Finite Group Databasebeta

← Group #252875

Character table — Group #252875

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444448888888888888888888161616161616161616161616161616161616
order12222222444444444444444444442444444444488888888222444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-111-111-1-111-1-1-1-11111-1-1-1-1111-111-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-1-1-111-111-1-111-1-1-1-1-1-1-1-111111-1-1-111-1-111-1-111-1-111
χ711111111111111111111-1-1-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-1-1-1-11-1-1111111-1-1-1-111
χ811111111111111111111-1-1-1-1-1-111-111-1-1-1-111-1-1-1-1-1-11111-1111-1-111-1-1-1-11111-1-1
χ91111111111111111-1-1-1-1111111111-1-1-1-11111-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ101111111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1-1-1-1-1
χ121111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1111111-1-1-1-11-1-1-1-1-11111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-11111111-1-1-111-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-1-1-1-111111-1-1-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1111-1-11111-1-111-1-1
χ172222222222-2-222-2-2222222-2-222-2-2-2-2-2220000-2-200000000000000000000000000
χ182222222222-2-222-2-22222-2-222-2-2-2-22-2-2-2-200002200000000000000000000000000
χ192222222222-2-222-2-2-2-2-2-222-2-222-2-2-222-2-200002200000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-222-2-2-2-2222220000-2-200000000000000000000000000
χ2122222222-2-222-2-22200002222-2-2-2-2-2000022220000000000-200-200000000000000
χ2222222222-2-222-2-22200002222-2-2-2-2-20000-2-2-2-20000000000200200000000000000
χ2322222222-2-222-2-2220000-2-2-2-222-2-22000022-2-20000000000-200200000000000000
χ2422222222-2-222-2-2220000-2-2-2-222-2-220000-2-2220000000000200-200000000000000
χ2522222222-2-2-2-2-2-2-2-2000022-2-2-2-222200000000000000000000002-22-20000000000
χ2622222222-2-2-2-2-2-2-2-2000022-2-2-2-22220000000000000000000000-22-220000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2222222-200000000000000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2222222-20000000000000000000000-222-20000000000
χ2922-22-2-22-22-2002-20022-2-22i−2i002i−2i000002i−2i00000022−2−2i2i2−i2−i200000000002−2i2−i20000
χ3022-22-2-22-22-2002-20022-2-22i−2i002i−2i000002i−2i000000−2−222−i2−i2i2i20000000000−22−i2i20000
χ3122-22-2-22-22-2002-20022-2-2−2i2i00−2i2i00000−2i2i00000022−2−2−i2−i2i2i200000000002−2−i2i20000
χ3222-22-2-22-22-2002-20022-2-2−2i2i00−2i2i00000−2i2i000000−2−222i2i2−i2−i20000000000−22i2−i20000
χ3322-22-2-22-22-2002-200-2-2222i−2i002i−2i00000−2i2i00000022−2−2i2i2−i2−i20000000000−22−i2i20000
χ3422-22-2-22-22-2002-200-2-2222i−2i002i−2i00000−2i2i000000−2−222−i2−i2i2i200000000002−2i2−i20000
χ3522-22-2-22-22-2002-200-2-222−2i2i00−2i2i000002i−2i00000022−2−2−i2−i2i2i20000000000−22i2−i20000
χ3622-22-2-22-22-2002-200-2-222−2i2i00−2i2i000002i−2i000000−2−222i2i2−i2−i200000000002−2−i2i20000
χ372-222-2-2-22222-2-2-22-22i−2i2i−2i0000002-202i−2i0000000000000000000000002-20000002i−2i
χ382-222-2-2-22222-2-2-22-22i−2i2i−2i0000002-202i−2i000000000000000000000000-22000000−2i2i
χ392-222-2-2-22222-2-2-22-2−2i2i−2i2i0000002-20−2i2i0000000000000000000000002-2000000−2i2i
χ402-222-2-2-22222-2-2-22-2−2i2i−2i2i0000002-20−2i2i000000000000000000000000-220000002i−2i
χ412-222-2-2-2222-22-2-2-222i−2i2i−2i000000-220−2i2i000000000000000002-2000000000002i−2i00
χ422-222-2-2-2222-22-2-2-222i−2i2i−2i000000-220−2i2i00000000000000000-2200000000000−2i2i00
χ432-222-2-2-2222-22-2-2-22−2i2i−2i2i000000-2202i−2i000000000000000002-200000000000−2i2i00
χ442-222-2-2-2222-22-2-2-22−2i2i−2i2i000000-2202i−2i00000000000000000-22000000000002i−2i00
χ4544-44-4-44-4-4400-440000004i−4i00−4i4i000000000000000000000000000000000000000
χ4644-44-4-44-4-4400-44000000−4i4i004i−4i000000000000000000000000000000000000000
χ4744-4-44-4-44004400-4-4000000000000000004i−4i000000000000000000000000000000
χ4844-4-44-4-44004400-4-400000000000000000−4i4i000000000000000000000000000000
χ4944-4-44-4-4400-4-4004400000000000000000004-40000000000000000000000000000
χ5044-4-44-4-4400-4-400440000000000000000000-440000000000000000000000000000
χ514-444-4-4-44-4-44-4444-40000000000-440000000000000000000000000000000000000
χ524-444-4-4-44-4-4-4444-4400000000004-40000000000000000000000000000000000000
χ534-44-44-44-4000000000000004i−4i0000000000000002-22-22i−2i2i−2i000000000000000000
χ544-44-44-44-4000000000000004i−4i000000000000000-22-22−2i2i−2i2i000000000000000000
χ554-44-44-44-400000000000000−4i4i0000000000000002-22-2−2i2i−2i2i000000000000000000
χ564-44-44-44-400000000000000−4i4i000000000000000-22-222i−2i2i−2i000000000000000000
χ574-4-4444-4-44-400-44004i−4i−4i4i000000000000000000000000000000000000000000000
χ584-4-4444-4-44-400-4400−4i4i4i−4i000000000000000000000000000000000000000000000
χ594-4-4444-4-4-44004-4000000000000000000000004i−4i00000000000000000000000000
χ604-4-4444-4-4-44004-400000000000000000000000−4i4i00000000000000000000000000
χ614-4-4-4-4444004-400-4400000000000000000000000000022−22−2222000000000000000000
χ624-4-4-4-4444004-400-44000000000000000000000000000−222222−22000000000000000000
χ634-4-4-4-444400-44004-40000000000000000000000022−22−22220000000000000000000000
χ644-4-4-4-444400-44004-400000000000000000000000−222222−220000000000000000000000
χ65888-8-88-8-8000000000000000000000000000000000000000000000000000000000

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