Finite Group Databasebeta

← Group #72260781

Character table — Group #72260781

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222222222444444888888888816161616161616161616161616161616161616161616161632323232323232323232323232323232
order1222222222444422224422224444442222444444444444888888884444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−iii−i−iii−i−i
χ101111111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−iii−i−iii
χ111111111111-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111iiii−i−i−i−i1-1-11−i−iiiii−i−i−i−iii
χ121111111111-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111−i−i−i−iiiii1-1-11ii−i−i−i−iiiii−i−i
χ131111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i-111-1−i−iii−i−iiiii−i−i
χ141111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii-111-1ii−i−iii−i−i−i−iii
χ151111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-11-11ii−i−i−i−iii−i−iii
χ161111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-11-11−i−iiiii−i−iii−i−i
χ172222222222222222-2-2222-2-2-2-2-22-22-200220022000000000000000000-2-2000000000000
χ182222222222222222-2-2222-2-2-2-2-22-22-200-2-200-2-200000000000000000022000000000000
χ1922222222222222-2-22222-22-2-2-2-2-22-22220022000000000000000000-2-200000000000000
χ2022222222222222-2-22222-22-2-2-2-2-22-22-2-200-2-20000000000000000002200000000000000
χ2122222222222222-2-2-2-222-2-22222-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ2222222222222222-2-2-2-222-2-22222-2-2-2-200000000-2-222-2-222000000000000000000000000
χ232222222222-2-2-2-222-2-2-2-22-222-2-2-22-22002200-2-2000000000000000000-22000000000000
χ242222222222-2-2-2-222-2-2-2-22-222-2-2-22-2200-2-200220000000000000000002-2000000000000
χ252222222222-2-2-2-2-2-222-2-2-2222-2-22-22-22200-2-2000000000000000000-2200000000000000
χ262222222222-2-2-2-2-2-222-2-2-2222-2-22-22-2-2-200220000000000000000002-200000000000000
χ272222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000022-2-2-2-222000000000000000000000000
χ282222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000-2-22222-2-2000000000000000000000000
χ292222-2-2-2-22222-2-222222-2-2-2-222-2-2-22200000000000000000000000000002-22-200000000
χ302222-2-2-2-22222-2-222222-2-2-2-222-2-2-2220000000000000000000000000000-22-2200000000
χ312222-2-2-2-22222-2-222-2-22-2-222-2-22-222-2000000000000000000000000000000002i−2i2i−2i0000
χ322222-2-2-2-22222-2-222-2-22-2-222-2-22-222-200000000000000000000000000000000−2i2i−2i2i0000
χ332222-2-2-2-22222-2-2-2-2222-22-22-2-222-2-220000000000000000000000000000000000002i−2i2i−2i
χ342222-2-2-2-22222-2-2-2-2222-22-22-2-222-2-22000000000000000000000000000000000000−2i2i−2i2i
χ352222-2-2-2-22222-2-2-2-2-2-22-222-222-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ362222-2-2-2-22222-2-2-2-2-2-22-222-222-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ372222-2-2-2-222-2-2222222-22-2-22-22-222-2-200000000000000000000000000002i−2i−2i2i00000000
χ382222-2-2-2-222-2-2222222-22-2-22-22-222-2-20000000000000000000000000000−2i2i2i−2i00000000
χ392222-2-2-2-222-2-22222-2-2-22-22-22-222-2-22000000000000000000000000000000002-2-220000
χ402222-2-2-2-222-2-22222-2-2-22-22-22-222-2-2200000000000000000000000000000000-222-20000
χ412222-2-2-2-222-2-222-2-222-222-2-22-22-222-20000000000000000000000000000000000002-2-22
χ422222-2-2-2-222-2-222-2-222-222-2-22-22-222-2000000000000000000000000000000000000-222-2
χ432222-2-2-2-222-2-222-2-2-2-2-22222-22-2-2-222000000000000000022-2-2-2-2220000000000000000
χ442222-2-2-2-222-2-222-2-2-2-2-22222-22-2-2-2220000000000000000-2-22222-2-20000000000000000
χ45444444-4-4-4-444440000-4-4000000000000000000000000002-22-22-22-20000000000000000
χ46444444-4-4-4-444440000-4-400000000000000000000000000-22-22-22-220000000000000000
χ47444444-4-4-4-4-4-4-4-4000044000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ48444444-4-4-4-4-4-4-4-400004400000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ494444-4-444-4-444-4-40000-44000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ504444-4-444-4-444-4-40000-4400000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ514444-4-444-4-4-4-44400004-4000000000000000000000000002-2-22-222-20000000000000000
χ524444-4-444-4-4-4-44400004-400000000000000000000000000-222-22-2-220000000000000000
χ5344-4-44-400004i−4i4i−4i00000000000000002-22-22i−2i2i−2i002-2002i−2i000000000000000000000000
χ5444-4-44-400004i−4i4i−4i00000000000000002-2-222i−2i−2i2i00-2200−2i2i000000000000000000000000
χ5544-4-44-400004i−4i4i−4i0000000000000000-222-2−2i2i2i−2i00-2200−2i2i000000000000000000000000
χ5644-4-44-400004i−4i4i−4i0000000000000000-22-22−2i2i−2i2i002-2002i−2i000000000000000000000000
χ5744-4-44-40000−4i4i−4i4i00000000000000002-22-2−2i2i−2i2i002-200−2i2i000000000000000000000000
χ5844-4-44-40000−4i4i−4i4i00000000000000002-2-22−2i2i2i−2i00-22002i−2i000000000000000000000000
χ5944-4-44-40000−4i4i−4i4i0000000000000000-222-22i−2i−2i2i00-22002i−2i000000000000000000000000
χ6044-4-44-40000−4i4i−4i4i0000000000000000-22-222i−2i2i−2i002-200−2i2i000000000000000000000000
χ6188-8-8-8800008i−8i−8i8i00000000000000000000000000000000000000000000000000000000
χ6288-8-8-880000−8i8i8i−8i00000000000000000000000000000000000000000000000000000000
χ638-88-800008-80000008-80000000000000000000000000000000000000000000000000000
χ648-88-800008-8000000-880000000000000000000000000000000000000000000000000000
χ658-88-80000-8800008-8000000000000000000000000000000000000000000000000000000
χ668-88-80000-880000-88000000000000000000000000000000000000000000000000000000
χ678-8-88008-800000000000000000000000000000000004-400000000000000000000000000
χ688-8-88008-80000000000000000000000000000000000-4400000000000000000000000000
χ698-8-8800-880000000000000000000000000000004-4000000000000000000000000000000
χ708-8-8800-88000000000000000000000000000000-44000000000000000000000000000000

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