Finite Group Databasebeta

← Group #309032

Character table — Group #309032

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-1-1-1-111-111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-11111-1-1-11
χ91111111111111111-1-1-1-111111111-1-11111-1-1-1-111111111-1-1-1-11-1-11-1-11111-1-1
χ101111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-111111-1-11-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1111-1-1-1-111-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-11-1-1-111-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1111-1-1-111-1-11-1
χ172222222222-2-2-2-2222222-2-2000000-2-20000000022-2-20000000002-2000000000
χ182222222222-2-2-2-2222222-2-2000000-2-200000000-2-222000000000-22000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2000000220000000022-2-2000000000-22000000000
χ202222222222-2-2-2-222-2-2-2-2-2-20000002200000000-2-2220000000002-2000000000
χ2122222222-2-22222-2-20000-2-22222220022-2-20000000000000000-200-200000000
χ2222222222-2-22222-2-20000-2-22222-2-200-2-2-2-20000000000000000200200000000
χ2322222222-2-22222-2-20000-2-2-2-2-2-22200-2-2220000000000000000200-200000000
χ2422222222-2-22222-2-20000-2-2-2-2-2-2-2-20022220000000000000000-200200000000
χ2522-222-2-2-22222-2-2-2-200002-222-2-20000002-20000000000002-22-2000000000000
χ2622-222-2-2-22222-2-2-2-200002-222-2-20000002-2000000000000-22-22000000000000
χ2722-222-2-2-22222-2-2-2-200002-2-2-222000000-220000000000002-2-22000000000000
χ2822-222-2-2-22222-2-2-2-200002-2-2-222000000-22000000000000-222-2000000000000
χ2922-222-2-2-2-2-222-2-2222i2i−2i−2i-2222-2-2002i−2i00-222i2i−2i−2i000000000000000000000000
χ3022-222-2-2-2-2-222-2-2222i2i−2i−2i-22-2-222002i−2i002-2−2i−2i2i2i000000000000000000000000
χ3122-222-2-2-2-2-222-2-222−2i−2i2i2i-2222-2-200−2i2i00-22−2i−2i2i2i000000000000000000000000
χ3222-222-2-2-2-2-222-2-222−2i−2i2i2i-22-2-22200−2i2i002-22i2i−2i−2i000000000000000000000000
χ3322-222-2-2-2-2-2-2-222222i2i−2i−2i2-2000000−2i2i0000000000002i2i−2i−2i000000002-2000000
χ3422-222-2-2-2-2-2-2-222222i2i−2i−2i2-2000000−2i2i000000000000−2i−2i2i2i00000000-22000000
χ3522-222-2-2-2-2-2-2-22222−2i−2i2i2i2-20000002i−2i0000000000002i2i−2i−2i00000000-22000000
χ3622-222-2-2-2-2-2-2-22222−2i−2i2i2i2-20000002i−2i000000000000−2i−2i2i2i000000002-2000000
χ372-222-2-2-22002-22-2000000002i−2i2i−2i2i−2i002-2000000i2−i2i2−i22−22−200000000002−2i2−i200
χ382-222-2-2-22002-22-2000000002i−2i2i−2i2i−2i002-2000000−i2i2−i2i2−22−220000000000−22−i2i200
χ392-222-2-2-22002-22-2000000002i−2i2i−2i−2i2i00-22000000i2−i2i2−i22−22−20000000000−22−i2i200
χ402-222-2-2-22002-22-2000000002i−2i2i−2i−2i2i00-22000000−i2i2−i2i2−22−2200000000002−2i2−i200
χ412-222-2-2-22002-22-200000000−2i2i−2i2i2i−2i00-22000000i2−i2i2−i2−22−2200000000002−2−i2i200
χ422-222-2-2-22002-22-200000000−2i2i−2i2i2i−2i00-22000000−i2i2−i2i22−22−20000000000−22i2−i200
χ432-222-2-2-22002-22-200000000−2i2i−2i2i−2i2i002-2000000i2−i2i2−i2−22−220000000000−22i2−i200
χ442-222-2-2-22002-22-200000000−2i2i−2i2i−2i2i002-2000000−i2i2−i2i22−22−200000000002−2−i2i200
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-4-44-4-44-400004-400000000000000000022−2222−22000000000000000000000000
χ47444-4-44-4-44-400004-4000000000000000000−2222−2222000000000000000000000000
χ48444-4-44-4-4-440000-444-44-4000000000000000000000000000000000000000000
χ49444-4-44-4-4-440000-44-44-44000000000000000000000000000000000000000000
χ5044-444-4-4-444-4-444-4-40000-440000000000000000000000000000000000000000
χ5144-4-4-4-4444-40000-444i−4i−4i4i000000000000000000000000000000000000000000
χ5244-4-4-4-4444-40000-44−4i4i4i−4i000000000000000000000000000000000000000000
χ5344-4-4-4-444-4400004-40000000000000000002i2−2i2−2i22i2000000000000000000000000
χ5444-4-4-4-444-4400004-4000000000000000000−2i22i22i2−2i2000000000000000000000000
χ554-444-4-4-4400-44-440000000000000000000000002i2−2i2−2i22i200000000000000000000
χ564-444-4-4-4400-44-44000000000000000000000000−2i22i22i2−2i200000000000000000000
χ574-4-44-444-4004-4-44000000004i−4i−4i4i000000000000000000000000000000000000
χ584-4-44-444-4004-4-4400000000−4i4i4i−4i000000000000000000000000000000000000
χ594-4-44-444-400-444-400000000000000000000000000002i2−2i2−2i22i20000000000000000
χ604-4-44-444-400-444-40000000000000000000000000000−2i22i22i2−2i20000000000000000
χ618-88-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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