Finite Group Databasebeta

← Group #269752

Character table — Group #269752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ5111111111111111111111-1-1-1-1111111111-1-111-1-1111111-1-1-1-111111111-1-1-11-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111-111-1-111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-111-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-1-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-111111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111-1-11-1-111-1-1-1-11
χ172222222222-2-2-222-22222-20000-222220000002200-2-200-2-2000000000000000-2000000000
χ182222222222-2-2-222-22222-20000-2-2-2-2-2000000-2-200-2-200220000000000000002000000000
χ192222222222-2-2-222-2-2-2-2-2-20000-22222000000-2-2002200-2-20000000000000002000000000
χ202222222222-2-2-222-2-2-2-2-2-20000-2-2-2-2-20000002200220022000000000000000-2000000000
χ2122222222-2-2222-2-220000-22222-200002222-2-2002200-2-200000000000000-2000000000000
χ2222222222-2-2222-2-220000-22222-20000-2-2-2-2-2-200-2-20022000000000000002000000000000
χ2322222222-2-2222-2-220000-2-2-2-2-2-2000022222200-2-200-2-2000000000000002000000000000
χ2422222222-2-2222-2-220000-2-2-2-2-2-20000-2-2-2-2220022002200000000000000-2000000000000
χ2522-22-2-2-2200-22200-20000022-2-20i2i2−i2−i22i2i−2i−2i00002i−2i0000i2−i2i2i2−i2−i2000022−2−200000000002−20
χ2622-22-2-2-2200-22200-20000022-2-20i2i2−i2−i2−2i−2i2i2i0000−2i2i0000i2−i2i2i2−i2−i20000−2−2220000000000−220
χ2722-22-2-2-2200-22200-20000022-2-20−i2−i2i2i22i2i−2i−2i00002i−2i0000−i2i2−i2−i2i2i20000−2−2220000000000−220
χ2822-22-2-2-2200-22200-20000022-2-20−i2−i2i2i2−2i−2i2i2i0000−2i2i0000−i2i2−i2−i2i2i2000022−2−200000000002−20
χ2922-22-2-2-2200-22200-200000-2-2220i2i2−i2−i22i2i−2i−2i0000−2i2i0000i2−i2−i2−i2i2i2000022−2−20000000000−220
χ3022-22-2-2-2200-22200-200000-2-2220i2i2−i2−i2−2i−2i2i2i00002i−2i0000i2−i2−i2−i2i2i20000−2−22200000000002−20
χ3122-22-2-2-2200-22200-200000-2-2220−i2−i2i2i22i2i−2i−2i0000−2i2i0000−i2i2i2i2−i2−i20000−2−22200000000002−20
χ3222-22-2-2-2200-22200-200000-2-2220−i2−i2i2i2−2i−2i2i2i00002i−2i0000−i2i2i2i2−i2−i2000022−2−20000000000−220
χ332-2-22-222-22-20002-2022-2-20000002i−2i2i−2ii2−i2i2−i2002i−2i0000i2−i2000000i2i2−i2−i22−22−2000000002−2000
χ342-2-22-222-22-20002-2022-2-20000002i−2i2i−2i−i2i2−i2i2002i−2i0000−i2i2000000−i2−i2i2i2−22−2200000000−22000
χ352-2-22-222-22-20002-2022-2-2000000−2i2i−2i2ii2−i2i2−i200−2i2i0000i2−i2000000i2i2−i2−i2−22−2200000000−22000
χ362-2-22-222-22-20002-2022-2-2000000−2i2i−2i2i−i2i2−i2i200−2i2i0000−i2i2000000−i2−i2i2i22−22−2000000002−2000
χ372-2-22-222-22-20002-20-2-2220000002i−2i2i−2ii2−i2i2−i200−2i2i0000i2−i2000000−i2−i2i2i22−22−200000000−22000
χ382-2-22-222-22-20002-20-2-2220000002i−2i2i−2i−i2i2−i2i200−2i2i0000−i2i2000000i2i2−i2−i2−22−22000000002−2000
χ392-2-22-222-22-20002-20-2-222000000−2i2i−2i2ii2−i2i2−i2002i−2i0000i2−i2000000−i2−i2i2i2−22−22000000002−2000
χ402-2-22-222-22-20002-20-2-222000000−2i2i−2i2i−i2i2−i2i2002i−2i0000−i2i2000000i2i2−i2−i22−22−200000000−22000
χ412-2-2-22-222222-22-2-2-2000022-22-2-2000000002-2000000000000002i−2i2i−2i000002i−2i0000000000
χ422-2-2-22-222222-22-2-2-2000022-22-2-2000000002-200000000000000−2i2i−2i2i00000−2i2i0000000000
χ432-2-2-22-222222-22-2-2-200002-22-22-200000000-22000000000000002i−2i2i−2i00000−2i2i0000000000
χ442-2-2-22-222222-22-2-2-200002-22-22-200000000-2200000000000000−2i2i−2i2i000002i−2i0000000000
χ452-2-2-22-222-2-22-2222-22-22-2-22-22-2200000000-2200002-200000000000000000000002-200000
χ462-2-2-22-222-2-22-2222-22-22-2-2-22-222000000002-200002-20000000000000000000000-2200000
χ472-2-2-22-222-2-22-2222-2-22-22-22-22-2200000000-220000-220000000000000000000000-2200000
χ482-2-2-22-222-2-22-2222-2-22-22-2-22-222000000002-20000-2200000000000000000000002-200000
χ492-2-2-22-222-2-2-22-22222-22-220000-200000000000000-2200002-22-20000000000002-20000000
χ502-2-2-22-222-2-2-22-22222-22-220000-200000000000000-220000-22-22000000000000-220000000
χ512-2-2-22-222-2-2-22-2222-22-2220000-2000000000000002-200002-22-2000000000000-220000000
χ522-2-2-22-222-2-2-22-2222-22-2220000-2000000000000002-20000-22-220000000000002-20000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-44-44-4000-440000000000000000000000000000000000022−22−222200000000000000000
χ55444-4-4-44-44-4000-4400000000000000000000000000000000000−222222−2200000000000000000
χ56444-4-4-44-4-440004-404-4-44000000000000000000000000000000000000000000000000000
χ57444-4-4-44-4-440004-40-444-4000000000000000000000000000000000000000000000000000
χ5844-44-4-4-44004-4-400400000000002i22i2−2i2−2i200000000000000−2i22i20000000000000000000000000
χ5944-44-4-4-44004-4-40040000000000−2i2−2i22i22i2000000000000002i2−2i20000000000000000000000000
χ604-4444-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ614-4444-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ624-4444-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ634-4444-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ644-44-4-44-440044-400-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ654-44-4-44-440044-400-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ664-44-4-44-4400-4-44004000004-4-440000000000000000000000000000000000000000000000
χ674-44-4-44-4400-4-4400400000-444-40000000000000000000000000000000000000000000000
χ684-4-44-444-4-44000-440000000000000002i2−2i22i2−2i200000000−2i22i2000000000000000000000000000
χ694-4-44-444-4-44000-44000000000000000−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000
χ704-4-4-44-44444-44-4-4-440000-400004000000000000000000000000000000000000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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