Finite Group Databasebeta

← Group #280050

Character table — Group #280050

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1-111111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111-1-1111-1-1-1-1-1-11
χ17222222222-22-2-222-22222-20000-200002222-2-200002200-2-2000000000000-2000000000000
χ18222222222-22-2-222-22222-20000-20000-2-2-2-2-2-20000-2-200220000000000002000000000000
χ19222222222-22-2-222-2-2-2-2-2-20000-200002222220000-2-200-2-20000000000002000000000000
χ20222222222-22-2-222-2-2-2-2-2-20000-20000-2-2-2-2220000220022000000000000-2000000000000
χ2122222222-22-222-2-220000-22222-2222200000022-2-200-2-200000000000000000-2000000000
χ2222222222-22-222-2-220000-22222-2-2-2-2-2000000-2-2-2-20022000000000000000002000000000
χ2322222222-22-222-2-220000-2-2-2-2-2-22222000000-2-22200-2-2000000000000000002000000000
χ2422222222-22-222-2-220000-2-2-2-2-2-2-2-2-2-20000002222002200000000000000000-2000000000
χ252-222-2-22-20-202-2002000002i2i−2i−2i022-2-222−2−2002i−2i0000002−2i2i2−i2−i2000022−2−200000000i2−i2000
χ262-222-2-22-20-202-2002000002i2i−2i−2i022-2-2−2−222002i−2i000000−22−i2−i2i2i20000−2−22200000000−i2i2000
χ272-222-2-22-20-202-2002000002i2i−2i−2i0-2-22222−2−200−2i2i0000002−2i2i2−i2−i20000−2−22200000000−i2i2000
χ282-222-2-22-20-202-2002000002i2i−2i−2i0-2-222−2−22200−2i2i000000−22−i2−i2i2i2000022−2−200000000i2−i2000
χ292-222-2-22-20-202-200200000−2i−2i2i2i022-2-222−2−200−2i2i0000002−2−i2−i2i2i2000022−2−200000000−i2i2000
χ302-222-2-22-20-202-200200000−2i−2i2i2i022-2-2−2−22200−2i2i000000−22i2i2−i2−i20000−2−22200000000i2−i2000
χ312-222-2-22-20-202-200200000−2i−2i2i2i0-2-22222−2−2002i−2i0000002−2−i2−i2i2i20000−2−22200000000i2−i2000
χ322-222-2-22-20-202-200200000−2i−2i2i2i0-2-222−2−222002i−2i000000−22i2i2−i2−i2000022−2−200000000−i2i2000
χ332-22-22-2-2220200-2-202i2i−2i−2i0000002−22−22-22-20000002i−2i2−2000000i2i2−i2−i22−22−20000000000i2−i20
χ342-22-22-2-2220200-2-202i2i−2i−2i0000002−22−2-22-22000000−2i2i2−2000000i2i2−i2−i2−22−220000000000−i2i20
χ352-22-22-2-2220200-2-202i2i−2i−2i000000−22−222-22-20000002i−2i−22000000−i2−i2i2i2−22−220000000000−i2i20
χ362-22-22-2-2220200-2-202i2i−2i−2i000000−22−22-22-22000000−2i2i−22000000−i2−i2i2i22−22−20000000000i2−i20
χ372-22-22-2-2220200-2-20−2i−2i2i2i0000002−22−22-22-2000000−2i2i2−2000000−i2−i2i2i22−22−20000000000−i2i20
χ382-22-22-2-2220200-2-20−2i−2i2i2i0000002−22−2-22-220000002i−2i2−2000000−i2−i2i2i2−22−220000000000i2−i20
χ392-22-22-2-2220200-2-20−2i−2i2i2i000000−22−222-22-2000000−2i2i−22000000i2i2−i2−i2−22−220000000000i2−i20
χ402-22-22-2-2220200-2-20−2i−2i2i2i000000−22−22-22-220000002i−2i−22000000i2i2−i2−i22−22−20000000000−i2i20
χ412-2-2-2222-222-2-2-22-222i−2i2i−2i20000-2000000002i−2i00000000002i−2i2i−2i0000000002-20000000000
χ422-2-2-2222-222-2-2-22-222i−2i2i−2i20000-2000000002i−2i0000000000−2i2i−2i2i000000000-220000000000
χ432-2-2-2222-222-2-2-22-22−2i2i−2i2i20000-200000000−2i2i00000000002i−2i2i−2i000000000-220000000000
χ442-2-2-2222-222-2-2-22-22−2i2i−2i2i20000-200000000−2i2i0000000000−2i2i−2i2i0000000002-20000000000
χ452-2-2-2222-22-2-2222-2-22i−2i2i−2i-22-22-2200000000−2i2i002-200000000000000000000002i−2i0000000
χ462-2-2-2222-22-2-2222-2-22i−2i2i−2i-2-22-22200000000−2i2i00-220000000000000000000000−2i2i0000000
χ472-2-2-2222-22-2-2222-2-2−2i2i−2i2i-22-22-22000000002i−2i002-20000000000000000000000−2i2i0000000
χ482-2-2-2222-22-2-2222-2-2−2i2i−2i2i-2-22-222000000002i−2i00-2200000000000000000000002i−2i0000000
χ492-2-2-2222-2-2-2222-22-2000022-22-2-2000000000000-2200000000002i−2i2i−2i00000000002i−2i00000
χ502-2-2-2222-2-2-2222-22-2000022-22-2-2000000000000-220000000000−2i2i−2i2i0000000000−2i2i00000
χ512-2-2-2222-2-2-2222-22-200002-22-22-20000000000002-200000000002i−2i2i−2i0000000000−2i2i00000
χ522-2-2-2222-2-2-2222-22-200002-22-22-20000000000002-20000000000−2i2i−2i2i00000000002i−2i00000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-44-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ55444-4-44-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ56444-4-44-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ57444-4-44-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ5844-444-4-4-440-400-4404-4-44000000000000000000000000000000000000000000000000000
χ5944-444-4-4-440-400-440-444-4000000000000000000000000000000000000000000000000000
χ6044-444-4-4-4-404004-40000000000000000000000000000000000022−22−222200000000000000000
χ6144-444-4-4-4-404004-400000000000000000000000000000000000−222222−2200000000000000000
χ6244-4-4-4-4440404-400-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6344-4-4-4-4440404-400-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6444-4-4-4-4440-40-4400400000000000000000000000000000022−22−2222000000000000000000000
χ6544-4-4-4-4440-40-44004000000000000000000000000000000−222222−22000000000000000000000
χ664-444-4-44-4040-4400-4000000000000002222−22−220000000000−22220000000000000000000000000
χ674-444-4-44-4040-4400-400000000000000−22−222222000000000022−220000000000000000000000000
χ684-44-44-4-44-40-400440000000000022−2222−22000000000000−2222000000000000000000000000000
χ694-44-44-4-44-40-4004400000000000−2222−222200000000000022−22000000000000000000000000000
χ704-4-4-4444-4-444-4-4-4440000-400004000000000000000000000000000000000000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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