Finite Group Databasebeta

← Group #336748

Character table — Group #336748

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888444444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-111-1-1-1
χ311111111111111111111111111-1-111-1-11111-1-111111111-1-1-1-11111-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-11-1-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-1-11111-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ10111111111111111111-1-1-1-1111111-1-111111111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1
χ11111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-1111111-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-11
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-11-1-1-1-1111-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-11-11
χ172222222222-2-2-222-2-2-2000022222200-2-20000-2-200-2-200000000000020000000000
χ182222222222-2-2-222-2-2-200002222-2-2002200002200-2-2000000000000-20000000000
χ192222222222-2-2-222-2-2-20000-2-2-2-22200220000-2-20022000000000000-20000000000
χ202222222222-2-2-222-2-2-20000-2-2-2-2-2-200-2-2000022002200000000000020000000000
χ2122222222-2-2222-2-22-2-22222000000220022-2-200-2-2000000000000000-2000000000
χ2222222222-2-2222-2-22-2-22222000000-2-200-2-22200-2-20000000000000002000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-20000002200-2-2220022000000000000000-2000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2000000-2-20022-2-200220000000000000002000000000
χ2522-22-2-2-222-20002-2000i2i2−i2−i222-2-200002-200002-2i2−i2000000i2i2−i2−i2i2i2−i2−i2000000i2−i2000
χ2622-22-2-2-222-20002-2000i2i2−i2−i222-2-20000-220000-22i2−i2000000−i2−i2i2i2i2i2−i2−i2000000−i2i2000
χ2722-22-2-2-222-20002-2000i2i2−i2−i2-2-22200002-20000-22i2−i2000000−i2−i2i2i2−i2−i2i2i2000000i2−i2000
χ2822-22-2-2-222-20002-2000i2i2−i2−i2-2-2220000-2200002-2i2−i2000000i2i2−i2−i2−i2−i2i2i2000000−i2i2000
χ2922-22-2-2-222-20002-2000−i2−i2i2i222-2-200002-200002-2−i2i2000000−i2−i2i2i2−i2−i2i2i2000000−i2i2000
χ3022-22-2-2-222-20002-2000−i2−i2i2i222-2-20000-220000-22−i2i2000000i2i2−i2−i2−i2−i2i2i2000000i2−i2000
χ3122-22-2-2-222-20002-2000−i2−i2i2i2-2-22200002-20000-22−i2i2000000i2i2−i2−i2i2i2−i2−i2000000−i2i2000
χ3222-22-2-2-222-20002-2000−i2−i2i2i2-2-2220000-2200002-2−i2i2000000−i2−i2i2i2i2i2−i2−i2000000i2−i2000
χ3322-2-22-22-200-22-2002002i−2i2i−2i2−22−2002-2002i−2i0000002−2i2i2−i2−i20000i2−i2i2−i200002−200000
χ3422-2-22-22-200-22-2002002i−2i2i−2i2−22−200-2200−2i2i0000002−2−i2−i2i2i20000i2−i2i2−i20000−2200000
χ3522-2-22-22-200-22-2002002i−2i2i−2i−22−22002-2002i−2i000000−22−i2−i2i2i20000−i2i2−i2i20000−2200000
χ3622-2-22-22-200-22-2002002i−2i2i−2i−22−2200-2200−2i2i000000−22i2i2−i2−i20000−i2i2−i2i200002−200000
χ3722-2-22-22-200-22-200200−2i2i−2i2i2−22−2002-200−2i2i0000002−2−i2−i2i2i20000−i2i2−i2i200002−200000
χ3822-2-22-22-200-22-200200−2i2i−2i2i2−22−200-22002i−2i0000002−2i2i2−i2−i20000−i2i2−i2i20000−2200000
χ3922-2-22-22-200-22-200200−2i2i−2i2i−22−22002-200−2i2i000000−22i2i2−i2−i20000i2−i2i2−i20000−2200000
χ4022-2-22-22-200-22-200200−2i2i−2i2i−22−2200-22002i−2i000000−22−i2−i2i2i20000i2−i2i2−i200002−200000
χ412-2-22-222-2-2-2-22222-22-20000000000000000000000002-22-22i−2i2i−2i0000002i−2i0000000
χ422-2-22-222-2-2-2-22222-22-20000000000000000000000002-22-2−2i2i−2i2i000000−2i2i0000000
χ432-2-22-222-2-2-2-22222-22-2000000000000000000000000-22-222i−2i2i−2i000000−2i2i0000000
χ442-2-22-222-2-2-2-22222-22-2000000000000000000000000-22-22−2i2i−2i2i0000002i−2i0000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-44-4-4000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ47444-4-44-4-4000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ48444-4-44-4-40000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ49444-4-44-4-40000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ5044-44-4-4-44-44000-440002i22i2−2i2−2i20000000000000000−2i22i20000000000000000000000000
χ5144-44-4-4-44-44000-44000−2i2−2i22i22i200000000000000002i2−2i20000000000000000000000000
χ5244-4-44-44-4004-4400-400000022−2222−2200000000000000−222200000000000000000000000
χ5344-4-44-44-4004-4400-4000000−2222−22220000000000000022−2200000000000000000000000
χ544-4444-4-4-44-4000-44000000000004-40000000000000000000000000000000000000
χ554-4444-4-4-44-4000-4400000000000-440000000000000000000000000000000000000
χ564-4444-4-4-4-440004-4000000000000000000000000000000022−22−2222000000000000000
χ574-4444-4-4-4-440004-40000000000000000000000000000000−222222−22000000000000000
χ584-44-4-4-4440044-400-4000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ594-44-4-4-4440044-400-400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ604-44-4-4-44400-4-440040000000000000000004-400000000000000000000000000000
χ614-44-4-4-44400-4-44004000000000000000000-4400000000000000000000000000000
χ624-4-44-444-4444-4-4-4-444-400000000000000000000000000000000000000000000000
χ634-4-44-444-444-444-4-4-4-4400000000000000000000000000000000000000000000000
χ644-4-44-444-4-4-44-4-4444-4400000000000000000000000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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