Finite Group Databasebeta

← Group #288357

Character table — Group #288357

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888822444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-11111-1-1
χ51111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-11111-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-11-1-111-1-1111-1
χ11111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1111-1-1-1-111-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-11-1-11111-1-1-11
χ13111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11-1111111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111111-1-1-1-1-111-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-11111-1-1111-1
χ17222222222-2-22-222-2-2-2222222002200000000-2-2000000000000-2-20000000000
χ18222222222-2-22-222-2-2-22222-2-200-2-200000000-2-2000000000000220000000000
χ19222222222-2-22-222-2-2-2-2-2-2-22200-2-200000000220000000000002-20000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2-2-200220000000022000000000000-220000000000
χ2122222222-222-22-2-22-2-2000000220022-2-2-2-222000000-2-2000000000000000000
χ2222222222-222-22-2-22-2-20000002200-2-222-2-2-2-200000022000000000000000000
χ2322222222-222-22-2-22-2-2000000-2-20022-2-222-2-200000022000000000000000000
χ2422222222-222-22-2-22-2-2000000-2-200-2-2222222000000-2-2000000000000000000
χ252-2-22-2-222222-2-22-2-2-2200000000002i−2i2i−2i0000002i2i−2i−2i0022-2-200000000000000
χ262-2-22-2-222222-2-22-2-2-2200000000002i−2i2i−2i000000−2i−2i2i2i00-2-22200000000000000
χ272-2-22-2-222222-2-22-2-2-220000000000−2i2i−2i2i0000002i2i−2i−2i00-2-22200000000000000
χ282-2-22-2-222222-2-22-2-2-220000000000−2i2i−2i2i000000−2i−2i2i2i0022-2-200000000000000
χ292-2-22-2-222-2222-2-22-22-222-2-20000002i−2i−2i2i00002-200000000000000002i−2i000000
χ302-2-22-2-222-2222-2-22-22-222-2-2000000−2i2i2i−2i00002-20000000000000000−2i2i000000
χ312-2-22-2-222-2222-2-22-22-2-2-2220000002i−2i−2i2i0000-220000000000000000−2i2i000000
χ322-2-22-2-222-2222-2-22-22-2-2-222000000−2i2i2i−2i0000-2200000000000000002i−2i000000
χ332-2-22-2-222-2-2-222-222-2222-2-200000000000000-2200000000002-2002-200000000
χ342-2-22-2-222-2-2-222-222-2222-2-200000000000000-220000000000-2200-2200000000
χ352-2-22-2-222-2-2-222-222-22-2-222000000000000002-200000000002-200-2200000000
χ362-2-22-2-222-2-2-222-222-22-2-222000000000000002-20000000000-22002-200000000
χ372-2-2-2222-2200-20-220002i−2i2i−2i2i−2i002-2000000i2−i2000000i2−i22−22−2000000002−2i2−i200
χ382-2-2-2222-2200-20-220002i−2i2i−2i2i−2i002-2000000−i2i2000000−i2i2−22−2200000000−22−i2i200
χ392-2-2-2222-2200-20-220002i−2i2i−2i−2i2i00-22000000i2−i2000000i2−i22−22−200000000−22−i2i200
χ402-2-2-2222-2200-20-220002i−2i2i−2i−2i2i00-22000000−i2i2000000−i2i2−22−22000000002−2i2−i200
χ412-2-2-2222-2200-20-22000−2i2i−2i2i2i−2i00-22000000i2−i2000000i2−i2−22−22000000002−2−i2i200
χ422-2-2-2222-2200-20-22000−2i2i−2i2i2i−2i00-22000000−i2i2000000−i2i22−22−200000000−22i2−i200
χ432-2-2-2222-2200-20-22000−2i2i−2i2i−2i2i002-2000000i2−i2000000i2−i2−22−2200000000−22i2−i200
χ442-2-2-2222-2200-20-22000−2i2i−2i2i−2i2i002-2000000−i2i2000000−i2i22−22−2000000002−2−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-44-440040-4-40000000000000000000000000000022−22−222200000000000000
χ47444-4-4-44-440040-4-400000000000000000000000000000−222222−2200000000000000
χ48444-4-4-44-4-400-40440004i−4i−4i4i0000000000000000000000000000000000000000
χ49444-4-4-44-4-400-4044000−4i4i4i−4i0000000000000000000000000000000000000000
χ5044-4-44-4-4404-40400-4000000004i−4i000000000000000000000000000000000000
χ5144-4-44-4-4404-40400-400000000−4i4i000000000000000000000000000000000000
χ5244-4-44-4-440-440-4004000000000000000000000022−2222−2200000000000000000000
χ5344-4-44-4-440-440-40040000000000000000000000−2222−222200000000000000000000
χ544-44-4-44-4404-40-400400000000000000004-40000000000000000000000000000
χ554-44-4-44-4404-40-40040000000000000000-440000000000000000000000000000
χ564-44-4-44-440-440400-400000000000000000000002i2−2i2−2i22i200000000000000000000
χ574-44-4-44-440-440400-40000000000000000000000−2i22i22i2−2i200000000000000000000
χ584-4-44-4-4444-4-4-444-444-400000000000000000000000000000000000000000000
χ594-4-4-4444-4-400404-400000000000000000002i2−2i2000000−2i22i2000000000000000000
χ604-4-4-4444-4-400404-40000000000000000000−2i22i20000002i2−2i2000000000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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