Finite Group Databasebeta

← Group #313813

Character table — Group #313813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444442222448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-11-11111-11-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111-11-1-1-1-11-111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-111-1-1111-1-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1-11
χ91111111111111111-1-1-1-11111111111-1-11111-1-1-1-11111111-1-1-1-1-1-11-1-11111-1-1
χ101111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111111-1-11-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-11-1-11111-1-1-1-111-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-111-1-1-1-111-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-11-1-1-111-1-11-1
χ17222222222-22-22-22-22222-2-200000000-2-200220000-2-200000-200002000000000
χ18222222222-22-22-22-22222-2-200000000-2-200-2-20000220000020000-2000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000000002200220000-2-20000020000-2000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000000002200-2-200002200000-200002000000000
χ2122222222-22-22-22-220000-2-22222222200-2-2000000000000-2000000-200000000
χ2222222222-22-22-22-220000-2-22222-2-2-2-200-2-20000000000002000000200000000
χ2322222222-22-22-22-220000-2-2-2-2-2-222-2-200220000000000002000000-200000000
χ2422222222-22-22-22-220000-2-2-2-2-2-2-2-2220022000000000000-2000000200000000
χ2522-2-2-22-2222-2-222-2-222-2-2-222i2i−2i−2i00002-22i−2i002i2i−2i−2i0000000000000000000000
χ2622-2-2-22-2222-2-222-2-222-2-2-22−2i−2i2i2i00002-2−2i2i00−2i−2i2i2i0000000000000000000000
χ2722-2-2-22-2222-2-222-2-2-2-222-222i2i−2i−2i0000-222i−2i00−2i−2i2i2i0000000000000000000000
χ2822-2-2-22-2222-2-222-2-2-2-222-22−2i−2i2i2i0000-22−2i2i002i2i−2i−2i0000000000000000000000
χ2922-2-2-22-222-2-222-2-2222-2-22-200000000-2200000000002i2i−2i−2i000000002i−2i000000
χ3022-2-2-22-222-2-222-2-2222-2-22-200000000-220000000000−2i−2i2i2i00000000−2i2i000000
χ3122-2-2-22-222-2-222-2-22-2-2222-2000000002-200000000002i2i−2i−2i00000000−2i2i000000
χ3222-2-2-22-222-2-222-2-22-2-2222-2000000002-20000000000−2i−2i2i2i000000002i−2i000000
χ3322-2-2-22-22-222-2-222-200002-22i2i−2i−2i000000−2i2i000000000000002-22i−2i0000000000
χ3422-2-2-22-22-222-2-222-200002-22i2i−2i−2i000000−2i2i00000000000000-22−2i2i0000000000
χ3522-2-2-22-22-222-2-222-200002-2−2i−2i2i2i0000002i−2i000000000000002-2−2i2i0000000000
χ3622-2-2-22-22-222-2-222-200002-2−2i−2i2i2i0000002i−2i00000000000000-222i−2i0000000000
χ372-22-22-2-22020-20-2020000002-22-22i−2i2i−2i0000i2−i20000i2−i2i2−i2i2−i200000000002−22−200
χ382-22-22-2-22020-20-2020000002-22-22i−2i2i−2i0000−i2i20000−i2i2−i2i2−i2i20000000000−22−2200
χ392-22-22-2-22020-20-2020000002-22-2−2i2i−2i2i0000i2−i20000i2−i2i2−i2i2−i20000000000−22−2200
χ402-22-22-2-22020-20-2020000002-22-2−2i2i−2i2i0000−i2i20000−i2i2−i2i2−i2i200000000002−22−200
χ412-22-22-2-22020-20-202000000-22-222i−2i−2i2i0000i2−i20000i2−i2−i2i2−i2i200000000002−2−2200
χ422-22-22-2-22020-20-202000000-22-222i−2i−2i2i0000−i2i20000−i2i2i2−i2i2−i20000000000−222−200
χ432-22-22-2-22020-20-202000000-22-22−2i2i2i−2i0000i2−i20000i2−i2−i2i2−i2i20000000000−222−200
χ442-22-22-2-22020-20-202000000-22-22−2i2i2i−2i0000−i2i20000−i2i2i2−i2i2−i200000000002−2−2200
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-4-4-44-44040-40-404-44-4000000000000000000000000000000000000000000
χ47444-4-4-44-44040-40-40-44-44000000000000000000000000000000000000000000
χ48444-4-4-44-4-40-404040000000000000000000002i2−2i22i2−2i20000000000000000000000
χ49444-4-4-44-4-40-40404000000000000000000000−2i22i2−2i22i20000000000000000000000
χ5044-444-4-4-440-40-40404-4-44000000000000000000000000000000000000000000
χ5144-444-4-4-440-40-4040-444-4000000000000000000000000000000000000000000
χ5244-444-4-4-4-404040-400000000000000000000022−22−22220000000000000000000000
χ5344-444-4-4-4-404040-4000000000000000000000−222222−220000000000000000000000
χ5444-4-4-44-44-4-444-4-4440000-440000000000000000000000000000000000000000
χ554-44-44-4-440-404040-40000000000000000002i2−2i20000−2i22i200000000000000000000
χ564-44-44-4-440-404040-4000000000000000000−2i22i200002i2−2i200000000000000000000
χ574-4-44-4-44404040-40-40000004i−4i−4i4i000000000000000000000000000000000000
χ584-4-44-4-44404040-40-4000000−4i4i4i−4i000000000000000000000000000000000000
χ594-4-44-4-4440-40-404040000000000000000000000000022−22−22220000000000000000
χ604-4-44-4-4440-40-4040400000000000000000000000000−222222−220000000000000000
χ618-888-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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