2-2-2-200000000000000000000000000002i−2i2i−2i
χ18222222-2-2-2-220000222-2-2-2-22222000022-2-20000000022-2-2-2-20000000000000000000000000000−2i2i−2i2i
χ19222222-2-2-2-220000222-2-2-2-2-2-2-2-2000022-2-200000000-2-2222200000000000000000000000000002-2-22
χ20222222-2-2-2-220000222-2-2-2-2-2-2-2-2000022-2-200000000-2-222220000000000000000000000000000-222-2
χ212222-2-222-2-2222-2-2222-2-2-2-222220000-2-2222222-2-2-2-2-2-22-2-220000000022-2-200000000000000000000
χ222222-2-222-2-2222-2-2222-2-2-2-2-2-2-2-20000-2-2222222-2-2-2-222-222-200000000-2-22200000000000000000000
χ232222-2-222-2-22-2-222222-2-2-2-222220000-2-222-2-2-2-22222-2-22-2-2200000000-2-22200000000000000000000
χ242222-2-222-2-22-2-222222-2-2-2-2-2-2-2-20000-2-222-2-2-2-2222222-222-20000000022-2-200000000000000000000
χ252222-2-2-2-22220000222222222220000-2-2-2-200000000-2-2-222-20000000000002-22-20000000000000000
χ262222-2-2-2-22220000222222222220000-2-2-2-200000000-2-2-222-2000000000000-22-220000000000000000
χ272222-2-2-2-222200002222222-2-2-2-20000-2-2-2-200000000222-2-220000000000002i−2i−2i2i0000000000000000
χ282222-2-2-2-222200002222222-2-2-2-20000-2-2-2-200000000222-2-22000000000000−2i2i2i−2i0000000000000000
χ292-2-222-22-22-220000-2-2222-2-22-2-22002i−2i2-22-2000000002-222-2-200002i2i−2i−2i0000000000000000002i−2i0000
χ302-2-222-22-22-220000-2-2222-2-22-2-2200−2i2i2-22-2000000002-222-2-20000−2i−2i2i2i000000000000000000−2i2i0000
χ312-2-222-22-22-220000-2-2222-2-2-222-2002i−2i2-22-200000000-22-2-22200002i2i−2i−2i000000000000000000−2i2i0000
χ322-2-222-22-22-220000-2-2222-2-2-222-200−2i2i2-22-200000000-22-2-2220000−2i−2i2i2i0000000000000000002i−2i0000
χ332-2-222-2-22-2220000-2-22-2-2222-2-2200002-2-22000000002-2-2-22200000000000000002-2002-20000000000
χ342-2-222-2-22-2220000-2-22-2-2222-2-2200002-2-22000000002-2-2-2220000000000000000-2200-220000000000
χ352-2-222-2-22-2220000-2-22-2-222-222-200002-2-2200000000-2222-2-200000000000000002i−2i00−2i2i0000000000
χ362-2-222-2-22-2220000-2-22-2-222-222-200002-2-2200000000-2222-2-20000000000000000−2i2i002i−2i0000000000
χ372-2-22-222-2-2220000-2-22-2-2222-2-222i−2i00-222-200000000-222-22-22i2i−2i−2i000000000000000000002i−2i000000
χ382-2-22-222-2-2220000-2-22-2-2222-2-22−2i2i00-222-200000000-222-22-2−2i−2i2i2i00000000000000000000−2i2i000000
χ392-2-22-222-2-2220000-2-22-2-222-222-22i−2i00-222-2000000002-2-22-222i2i−2i−2i00000000000000000000−2i2i000000
χ402-2-22-222-2-2220000-2-22-2-222-222-2−2i2i00-222-2000000002-2-22-22−2i−2i2i2i000000000000000000002i−2i000000
χ412-2-22-22-222-220000-2-2222-2-22-2-220000-22-2200000000-22-22-220000000000000000002-2002-200000000
χ422-2-22-22-222-220000-2-2222-2-22-2-220000-22-2200000000-22-22-22000000000000000000-2200-2200000000
χ432-2-22-22-222-220000-2-2222-2-2-222-20000-22-22000000002-22-22-20000000000000000002i−2i00−2i2i00000000
χ442-2-22-22-222-220000-2-2222-2-2-222-20000-22-22000000002-22-22-2000000000000000000−2i2i002i−2i00000000
χ454444444444-14444-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1000000000000000000000000
χ464444444444-14444-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000011111111000000000000000000000000
χ474444444444-1-4-4-4-4-1-1-1-1-1-1-1000044-4-4-1-1-1-111111111000000-1-1-1-11111000000000000000000000000
χ484444444444-1-4-4-4-4-1-1-1-1-1-1-10000-4-444-1-1-1-1111111110000001111-1-1-1-1000000000000000000000000
χ494444-4-444-4-4-144-4-4-1-1-111110000000011-1-1-1-1-1-11111000000i5−i5i5−i5i5−i5i5−i5000000000000000000000000
