Finite Group Databasebeta

← Group #247321

Character table — Group #247321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444448888888888888888888161616161616161616161616161616161616
order12222222444444442244444444442222444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-11111-1-11-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-111-1-11111-1-11-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111111-111-1111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111
χ91111111111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-11111-1-1-1-1-1-1-111111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-11111-1-1-1111-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-11111-1-1-1-1111-1-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-11111111-1-1-111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-11111-1111-1-111-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1111111-1-1-1-11-1-1-11111-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-111111-1-1-111-1-11111-1-111-1-1
χ1722222222222-2-2-2-222222-2-22222-2-2-2-20000-2-2-22200000000000000000000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-2-2-222000022-2-2-200000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2222222-2-2220000-2-22-2-200000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2-200002222200000000000000000000000000
χ2122222222-2-2-22222-222-2-2-2-20000-2-20022-2-20020000000000200-200000000000000
χ2222222222-2-2-22222-222-2-2-2-20000-2-200-2-2220020000000000-200200000000000000
χ2322222222-2-2-22222-2-2-222220000-2-200222200-20000000000-200-200000000000000
χ2422222222-2-2-22222-2-2-222220000-2-200-2-2-2-200-20000000000200200000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22200002200000000-2000000000002-202-2000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200002200000000-200000000000-220-22000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2000022000000002000000000002-20-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-200002200000000200000000000-2202-2000000000000
χ292-222-22-2-22-2-2000022-22-2002i2i−2i−2i000000000002i−2i22−2−222−2−20000000000i2−i2i2−i20000
χ302-222-22-2-22-2-2000022-22-2002i2i−2i−2i000000000002i−2i−2−222−2−2220000000000−i2i2−i2i20000
χ312-222-22-2-22-2-2000022-22-200−2i−2i2i2i00000000000−2i2i22−2−222−2−20000000000−i2i2−i2i20000
χ322-222-22-2-22-2-2000022-22-200−2i−2i2i2i00000000000−2i2i−2−222−2−2220000000000i2−i2i2−i20000
χ332-222-22-2-22-2-200002-22-22002i2i−2i−2i00000000000−2i2i22−2−2−2−2220000000000i2−i2−i2i20000
χ342-222-22-2-22-2-200002-22-22002i2i−2i−2i00000000000−2i2i−2−22222−2−20000000000−i2i2i2−i20000
χ352-222-22-2-22-2-200002-22-2200−2i−2i2i2i000000000002i−2i22−2−2−2−2220000000000−i2i2i2−i20000
χ362-222-22-2-22-2-200002-22-2200−2i−2i2i2i000000000002i−2i−2−22222−2−20000000000i2−i2−i2i20000
χ372-2-2-2-2222-22-22-22-220000002-22-22-20000002-2000000000000000002-20000002-200
χ382-2-2-2-2222-22-22-22-220000002-22-22-20000002-200000000000000000-22000000-2200
χ392-2-2-2-2222-22-22-22-22000000-22-222-2000000-22000000000000000002-2000000-2200
χ402-2-2-2-2222-22-22-22-22000000-22-222-2000000-2200000000000000000-220000002-200
χ412-2-2-2-2222-22-2-22-2220000002-22-2-22000000-2200000000000000000002-20000002-2
χ422-2-2-2-2222-22-2-22-2220000002-22-2-22000000-220000000000000000000-22000000-22
χ432-2-2-2-2222-22-2-22-222000000-22-22-220000002-200000000000000000002-2000000-22
χ442-2-2-2-2222-22-2-22-222000000-22-22-220000002-20000000000000000000-220000002-2
χ45444-4-4-4-440004-4-4400000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ46444-4-4-4-440004-4-440000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ47444-4-4-4-44000-444-40000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ48444-4-4-4-44000-444-4000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ4944-4-444-4-444-40000-40000000000004-400000000000000000000000000000000000
χ5044-4-444-4-444-40000-4000000000000-4400000000000000000000000000000000000
χ5144-4-444-4-4-4-44000040000004i−4i−4i4i000000000000000000000000000000000000000
χ5244-4-444-4-4-4-4400004000000−4i4i4i−4i000000000000000000000000000000000000000
χ534-444-44-4-4-4440000-44-4-44000000000000000000000000000000000000000000000
χ544-444-44-4-4-4440000-4-444-4000000000000000000000000000000000000000000000
χ554-44-44-44-40000000000004-4000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ564-44-44-44-40000000000004-400000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ574-44-44-44-4000000000000-44000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ584-44-44-44-4000000000000-4400000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ594-4-444-4-4400044-4-4000000000000000004i−4i0000000000000000000000000000000
χ604-4-444-4-4400044-4-400000000000000000−4i4i0000000000000000000000000000000
χ614-4-444-4-44000-4-4440000000000000004-4000000000000000000000000000000000
χ624-4-444-4-44000-4-444000000000000000-44000000000000000000000000000000000
χ634-4-4-4-44444-444-44-4-40000000000-440000000000000000000000000000000000000
χ644-4-4-4-44444-44-44-44-400000000004-40000000000000000000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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