Finite Group Databasebeta

← Group #269847

Character table — Group #269847

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1111-1-111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1111111111-1-1111-1-1-1-1-1-11
χ17222222222-2-2222-2-22222-20000-22222000022-2-20000-2-200000000000000-2000000000000
χ18222222222-2-2222-2-22222-20000-2-2-2-2-20000-2-2-2-2000022000000000000002000000000000
χ19222222222-2-2222-2-2-2-2-2-2-20000-222220000-2-2220000-2-2000000000000002000000000000
χ20222222222-2-2222-2-2-2-2-2-2-20000-2-2-2-2-20000222200002200000000000000-2000000000000
χ2122222222-222-2-2-2220000-22222-2000022220000-2-222000000-2-200000000000-2000000000
χ2222222222-222-2-2-2220000-22222-20000-2-2-2-20000-2-2-2-200000022000000000002000000000
χ2322222222-222-2-2-2220000-2-2-2-2-2-200002222000022-2-2000000-2-2000000000002000000000
χ2422222222-222-2-2-2220000-2-2-2-2-2-20000-2-2-2-2000022220000002200000000000-2000000000
χ2522-2-2-222-202-20002-2000002i2i−2i−2i0i2i2−i2−i222-2-20000002i−2ii2−i222−2−2000000i2i2−i2−i2000000002−2000
χ2622-2-2-222-202-20002-2000002i2i−2i−2i0i2i2−i2−i2-2-222000000−2i2ii2−i222−2−2000000−i2−i2i2i200000000−22000
χ2722-2-2-222-202-20002-2000002i2i−2i−2i0−i2−i2i2i222-2-20000002i−2i−i2i2−2−222000000−i2−i2i2i200000000−22000
χ2822-2-2-222-202-20002-2000002i2i−2i−2i0−i2−i2i2i2-2-222000000−2i2i−i2i2−2−222000000i2i2−i2−i2000000002−2000
χ2922-2-2-222-202-20002-200000−2i−2i2i2i0i2i2−i2−i222-2-2000000−2i2ii2−i2−2−222000000i2i2−i2−i200000000−22000
χ3022-2-2-222-202-20002-200000−2i−2i2i2i0i2i2−i2−i2-2-2220000002i−2ii2−i2−2−222000000−i2−i2i2i2000000002−2000
χ3122-2-2-222-202-20002-200000−2i−2i2i2i0−i2−i2i2i222-2-2000000−2i2i−i2i222−2−2000000−i2−i2i2i2000000002−2000
χ3222-2-2-222-202-20002-200000−2i−2i2i2i0−i2−i2i2i2-2-2220000002i−2i−i2i222−2−2000000i2i2−i2−i200000000−22000
χ332-222-22-2-2-200-2220022-2-20000002i−2i2i−2i2−22−22i−2i0000000000002−222−2−2i2−i2i2−i20000000000i2−i20
χ342-222-22-2-2-200-2220022-2-20000002i−2i2i−2i−22−222i−2i000000000000−22−2−222−i2i2−i2i20000000000−i2i20
χ352-222-22-2-2-200-2220022-2-2000000−2i2i−2i2i2−22−2−2i2i0000000000002−222−2−2−i2i2−i2i20000000000−i2i20
χ362-222-22-2-2-200-2220022-2-2000000−2i2i−2i2i−22−22−2i2i000000000000−22−2−222i2−i2i2−i20000000000i2−i20
χ372-222-22-2-2-200-22200-2-2220000002i−2i2i−2i2−22−2−2i2i0000000000002−2−2−222i2−i2i2−i20000000000−i2i20
χ382-222-22-2-2-200-22200-2-2220000002i−2i2i−2i−22−22−2i2i000000000000−2222−2−2−i2i2−i2i20000000000i2−i20
χ392-222-22-2-2-200-22200-2-222000000−2i2i−2i2i2−22−22i−2i0000000000002−2−2−222−i2i2−i2i20000000000i2−i20
χ402-222-22-2-2-200-22200-2-222000000−2i2i−2i2i−22−222i−2i000000000000−2222−2−2i2−i2i2−i20000000000−i2i20
χ412-22-2-2-222222-22-2-2-22-22-220000-200000000002-20000002i−2i2i−2i000000000002i−2i0000000000
χ422-22-2-2-222222-22-2-2-22-22-220000-200000000002-2000000−2i2i−2i2i00000000000−2i2i0000000000
χ432-22-2-2-222222-22-2-2-2-22-2220000-20000000000-220000002i−2i2i−2i00000000000−2i2i0000000000
χ442-22-2-2-222222-22-2-2-2-22-2220000-20000000000-22000000−2i2i−2i2i000000000002i−2i0000000000
χ452-22-2-2-2222-2-2-22-2222-22-2-22-22-220000000000-222-200000000000000000000002-20000000
χ462-22-2-2-2222-2-2-22-2222-22-2-2-22-2220000000000-22-220000000000000000000000-220000000
χ472-22-2-2-2222-2-2-22-222-22-22-22-22-2200000000002-22-20000000000000000000000-220000000
χ482-22-2-2-2222-2-2-22-222-22-22-2-22-22200000000002-2-2200000000000000000000002-20000000
χ492-22-2-2-222-2-2-22-2222000022-22-2-2000000000000-2200000000002-22-200000000002-200000
χ502-22-2-2-222-2-2-22-2222000022-22-2-2000000000000-220000000000-22-220000000000-2200000
χ512-22-2-2-222-2-2-22-222200002-22-22-20000000000002-200000000002-22-20000000000-2200000
χ522-22-2-2-222-2-2-22-222200002-22-22-20000000000002-20000000000-22-2200000000002-200000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-4400-4-4400000000000000000000000000000000000022−22−222200000000000000000
χ55444-44-4-4-4400-4-44000000000000000000000000000000000000−222222−2200000000000000000
χ56444-44-4-4-4-40044-4004-4-44000000000000000000000000000000000000000000000000000
χ57444-44-4-4-4-40044-400-444-4000000000000000000000000000000000000000000000000000
χ5844-4-4-444-40-44000-4400000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ5944-4-4-444-40-44000-440000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ604-444-44-4-44004-4-4000000000000000022−2222−2200000000000000−2222000000000000000000000
χ614-444-44-4-44004-4-40000000000000000−2222−22220000000000000022−22000000000000000000000
χ624-44-4-4-444-4444-44-4-40000-400004000000000000000000000000000000000000000000000
χ634-4-444-44-404-4000-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ644-4-444-44-404-4000-440000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ654-4-444-44-40-440004-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ664-4-444-44-40-440004-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-4-4-444-4400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ684-4-4-444-4400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ694-4-4-444-44000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ704-4-4-444-44000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ7188-88-8-8-88000000000000000000000000000000000000000000000000000000000000000

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