Finite Group Databasebeta

← Group #308069

Character table — Group #308069

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-111-1-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1111-1-111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
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
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111111-1-1111-1-1-1-1-1-11
χ172222222222-22-2-2-220000-22222-20000222200-2-20022-2-200000000000000000-2000000000
χ182222222222-22-2-2-220000-22222-20000-2-2-2-200-2-200-2-222000000000000000002000000000
χ192222222222-22-2-2-220000-2-2-2-2-2-200002222002200-2-2-2-2000000000000000002000000000
χ202222222222-22-2-2-220000-2-2-2-2-2-20000-2-2-2-2002200222200000000000000000-2000000000
χ2122222222-2-22-2222-22222-20000-222220000-2-2002200000000-2-200000000-2000000000000
χ2222222222-2-22-2222-22222-20000-2-2-2-2-20000-2-200-2-20000000022000000002000000000000
χ2322222222-2-22-2222-2-2-2-2-2-20000-2222200002200-2-200000000-2-2000000002000000000000
χ2422222222-2-22-2222-2-2-2-2-2-20000-2-2-2-2-20000220022000000002200000000-2000000000000
χ2522-22-22-2-2222-2-22-2-222-2-220000-2000000002-20000000022-2-2000000000002-20000000000
χ2622-22-22-2-2222-2-22-2-222-2-220000-2000000002-200000000-2-22200000000000-220000000000
χ2722-22-22-2-2222-2-22-2-2-2-22220000-200000000-220000000022-2-200000000000-220000000000
χ2822-22-22-2-2222-2-22-2-2-2-22220000-200000000-2200000000-2-222000000000002-20000000000
χ2922-22-22-2-2-2-222-22-2222-2-2-22i2i−2i−2i200000000-222i−2i0000000000000000000000002i−2i0000000
χ3022-22-22-2-2-2-222-22-2222-2-2-2−2i−2i2i2i200000000-22−2i2i000000000000000000000000−2i2i0000000
χ3122-22-22-2-2-2-222-22-22-2-222-22i2i−2i−2i2000000002-22i−2i000000000000000000000000−2i2i0000000
χ3222-22-22-2-2-2-222-22-22-2-222-2−2i−2i2i2i2000000002-2−2i2i0000000000000000000000002i−2i0000000
χ3322-22-22-2-2-2-2-222-222000022i2i−2i−2i-20000000000−2i2i00000000000022-2-200000000002i−2i00000
χ3422-22-22-2-2-2-2-222-222000022i2i−2i−2i-20000000000−2i2i000000000000-2-2220000000000−2i2i00000
χ3522-22-22-2-2-2-2-222-22200002−2i−2i2i2i-200000000002i−2i00000000000022-2-20000000000−2i2i00000
χ3622-22-22-2-2-2-2-222-22200002−2i−2i2i2i-200000000002i−2i000000000000-2-22200000000002i−2i00000
χ372-222-2-22-22-20-20002000002i−2i2i−2i022−2−222-2-20000002i−2i00i2−i2i2−i22−2000022−2−200000000i2−i2000
χ382-222-2-22-22-20-20002000002i−2i2i−2i022−2−2-2-222000000−2i2i00i2−i2i2−i22−20000−2−22200000000−i2i2000
χ392-222-2-22-22-20-20002000002i−2i2i−2i0−2−22222-2-20000002i−2i00−i2i2−i2i2−220000−2−22200000000−i2i2000
χ402-222-2-22-22-20-20002000002i−2i2i−2i0−2−222-2-222000000−2i2i00−i2i2−i2i2−22000022−2−200000000i2−i2000
χ412-222-2-22-22-20-2000200000−2i2i−2i2i022−2−222-2-2000000−2i2i00−i2i2−i2i22−2000022−2−200000000−i2i2000
χ422-222-2-22-22-20-2000200000−2i2i−2i2i022−2−2-2-2220000002i−2i00−i2i2−i2i22−20000−2−22200000000i2−i2000
χ432-222-2-22-22-20-2000200000−2i2i−2i2i0−2−22222-2-2000000−2i2i00i2−i2i2−i2−220000−2−22200000000i2−i2000
χ442-222-2-22-22-20-2000200000−2i2i−2i2i0−2−222-2-2220000002i−2i00i2−i2i2−i2−22000022−2−200000000−i2i2000
χ452-22-222-2-200-20-22202-22-20000002i−2i2i−2i2−22−200002i−2i002−20000002−22−2i2−i2i2−i20000000000i2−i20
χ462-22-222-2-200-20-22202-22-20000002i−2i2i−2i−22−2200002i−2i00−22000000−22−22−i2i2−i2i20000000000−i2i20
χ472-22-222-2-200-20-22202-22-2000000−2i2i−2i2i2−22−20000−2i2i002−20000002−22−2−i2i2−i2i20000000000−i2i20
χ482-22-222-2-200-20-22202-22-2000000−2i2i−2i2i−22−220000−2i2i00−22000000−22−22i2−i2i2−i20000000000i2−i20
χ492-22-222-2-200-20-2220-22-220000002i−2i2i−2i2−22−20000−2i2i002−2000000−22−22i2−i2i2−i20000000000−i2i20
χ502-22-222-2-200-20-2220-22-220000002i−2i2i−2i−22−220000−2i2i00−220000002−22−2−i2i2−i2i20000000000i2−i20
χ512-22-222-2-200-20-2220-22-22000000−2i2i−2i2i2−22−200002i−2i002−2000000−22−22−i2i2−i2i20000000000i2−i20
χ522-22-222-2-200-20-2220-22-22000000−2i2i−2i2i−22−2200002i−2i00−220000002−22−2i2−i2i2−i20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-440000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ55444-4-4-4-440000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ56444-4-4-4-44000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ57444-4-4-4-44000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ5844-44-44-4-444-4-44-44-40000-400004000000000000000000000000000000000000000000000
χ594-444-4-44-4-4404000-400000000002222−22−22000000000000000000−2222000000000000000000000
χ604-444-4-44-4-4404000-40000000000−22−22222200000000000000000022−22000000000000000000000
χ614-44-444-4-400404-4-400000000000000022−2222−2200000000−2222000000000000000000000000000
χ624-44-444-4-400404-4-4000000000000000−2222−22220000000022−22000000000000000000000000000
χ634-4-444-4-444-404000-400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ644-4-444-4-444-404000-40000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ654-4-444-4-44-440-40004000004-4-440000000000000000000000000000000000000000000000
χ664-4-444-4-44-440-4000400000-444-40000000000000000000000000000000000000000000000
χ674-4-4-4-44440040-4-440000000000000000000000000000000000022−22−222200000000000000000
χ684-4-4-4-44440040-4-4400000000000000000000000000000000000−222222−2200000000000000000
χ694-4-4-4-444400-4044-404-4-44000000000000000000000000000000000000000000000000000
χ704-4-4-4-444400-4044-40-444-4000000000000000000000000000000000000000000000000000
χ7188-8-88-88-8000000000000000000000000000000000000000000000000000000000000000

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