Finite Group Databasebeta

← Group #280048

Character table — Group #280048

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882224444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-1-111-1-1-1-1-1
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
χ5111111111111111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-111-1-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-111111-1-111-1-1-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-11-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-111-1111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111111-1-1-1-1111-1-1-1-11
χ172222222222-2-22-2-222222-20000-200002222000022-2-2000000-2-200000000-2000000000000
χ182222222222-2-22-2-222222-20000-20000-2-2-2-20000-2-2-2-200000022000000002000000000000
χ192222222222-2-22-2-22-2-2-2-2-20000-2000022220000-2-222000000-2-2000000002000000000000
χ202222222222-2-22-2-22-2-2-2-2-20000-20000-2-2-2-2000022220000002200000000-2000000000000
χ2122222222-2-222-222-20000-22222-222220000-2-2220000-2-20000000000000000000-20000000
χ2222222222-2-222-222-20000-22222-2-2-2-2-20000-2-2-2-2000022000000000000000000020000000
χ2322222222-2-222-222-20000-2-2-2-2-2-22222000022-2-20000-2-2000000000000000000020000000
χ2422222222-2-222-222-20000-2-2-2-2-2-2-2-2-2-2000022220000220000000000000000000-20000000
χ2522-2-22-22-2002-202-200000022-2-202i2i−2i−2ii2i2−i2−i2002i−2i0000000000i2−i2i2i2−i2−i222−2−200000000002−20
χ2622-2-22-22-2002-202-200000022-2-202i2i−2i−2i−i2−i2i2i2002i−2i0000000000−i2i2−i2−i2i2i2−2−2220000000000−220
χ2722-2-22-22-2002-202-200000022-2-20−2i−2i2i2ii2i2−i2−i200−2i2i0000000000i2−i2i2i2−i2−i2−2−2220000000000−220
χ2822-2-22-22-2002-202-200000022-2-20−2i−2i2i2i−i2−i2i2i200−2i2i0000000000−i2i2−i2−i2i2i222−2−200000000002−20
χ2922-2-22-22-2002-202-2000000-2-22202i2i−2i−2ii2i2−i2−i200−2i2i0000000000i2−i2−i2−i2i2i222−2−20000000000−220
χ3022-2-22-22-2002-202-2000000-2-22202i2i−2i−2i−i2−i2i2i200−2i2i0000000000−i2i2i2i2−i2−i2−2−22200000000002−20
χ3122-2-22-22-2002-202-2000000-2-2220−2i−2i2i2ii2i2−i2−i2002i−2i0000000000i2−i2−i2−i2i2i2−2−22200000000002−20
χ3222-2-22-22-2002-202-2000000-2-2220−2i−2i2i2i−i2−i2i2i2002i−2i0000000000−i2i2i2i2−i2−i222−2−20000000000−220
χ332-22-22-2-222200-200-22i2i−2i−2i0000002−22−22-22-200002i−2i002−2i2i2−i2−i20000002−22−200000000i2−i2000
χ342-22-22-2-222200-200-22i2i−2i−2i0000002−22−2-22-220000−2i2i002−2i2i2−i2−i2000000−22−2200000000−i2i2000
χ352-22-22-2-222200-200-22i2i−2i−2i000000−22−222-22-200002i−2i00−22−i2−i2i2i2000000−22−2200000000−i2i2000
χ362-22-22-2-222200-200-22i2i−2i−2i000000−22−22-22-220000−2i2i00−22−i2−i2i2i20000002−22−200000000i2−i2000
χ372-22-22-2-222200-200-2−2i−2i2i2i0000002−22−22-22-20000−2i2i002−2−i2−i2i2i20000002−22−200000000−i2i2000
χ382-22-22-2-222200-200-2−2i−2i2i2i0000002−22−2-22-2200002i−2i002−2−i2−i2i2i2000000−22−2200000000i2−i2000
χ392-22-22-2-222200-200-2−2i−2i2i2i000000−22−222-22-20000−2i2i00−22i2i2−i2−i2000000−22−2200000000i2−i2000
χ402-22-22-2-222200-200-2−2i−2i2i2i000000−22−22-22-2200002i−2i00−22i2i2−i2−i20000002−22−200000000−i2i2000
χ412-22-2-222-22-2222-2-2-22i−2i2i−2i-22-22-22000000002-200002i−2i00000000000000000000002i−2i00000
χ422-22-2-222-22-2222-2-2-22i−2i2i−2i-2-22-22200000000-2200002i−2i0000000000000000000000−2i2i00000
χ432-22-2-222-22-2222-2-2-2−2i2i−2i2i-22-22-22000000002-20000−2i2i0000000000000000000000−2i2i00000
χ442-22-2-222-22-2222-2-2-2−2i2i−2i2i-2-22-22200000000-220000−2i2i00000000000000000000002i−2i00000
χ452-22-2-222-22-2-2-2222-22i−2i2i−2i20000-200000000000000−2i2i000000002i−2i2i−2i000002-20000000000
χ462-22-2-222-22-2-2-2222-22i−2i2i−2i20000-200000000000000−2i2i00000000−2i2i−2i2i00000-220000000000
χ472-22-2-222-22-2-2-2222-2−2i2i−2i2i20000-2000000000000002i−2i000000002i−2i2i−2i00000-220000000000
χ482-22-2-222-22-2-2-2222-2−2i2i−2i2i20000-2000000000000002i−2i00000000−2i2i−2i2i000002-20000000000
χ492-22-2-222-2-2222-2-2-22000022-22-2-200000000-22000000002i−2i2i−2i00000000000002i−2i00000000
χ502-22-2-222-2-2222-2-2-22000022-22-2-200000000-2200000000−2i2i−2i2i0000000000000−2i2i00000000
χ512-22-2-222-2-2222-2-2-2200002-22-22-2000000002-2000000002i−2i2i−2i0000000000000−2i2i00000000
χ522-22-2-222-2-2222-2-2-2200002-22-22-2000000002-200000000−2i2i−2i2i00000000000002i−2i00000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ544444-4-4-4-44-400-40044-4-44000000000000000000000000000000000000000000000000000
χ554444-4-4-4-44-400-4004-444-4000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-4400400-4000000000000000000000000000022−22−222200000000000000000000000
χ574444-4-4-4-4-4400400-40000000000000000000000000000−222222−2200000000000000000000000
χ5844-4-44-44-400-440-440000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ5944-4-44-44-400-440-44000000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ604-44-44-4-44-4-4004004000000000022−2222−22000000000000−2222000000000000000000000000000
χ614-44-44-4-44-4-40040040000000000−2222−222200000000000022−22000000000000000000000000000
χ624-44-4-444-4-44-4-4-44440000-400004000000000000000000000000000000000000000000000
χ634-4-4444-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ644-4-4444-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ654-4-4444-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ664-4-4444-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ674-4-44-4-444004-40-440000004-4-440000000000000000000000000000000000000000000000
χ684-4-44-4-444004-40-44000000-444-40000000000000000000000000000000000000000000000
χ694-4-44-4-44400-4404-40000000000000000000000000000000000022−22−222200000000000000000
χ704-4-44-4-44400-4404-400000000000000000000000000000000000−222222−2200000000000000000
χ7188-8-8-88-88000000000000000000000000000000000000000000000000000000000000000

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