Finite Group Databasebeta

← Group #288342

Character table — Group #288342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111111111111111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-1-1-1-1111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-1111-1
χ11111111111111111111-1-1-1-111-1-111111111-1-111-1-1-1-111-1-1-1-11-1-1-111-1-1-1-111-11
χ12111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-1-11
χ13111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111-1111-1-1-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1111111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111111-1-1-111-1-111-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-111-1-1111-1
χ172222222222-22-2-2-22-2-2000022000022-2-2-2-200220000-2-2000000000000000000
χ182222222222-22-2-2-22-2-20000220000-2-222-2-200-2-2000022000000000000000000
χ192222222222-22-2-2-22-2-20000-2-2000022-2-22200-2-2000022000000000000000000
χ202222222222-22-2-2-22-2-20000-2-20000-2-2222200220000-2-2000000000000000000
χ2122222222-2-22-2222-2-2-22222002222000000-2-2000000000000-2-2000000000000
χ2222222222-2-22-2222-2-2-2222200-2-2-2-2000000-2-200000000000022000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-20022-2-2000000220000000000002-2000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-200-2-22200000022000000000000-22000000000000
χ252-2-222-2-2200202-2-20002i2i−2i−2i002i−2i2-2000000002−200002−2i2i2−i2−i200000000i2−i22−200
χ262-2-222-2-2200202-2-20002i2i−2i−2i002i−2i2-200000000−220000−22−i2−i2i2i200000000−i2i2−2200
χ272-2-222-2-2200202-2-20002i2i−2i−2i00−2i2i-22000000002−200002−2i2i2−i2−i200000000−i2i2−2200
χ282-2-222-2-2200202-2-20002i2i−2i−2i00−2i2i-2200000000−220000−22−i2−i2i2i200000000i2−i22−200
χ292-2-222-2-2200202-2-2000−2i−2i2i2i002i−2i-22000000002−200002−2−i2−i2i2i200000000i2−i2−2200
χ302-2-222-2-2200202-2-2000−2i−2i2i2i002i−2i-2200000000−220000−22i2i2−i2−i200000000−i2i22−200
χ312-2-222-2-2200202-2-2000−2i−2i2i2i00−2i2i2-2000000002−200002−2−i2−i2i2i200000000−i2i22−200
χ322-2-222-2-2200202-2-2000−2i−2i2i2i00−2i2i2-200000000−220000−22i2i2−i2−i200000000i2−i2−2200
χ332-2-2-2-2222222-2-22-2-2-2200000000002i−2i2i−2i0000002i2i−2i−2i002-22-200000000000000
χ342-2-2-2-2222222-2-22-2-2-2200000000002i−2i2i−2i000000−2i−2i2i2i00-22-2200000000000000
χ352-2-2-2-2222222-2-22-2-2-220000000000−2i2i−2i2i0000002i2i−2i−2i00-22-2200000000000000
χ362-2-2-2-2222222-2-22-2-2-220000000000−2i2i−2i2i000000−2i−2i2i2i002-22-200000000000000
χ372-2-2-2-222222-2-22-22-22-22-22-20000002i−2i−2i2i002-20000000000000000002i−2i000000
χ382-2-2-2-222222-2-22-22-22-22-22-2000000−2i2i2i−2i002-2000000000000000000−2i2i000000
χ392-2-2-2-222222-2-22-22-22-2-22-220000002i−2i−2i2i00-22000000000000000000−2i2i000000
χ402-2-2-2-222222-2-22-22-22-2-22-22000000−2i2i2i−2i00-220000000000000000002i−2i000000
χ412-2-2-2-2222-2-2-222-222-222-22-2000000000000-22000000000000002-22-200000000
χ422-2-2-2-2222-2-2-222-222-222-22-2000000000000-2200000000000000-22-2200000000
χ432-2-2-2-2222-2-2-222-222-22-22-220000000000002-2000000000000002-2-2200000000
χ442-2-2-2-2222-2-2-222-222-22-22-220000000000002-200000000000000-222-200000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-4-440040-4-44000000000000000000000000000002i2−2i2−2i22i200000000000000
χ47444-4-4-4-440040-4-4400000000000000000000000000000−2i22i22i2−2i200000000000000
χ48444-4-4-4-4400-4044-40004i−4i−4i4i0000000000000000000000000000000000000000
χ49444-4-4-4-4400-4044-4000−4i4i4i−4i0000000000000000000000000000000000000000
χ5044-44-44-4-44-404000-4000000000000000000000022−2222−2200000000000000000000
χ5144-44-44-4-44-404000-40000000000000000000000−2222−222200000000000000000000
χ5244-44-44-4-4-440-4000400000000000000004i−4i0000000000000000000000000000
χ5344-44-44-4-4-440-400040000000000000000−4i4i0000000000000000000000000000
χ544-44-444-4-44-40-4000400000000000000000000002i2−2i2−2i22i200000000000000000000
χ554-44-444-4-44-40-400040000000000000000000000−2i22i22i2−2i200000000000000000000
χ564-44-444-4-4-4404000-40000004-400000000000000000000000000000000000000
χ574-44-444-4-4-4404000-4000000-4400000000000000000000000000000000000000
χ584-4-444-4-4400-40-44400000000000000000000022−220000−2222000000000000000000
χ594-4-444-4-4400-40-444000000000000000000000−2222000022−22000000000000000000
χ604-4-4-4-4444-4-444-44-444-400000000000000000000000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-888-8-88-8000000000000000000000000000000000000000000000000000000

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