Finite Group Databasebeta

← Group #271674

Character table — Group #271674

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444442244444444888888888888888844444444224444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11-1-11-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-111111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-111111111-1-1
χ91111111111111111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11-111-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1111-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-11111-1-1-11
χ121111111111111111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-111-1-1111-1
χ131111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-1-11-111-1-1-111-1-111-11
χ141111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-111-1-11-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1111111111-1-1-1-1-111-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11-1111111-1-111-1-1-11
χ1722222222222-2-2-2-222222-2-2-2-2-2-200000000000000002200220000-2-200000000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-20000000000000000-2-200-2-200002200000000000000
χ1922222222222-2-2-2-22-2-2-2-222-222-200000000000000002200-2-200002-200000000000000
χ2022222222222-2-2-2-22-2-2-2-222-222-20000000000000000-2-200220000-2200000000000000
χ2122222222-2-2-22222-222-2-222-2-2-2-20000000000000000002200-2-20000-20020000000000
χ2222222222-2-2-22222-222-2-222-2-2-2-2000000000000000000-2-200220000200-20000000000
χ2322222222-2-2-22222-2-2-222-2-2-222-20000000000000000002200-2-20000200-20000000000
χ2422222222-2-2-22222-2-2-222-2-2-222-2000000000000000000-2-200220000-20020000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000002-20002-200000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000-22000-2200000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-2-220000000000000000000000002-2000-2200000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-2-22000000000000000000000000-220002-200000000000
χ2922-22-22-2-22-2-2000022-22-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22i−2i002i−2i00000000002−22−2000000
χ3022-22-22-2-22-2-2000022-22-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−2i2i00−2i2i0000000000−22−22000000
χ3122-22-22-2-22-2-2000022-22-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22i−2i002i−2i0000000000−22−22000000
χ3222-22-22-2-22-2-2000022-22-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−2i2i00−2i2i00000000002−22−2000000
χ3322-22-22-2-22-2-200002-22-22000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22i−2i00−2i2i00000000002−2−22000000
χ3422-22-22-2-22-2-200002-22-22000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−2i2i002i−2i0000000000−222−2000000
χ3522-22-22-2-22-2-200002-22-22000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22i−2i00−2i2i0000000000−222−2000000
χ3622-22-22-2-22-2-200002-22-22000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−2i2i002i−2i00000000002−2−22000000
χ372-2-22-2-22222-22-22-2-2000000200-2000000002i2i−2i−2i2i2i−2i−2i002-2002-2000000000000002i−2i00
χ382-2-22-2-22222-22-22-2-2000000200-2000000002i2i−2i−2i2i2i−2i−2i00-2200-2200000000000000−2i2i00
χ392-2-22-2-22222-22-22-2-2000000200-200000000−2i−2i2i2i−2i−2i2i2i002-2002-200000000000000−2i2i00
χ402-2-22-2-22222-22-22-2-2000000200-200000000−2i−2i2i2i−2i−2i2i2i00-2200-22000000000000002i−2i00
χ412-2-22-2-222-2-222-22-22000000-200222-2-222-2-200000000002-200-220000000000002-20000
χ422-2-22-2-222-2-222-22-22000000-200222-2-222-2-20000000000-22002-2000000000000-220000
χ432-2-22-2-222-2-222-22-22000000-2002-2-222-2-22200000000002-200-22000000000000-220000
χ442-2-22-2-222-2-222-22-22000000-2002-2-222-2-2220000000000-22002-20000000000002-20000
χ45444-4-4-4-440000000000004i−4i00002-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ46444-4-4-4-440000000000004i−4i0000-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ47444-4-4-4-44000000000000−4i4i00002-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ48444-4-4-4-44000000000000−4i4i0000-22-22-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ4944-44-44-4-4-4440000-44-4-44000000000000000000000000000000000000000000000000
χ5044-44-44-4-4-4440000-4-444-4000000000000000000000000000000000000000000000000
χ5144-4-44-44-400044-4-4000000000000000000022−2222−22−2222−222200000000000000000000000000
χ5244-4-44-44-400044-4-40000000000000000000−2222−222222−2222−2200000000000000000000000000
χ5344-4-44-44-4000-4-444000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ5444-4-44-44-4000-4-44400000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ554-4444-4-4-44-440000-40000000000000000002222−22−22−22−22222200000000000000000000000000
χ564-4444-4-4-44-440000-4000000000000000000−22−2222222222−22−2200000000000000000000000000
χ574-4444-4-4-4-44-40000400000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ584-4444-4-4-4-44-4000040000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ594-44-4-444-40004-4-4400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ604-44-4-444-40004-4-440000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000
χ614-44-4-444-4000-444-4000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ624-44-4-444-4000-444-400000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ634-4-44-4-44444-4-44-44-4000000-4004000000000000000000000000000000000000000000
χ644-4-44-4-444-4-44-44-444000000400-4000000000000000000000000000000000000000000
χ654-4-4-444-440000000000000004-402-2-222-2-222-2-222-2-2200000000000000000000000000
χ664-4-4-444-440000000000000004-40-222-2-222-2-222-2-222-200000000000000000000000000
χ674-4-4-444-44000000000000000-4402-2-222-2-22-222-2-222-200000000000000000000000000
χ684-4-4-444-44000000000000000-440-222-2-222-22-2-222-2-2200000000000000000000000000

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