Finite Group Databasebeta

← Group #313753

Character table — Group #313753

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111111-1-1-11-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11-1-1-11111-1-111-1-11-1
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-11-1
χ91111111111111111-1-1-1-11111111111-1-11111-1-1-1-1111111-11-1-1-11-1-1-1-11111-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1111-111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111-11-1-11111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-11111-1-1-1-1-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-11-1-1-1-11111-1-1111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-11-111-1-111-1-1-11
χ17222222222-22-22-22-20000-2-2222222220000-2-200000000000-2000-20000000000
χ18222222222-22-22-22-20000-2-22222-2-2-2-20000-2-200000000000200020000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222-2-2000022000000000002000-20000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-22200002200000000000-200020000000000
χ2122222222-22-22-22-222222-2-200000000-2-222000000-2-200002000-200000000000
χ2222222222-22-22-22-222222-2-200000000-2-2-2-2000000220000-2000200000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000002222000000-2-20000-2000200000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000000022-2-20000002200002000-200000000000
χ252-222-2-22-2-202020-2000000022-2-22-22-200i2−i2000000i2−i2i2i2−i2−i20000000000i2−i2i2−i200
χ262-222-2-22-2-202020-2000000022-2-22-22-200−i2i2000000−i2i2−i2−i2i2i20000000000−i2i2−i2i200
χ272-222-2-22-2-202020-2000000022-2-2-22-2200i2−i2000000i2−i2i2i2−i2−i20000000000−i2i2−i2i200
χ282-222-2-22-2-202020-2000000022-2-2-22-2200−i2i2000000−i2i2−i2−i2i2i20000000000i2−i2i2−i200
χ292-222-2-22-2-202020-20000000-2-2222-2-2200i2−i2000000i2−i2−i2−i2i2i20000000000i2−i2−i2i200
χ302-222-2-22-2-202020-20000000-2-2222-2-2200−i2i2000000−i2i2i2i2−i2−i20000000000−i2i2i2−i200
χ312-222-2-22-2-202020-20000000-2-222-222-200i2−i2000000i2−i2−i2−i2i2i20000000000−i2i2i2−i200
χ322-222-2-22-2-202020-20000000-2-222-222-200−i2i2000000−i2i2i2i2−i2−i20000000000i2−i2−i2i200
χ332-2-222-2-2222-2-222-2-222-2-2-222i−2i2i−2i00002-2002i−2i2i2i−2i−2i0000000000000000000000
χ342-2-222-2-2222-2-222-2-222-2-2-22−2i2i−2i2i00002-200−2i2i−2i−2i2i2i0000000000000000000000
χ352-2-222-2-2222-2-222-2-2-2-222-222i−2i2i−2i0000-22002i−2i−2i−2i2i2i0000000000000000000000
χ362-2-222-2-2222-2-222-2-2-2-222-22−2i2i−2i2i0000-2200−2i2i2i2i−2i−2i0000000000000000000000
χ372-2-222-2-222-2-222-2-2200002-22i−2i2i−2i00000000−2i2i0000000000002i−2i002-200000000
χ382-2-222-2-222-2-222-2-2200002-22i−2i2i−2i00000000−2i2i000000000000−2i2i00-2200000000
χ392-2-222-2-222-2-222-2-2200002-2−2i2i−2i2i000000002i−2i0000000000002i−2i00-2200000000
χ402-2-222-2-222-2-222-2-2200002-2−2i2i−2i2i000000002i−2i000000000000−2i2i002-200000000
χ412-2-222-2-22-222-2-222-222-2-22-200000000-2200000000002i−2i2i−2i000000002i−2i000000
χ422-2-222-2-22-222-2-222-222-2-22-200000000-220000000000−2i2i−2i2i00000000−2i2i000000
χ432-2-222-2-22-222-2-222-2-2-2222-2000000002-200000000002i−2i2i−2i00000000−2i2i000000
χ442-2-222-2-22-222-2-222-2-2-2222-2000000002-20000000000−2i2i−2i2i000000002i−2i000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-44-4-4-4040-40-4040000000000000000000022−2222−220000000000000000000000
χ47444-44-4-4-4040-40-40400000000000000000000−2222−22220000000000000000000000
χ48444-44-4-4-40-404040-44-44-4000000000000000000000000000000000000000000
χ49444-44-4-4-40-404040-4-44-44000000000000000000000000000000000000000000
χ5044-44-44-4-44040-40-400000000000000000000000000022−22−22220000000000000000
χ5144-44-44-4-44040-40-4000000000000000000000000000−222222−220000000000000000
χ5244-44-44-4-4-40-4040400000004i−4i−4i4i000000000000000000000000000000000000
χ5344-44-44-4-4-40-404040000000−4i4i4i−4i000000000000000000000000000000000000
χ544-444-4-44-440-40-404000000000000000002i2−2i2000000−2i22i200000000000000000000
χ554-444-4-44-440-40-40400000000000000000−2i22i20000002i2−2i200000000000000000000
χ564-4-444-4-44-4-444-4-4440000-440000000000000000000000000000000000000000
χ574-4-4-4444-404040-40-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ584-4-4-4444-404040-40-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ594-4-4-4444-40-40-404044-4-44000000000000000000000000000000000000000000
χ604-4-4-4444-40-40-40404-444-4000000000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-88-8-88-88000000000000000000000000000000000000000000000000000000

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