Finite Group Databasebeta

← Group #336721

Character table — Group #336721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888824448888244
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-11-1-111-1-1-1
χ311111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-111111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1
χ61111111111111111111111-1-1-1-1111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-111111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-111-1-1-111-11-1
χ9111111111111111111-1-1-1-1111111-1-111111111-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-111-1
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-111-1-1-1-11
χ11111111111111111111-1-1-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-111-111
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1111-1-1-111
χ1722222222222-2-2-2-22-2-20000222200000022-2-22200-2-2000000000000-20000000000
χ1822222222222-2-2-2-22-2-200002222000000-2-222-2-200-2-200000000000020000000000
χ1922222222222-2-2-2-22-2-20000-2-2-2-20000002222-2-20022000000000000-20000000000
χ2022222222222-2-2-2-22-2-20000-2-2-2-2000000-2-2-2-222002200000000000020000000000
χ2122222222-2-2-22222-2-2-22222000022-2-2-2-2000000-2-20000000000000000020000000
χ2222222222-2-2-22222-2-2-222220000-2-22222000000-2-200000000000000000-20000000
χ2322222222-2-2-22222-2-2-2-2-2-2-200002222-2-20000002200000000000000000-20000000
χ2422222222-2-2-22222-2-2-2-2-2-2-20000-2-2-2-222000000220000000000000000020000000
χ2522-222-2-2-2-2-2222-2-222-20000000000000000000000002i2i−2i−2i22-2-2000002i−2i00000000
χ2622-222-2-2-2-2-2222-2-222-20000000000000000000000002i2i−2i−2i-2-22200000−2i2i00000000
χ2722-222-2-2-2-2-2222-2-222-2000000000000000000000000−2i−2i2i2i22-2-200000−2i2i00000000
χ2822-222-2-2-2-2-2222-2-222-2000000000000000000000000−2i−2i2i2i-2-222000002i−2i00000000
χ292-222-22-2-20002-22-20002i2i−2i−2ii2i2−i2−i2002-22i−2i00000000i2−i200002−22−222−2−2000000i2−i2000
χ302-222-22-2-20002-22-20002i2i−2i−2ii2i2−i2−i200-22−2i2i00000000i2−i20000−22−2222−2−2000000−i2i2000
χ312-222-22-2-20002-22-20002i2i−2i−2i−i2−i2i2i2002-22i−2i00000000−i2i20000−22−22−2−222000000−i2i2000
χ322-222-22-2-20002-22-20002i2i−2i−2i−i2−i2i2i200-22−2i2i00000000−i2i200002−22−2−2−222000000i2−i2000
χ332-222-22-2-20002-22-2000−2i−2i2i2ii2i2−i2−i2002-2−2i2i00000000i2−i20000−22−22−2−222000000i2−i2000
χ342-222-22-2-20002-22-2000−2i−2i2i2ii2i2−i2−i200-222i−2i00000000i2−i200002−22−2−2−222000000−i2i2000
χ352-222-22-2-20002-22-2000−2i−2i2i2i−i2−i2i2i2002-2−2i2i00000000−i2i200002−22−222−2−2000000−i2i2000
χ362-222-22-2-20002-22-2000−2i−2i2i2i−i2−i2i2i200-222i−2i00000000−i2i20000−22−2222−2−2000000i2−i2000
χ372-22-22-2-222-220000-2002−22−22i−2i2i−2i0000002i−2i002-22−2002−22−20000i2−i2i2−i20000i2−i200000
χ382-22-22-2-222-220000-2002−22−22i−2i2i−2i000000−2i2i00-222−200−22−220000i2−i2i2−i20000−i2i200000
χ392-22-22-2-222-220000-2002−22−2−2i2i−2i2i0000002i−2i00-222−200−22−220000−i2i2−i2i20000i2−i200000
χ402-22-22-2-222-220000-2002−22−2−2i2i−2i2i000000−2i2i002-22−2002−22−20000−i2i2−i2i20000−i2i200000
χ412-22-22-2-222-220000-200−22−222i−2i2i−2i0000002i−2i002-2−2200−22−220000−i2i2−i2i20000−i2i200000
χ422-22-22-2-222-220000-200−22−222i−2i2i−2i000000−2i2i00-22−22002−22−20000−i2i2−i2i20000i2−i200000
χ432-22-22-2-222-220000-200−22−22−2i2i−2i2i0000002i−2i00-22−22002−22−20000i2−i2i2−i20000−i2i200000
χ442-22-22-2-222-220000-200−22−22−2i2i−2i2i000000−2i2i002-2−2200−22−220000i2−i2i2−i20000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-44-400000000002i2−2i2−2i22i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ47444-4-4-44-400000000002i2−2i2−2i22i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ48444-4-4-44-40000000000−2i22i22i2−2i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ49444-4-4-44-40000000000−2i22i22i2−2i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ5044-444-4-4-444-444-4-4-4-4400000000000000000000000000000000000000000000000
χ5144-444-4-4-444-4-4-444-44-400000000000000000000000000000000000000000000000
χ5244-444-4-4-4-4-44-4-4444-4400000000000000000000000000000000000000000000000
χ534-444-44-4-4000-44-4400000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000
χ544-444-44-4-4000-44-440000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000
χ554-44-44-4-44-44-4000040022−2222−220000000000000000−22220000000000000000000000000
χ564-44-44-4-44-44-40000400−2222−2222000000000000000022−220000000000000000000000000
χ574-4-44-4-4440004-4-44000000000000000000000000000000022−22−2222000000000000000
χ584-4-44-4-4440004-4-440000000000000000000000000000000−222222−22000000000000000
χ594-4-44-4-444000-444-4000000000004-40000000000000000000000000000000000000
χ604-4-44-4-444000-444-400000000000-440000000000000000000000000000000000000
χ614-4-4-4444-44-4-4000040000000000000000004-400000000000000000000000000000
χ624-4-4-4444-44-4-400004000000000000000000-4400000000000000000000000000000
χ634-4-4-4444-4-4440000-4000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ644-4-4-4444-4-4440000-400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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