Finite Group Databasebeta

← Group #306365

Character table — Group #306365

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1
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
χ5111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-111111111-11-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-1-111111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111111111-1-111-1-1-1-1-1-11
χ17222222222-22-22-22-20000-22222-20000222200-2-2002200-2-2000000000000-2000000000000
χ18222222222-22-22-22-20000-22222-20000-2-2-2-200-2-200-2-200220000000000002000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-200002222002200-2-200-2-20000000000002000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-2002200220022000000000000-2000000000000
χ2122222222-22-22-22-222222-20000-2222200002200-2-200-2-2000000000000000-200000000000
χ2222222222-22-22-22-222222-20000-2-2-2-2-20000-2-200-2-20022000000000000000200000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-222220000-2-2002200-2-2000000000000000200000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-2-2-2-2-200002200220022000000000000000-200000000000
χ2522-2-222-2-22-2-222-2-2222-2-2-2000020000000000002-20000002i2i−2i−2i000000000000002i−2i00000
χ2622-2-222-2-22-2-222-2-2222-2-2-2000020000000000002-2000000−2i−2i2i2i00000000000000−2i2i00000
χ2722-2-222-2-22-2-222-2-22-2-222-200002000000000000-220000002i2i−2i−2i00000000000000−2i2i00000
χ2822-2-222-2-22-2-222-2-22-2-222-200002000000000000-22000000−2i−2i2i2i000000000000002i−2i00000
χ2922-2-222-2-2-222-2-222-20000-22i2i−2i−2i200000000002i−2i00000000000022-2-20000002i−2i000000000
χ3022-2-222-2-2-222-2-222-20000-22i2i−2i−2i200000000002i−2i000000000000-2-222000000−2i2i000000000
χ3122-2-222-2-2-222-2-222-20000-2−2i−2i2i2i20000000000−2i2i00000000000022-2-2000000−2i2i000000000
χ3222-2-222-2-2-222-2-222-20000-2−2i−2i2i2i20000000000−2i2i000000000000-2-2220000002i−2i000000000
χ3322-2-222-2-2-2-222-2-22222-2-222i2i−2i−2i-20000000000−2i2i-2200000000000000000000002i−2i0000000
χ3422-2-222-2-2-2-222-2-22222-2-22−2i−2i2i2i-200000000002i−2i-220000000000000000000000−2i2i0000000
χ3522-2-222-2-2-2-222-2-222-2-22222i2i−2i−2i-20000000000−2i2i2-20000000000000000000000−2i2i0000000
χ3622-2-222-2-2-2-222-2-222-2-2222−2i−2i2i2i-200000000002i−2i2-200000000000000000000002i−2i0000000
χ372-2222-2-2-2-20-202020000002i−2i2i−2i022−2−222-2-20000002i−2i2−200i2−i2i2−i2000022−2−20000000000i2−i20
χ382-2222-2-2-2-20-202020000002i−2i2i−2i022−2−2-2-222000000−2i2i2−200i2−i2i2−i20000−2−2220000000000−i2i20
χ392-2222-2-2-2-20-202020000002i−2i2i−2i0−2−22222-2-20000002i−2i−2200−i2i2−i2i20000−2−2220000000000−i2i20
χ402-2222-2-2-2-20-202020000002i−2i2i−2i0−2−222-2-222000000−2i2i−2200−i2i2−i2i2000022−2−20000000000i2−i20
χ412-2222-2-2-2-20-20202000000−2i2i−2i2i022−2−222-2-2000000−2i2i2−200−i2i2−i2i2000022−2−20000000000−i2i20
χ422-2222-2-2-2-20-20202000000−2i2i−2i2i022−2−2-2-2220000002i−2i2−200−i2i2−i2i20000−2−2220000000000i2−i20
χ432-2222-2-2-2-20-20202000000−2i2i−2i2i0−2−22222-2-2000000−2i2i−2200i2−i2i2−i20000−2−2220000000000i2−i20
χ442-2222-2-2-2-20-20202000000−2i2i−2i2i0−2−222-2-2220000002i−2i−2200i2−i2i2−i2000022−2−20000000000−i2i20
χ452-22-2-222-2020-20-2022-22-20000002-22-2i2−i2i2−i22-200000000i2−i20000i2−i2i2−i2i2−i2i2−i200000000i2−i2000
χ462-22-2-222-2020-20-2022-22-20000002-22-2−i2i2−i2i22-200000000−i2i20000−i2i2−i2i2−i2i2−i2i200000000−i2i2000
χ472-22-2-222-2020-20-2022-22-2000000-22-22i2−i2i2−i2-2200000000i2−i20000i2−i2i2−i2−i2i2−i2i200000000−i2i2000
χ482-22-2-222-2020-20-2022-22-2000000-22-22−i2i2−i2i2-2200000000−i2i20000−i2i2−i2i2i2−i2i2−i200000000i2−i2000
χ492-22-2-222-2020-20-202-22-220000002-22-2i2−i2i2−i2-2200000000i2−i20000−i2i2−i2i2i2−i2i2−i200000000−i2i2000
χ502-22-2-222-2020-20-202-22-220000002-22-2−i2i2−i2i2-2200000000−i2i20000i2−i2i2−i2−i2i2−i2i200000000i2−i2000
χ512-22-2-222-2020-20-202-22-22000000-22-22i2−i2i2−i22-200000000i2−i20000−i2i2−i2i2−i2i2−i2i200000000i2−i2000
χ522-22-2-222-2020-20-202-22-22000000-22-22−i2i2−i2i22-200000000−i2i20000i2−i2i2−i2i2−i2i2−i200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-4400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ55444-4-4-4-4400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ56444-4-4-4-44000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ57444-4-4-4-44000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ5844-4-444-4-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ594-4444-4-4-44040-40-4000000000002222−22−22000000000000−2222000000000000000000000000000
χ604-4444-4-4-44040-40-400000000000−22−22222200000000000022−22000000000000000000000000000
χ614-44-4-444-40-404040-4000000000000002i2−2i22i2−2i20000000000−2i22i20000000000000000000000000
χ624-44-4-444-40-404040-400000000000000−2i22i2−2i22i200000000002i2−2i20000000000000000000000000
χ634-4-44-44-4404040-40-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-4-44-44-4404040-40-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ654-4-44-44-440-40-404044-4-44000000000000000000000000000000000000000000000000000
χ664-4-44-44-440-40-40404-444-4000000000000000000000000000000000000000000000000000
χ674-4-4-44-44440-40-4040000004-4-440000000000000000000000000000000000000000000000
χ684-4-4-44-44440-40-404000000-444-40000000000000000000000000000000000000000000000
χ694-4-4-44-444-404040-4000000000000000000000000000000022−22−2222000000000000000000000
χ704-4-4-44-444-404040-40000000000000000000000000000000−222222−22000000000000000000000
χ7188-88-8-88-8000000000000000000000000000000000000000000000000000000000000000

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