χ504444-4-444-4-4-144-4-4-1-1-111110000000011-1-1-1-1-1-11111000000−i5i5−i5i5−i5i5−i5i5000000000000000000000000
χ514444-4-444-4-4-1-4-444-1-1-111110000000011-1-11111-1-1-1-1000000i5−i5i5−i5−i5i5−i5i5000000000000000000000000
χ524444-4-444-4-4-1-4-444-1-1-111110000000011-1-11111-1-1-1-1000000−i5i5−i5i5i5−i5i5−i5000000000000000000000000
χ5344-4-400000040022−224-4-4000044-4-40000000000002222−22−22000000000000000022−2200000000000000000000
χ5444-4-400000040022−224-4-40000-4-4440000000000002222−22−220000000000000000−222200000000000000000000
χ5544-4-4000000400−22224-4-4000044-4-4000000000000−22−2222220000000000000000−222200000000000000000000
χ5644-4-4000000400−22224-4-40000-4-444000000000000−22−222222000000000000000022−2200000000000000000000
χ574-44-4000000422−2200-44-400004-44-4000000002222−22−2200000000000000000022−220000000000000000000000
χ584-44-4000000422−2200-44-40000-44-44000000002222−22−22000000000000000000−22220000000000000000000000
χ594-44-40000004−222200-44-400004-44-400000000−22−222222000000000000000000−22220000000000000000000000
χ604-44-40000004−222200-44-40000-44-4400000000−22−22222200000000000000000022−220000000000000000000000
χ614-4-444-44-44-4-1000011-1-1-1110000004i−4i-11-11i5−i5i5−i5i5−i5i5−i50000005−5−55−i−iii000000000000000000000000
χ624-4-444-44-44-4-1000011-1-1-1110000004i−4i-11-11−i5i5−i5i5−i5i5−i5i5000000−555−5−i−iii000000000000000000000000
χ634-4-444-44-44-4-1000011-1-1-111000000−4i4i-11-11i5−i5i5−i5i5−i5i5−i5000000−555−5ii−i−i000000000000000000000000
χ644-4-444-44-44-4-1000011-1-1-111000000−4i4i-11-11−i5i5−i5i5−i5i5−i5i50000005−5−55ii−i−i000000000000000000000000
χ654-4-44-444-4-44-1000011-111-1-100004i−4i001-1-11i5−i5i5−i5−i5i5−i5i5000000−i−iii−555−5000000000000000000000000
χ664-4-44-444-4-44-1000011-111-1-100004i−4i001-1-11−i5i5−i5i5i5−i5i5−i5000000−i−iii5−5−55000000000000000000000000
χ674-4-44-444-4-44-1000011-111-1-10000−4i4i001-1-11i5−i5i5−i5−i5i5−i5i5000000ii−i−i5−5−55000000000000000000000000
χ684-4-44-444-4-44-1000011-111-1-10000−4i4i001-1-11−i5i5−i5i5i5−i5i5−i5000000ii−i−i−555−5000000000000000000000000
χ69888888-8-8-8-8-20000-2-2-2222200000000-2-2220000000000000000000000000000000000000000000000
χ708888-8-8-8-888-20000-2-2-2-2-2-2-20000000022220000000000000000000000000000000000000000000000
χ7188-8-8000000-20042−42-2222i5−2i52i5−2i5000000000000i10−i10−i10i10−2−22200000000000000000000000000000000000000
χ7288-8-8000000-20042−42-222−2i52i5−2i52i5000000000000−i10i10i10−i10−2−22200000000000000000000000000000000000000
χ7388-8-8000000-200−4242-2222i5−2i52i5−2i5000000000000−i10i10i10−i1022−2−200000000000000000000000000000000000000
χ7488-8-8000000-200−4242-222−2i52i5−2i52i5000000000000i10−i10−i10i1022−2−200000000000000000000000000000000000000
χ758-88-8000000-242−42002-222i5−2i5−2i52i5000000000000−2−222−i10i10i10−i1000000000000000000000000000000000000000
χ768-88-8000000-242−42002-22−2i52i52i5−2i5000000000000−2−222i10−i10−i10i1000000000000000000000000000000000000000
χ778-88-8000000-2−4242002-222i5−2i5−2i52i500000000000022−2−2i10−i10−i10i1000000000000000000000000000000000000000
χ788-88-8000000-2−4242002-22−2i52i52i5−2i500000000000022−2−2−i10i10i10−i1000000000000000000000000000000000000000
χ798-8-888-8-88-88-2000022-222-2-200000000-222-20000000000000000000000000000000000000000000000
χ808-8-88-88-888-8-2000022-2-2-222000000002-22-20000000000000000000000000000000000000000000000

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