Finite Group Databasebeta

← Group #344052

Character table — Group #344052

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-11-1-11-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1-1111111-1-1-1-1-1-1-11
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11-1-111-1-111111-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-1-1-1-11-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-111-1-1111111-11
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-11-1-1-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111-1-1-11111-1-1-1-1-1-1111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111111111-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-11111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-1-1-11-1-1-1-111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-11111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-11-1-1-111-1-111-1-111
χ172222222222-2-2-222-2-2-2000000002222-2-2-2-20000000022002200-20000-2000000000000
χ182222222222-2-2-222-2-2-2000000002222-2-2-2-200000000-2-200-2-200200002000000000000
χ192222222222-2-2-222-2-2-200000000-2-2-2-22222000000002200-2-20020000-2000000000000
χ202222222222-2-2-222-2-2-200000000-2-2-2-2222200000000-2-2002200-200002000000000000
χ2122222222-2-2222-2-22-2-22222-2-2-2-20000000000000000002200220-200-20000000000000
χ2222222222-2-2222-2-22-2-22222-2-2-2-2000000000000000000-2-200-2-2020020000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-222220000000000000000002200-2-20-20020000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-22222000000000000000000-2-200220200-20000000000000
χ2522-2-22-22-2-2-22-2222-22-200000000000000002i2i2i2i−2i−2i−2i−2i00000000002-2002i−2i0000000000
χ2622-2-22-22-2-2-22-2222-22-200000000000000002i2i2i2i−2i−2i−2i−2i0000000000-2200−2i2i0000000000
χ2722-2-22-22-2-2-22-2222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i00000000002-200−2i2i0000000000
χ2822-2-22-22-2-2-22-2222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i0000000000-22002i−2i0000000000
χ2922-2-2-22-222-20002-2000i2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i22-2002-20000000000i2−i2i2−i2000000
χ3022-2-2-22-222-20002-2000i2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2-2200-220000000000−i2i2−i2i2000000
χ3122-2-2-22-222-20002-2000i2i2−i2−i2i2i2−i2−i2-2-2220000−i2−i2i2i2−i2−i2i2i22-200-220000000000i2−i2−i2i2000000
χ3222-2-2-22-222-20002-2000i2i2−i2−i2i2i2−i2−i2-2-2220000−i2−i2i2i2−i2−i2i2i2-22002-20000000000−i2i2i2−i2000000
χ3322-2-2-22-222-20002-2000−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i22-2002-20000000000−i2i2−i2i2000000
χ3422-2-2-22-222-20002-2000−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2-2200-220000000000i2−i2i2−i2000000
χ3522-2-2-22-222-20002-2000−i2−i2i2i2−i2−i2i2i2-2-2220000i2i2−i2−i2i2i2−i2−i22-200-220000000000−i2i2i2−i2000000
χ3622-2-2-22-222-20002-2000−i2−i2i2i2−i2−i2i2i2-2-2220000i2i2−i2−i2i2i2−i2−i2-22002-20000000000i2−i2−i2i2000000
χ372-22-2-222-2002-2-2002002i−2i2i−2i0000i2−i2i2−i2i2i2−i2−i22−22−22−22−2002-2002i−2i000000000000i2−i22−200
χ382-22-2-222-2002-2-2002002i−2i2i−2i0000i2−i2i2−i2i2i2−i2−i22−22−22−22−200-2200−2i2i000000000000−i2i2−2200
χ392-22-2-222-2002-2-2002002i−2i2i−2i0000−i2i2−i2i2−i2−i2i2i2−22−22−22−22002-2002i−2i000000000000−i2i2−2200
χ402-22-2-222-2002-2-2002002i−2i2i−2i0000−i2i2−i2i2−i2−i2i2i2−22−22−22−2200-2200−2i2i000000000000i2−i22−200
χ412-22-2-222-2002-2-200200−2i2i−2i2i0000i2−i2i2−i2i2i2−i2−i2−22−22−22−22002-200−2i2i000000000000i2−i2−2200
χ422-22-2-222-2002-2-200200−2i2i−2i2i0000i2−i2i2−i2i2i2−i2−i2−22−22−22−2200-22002i−2i000000000000−i2i22−200
χ432-22-2-222-2002-2-200200−2i2i−2i2i0000−i2i2−i2i2−i2−i2i2i22−22−22−22−2002-200−2i2i000000000000−i2i22−200
χ442-22-2-222-2002-2-200200−2i2i−2i2i0000−i2i2−i2i2−i2−i2i2i22−22−22−22−200-22002i−2i000000000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-44-4000-440000000000000004-44-40000000000000000000000000000000000
χ474444-4-4-4-44-4000-44000000000000000-44-440000000000000000000000000000000000
χ484444-4-4-4-4-440004-400000000000000000002222−22−22−22−22222200000000000000000000000000
χ494444-4-4-4-4-440004-40000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5044-4-44-44-4444-44-4-4-4-4400000000000000000000000000000000000000000000000000
χ5144-4-44-44-444-44-4-4-444-400000000000000000000000000000000000000000000000000
χ5244-4-44-44-4-4-4-44-4444-4400000000000000000000000000000000000000000000000000
χ5344-4-4-44-44-44000-440002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ5444-4-4-44-44-44000-44000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ554-44-44-4-44000000000000002i2−2i22i2−2i200002i2−2i2−2i22i22-2-22-222-200000000000000000000000000
χ564-44-44-4-44000000000000002i2−2i22i2−2i20000−2i22i22i2−2i2-222-22-2-2200000000000000000000000000
χ574-44-44-4-4400000000000000−2i22i2−2i22i200002i2−2i2−2i22i2-222-22-2-2200000000000000000000000000
χ584-44-44-4-4400000000000000−2i22i2−2i22i20000−2i22i22i2−2i22-2-22-222-200000000000000000000000000
χ594-44-4-444-400-44400-400000000002i2−2i22i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ604-44-4-444-400-44400-40000000000−2i22i2−2i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ614-4-4444-4-4000000000022−22−222200002i2−2i2−2i22i20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ624-4-4444-4-4000000000022−22−22220000−2i22i22i2−2i200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ634-4-4444-4-40000000000−222222−2200002i2−2i2−2i22i200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ644-4-4444-4-40000000000−222222−220000−2i22i22i2−2i20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ654-4-44-4-4440044-400-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ664-4-44-4-4440044-400-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ674-4-44-4-44400-4-440040000004-4-44000000000000000000000000000000000000000000
χ684-4-44-4-44400-4-44004000000-444-4000000000000000000000000000000000000000000

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