Finite Group Databasebeta

← Group #288321

Character table — Group #288321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888822
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-111-11
χ12111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-111-1-11-1
χ13111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1111-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-111-1-1111-1
χ17222222222-2-2222-2-2-2-22222002222000000-2-2000000000000-2-2000000000000
χ18222222222-2-2222-2-2-2-2222200-2-2-2-2000000-2-200000000000022000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-20022-2-200000022000000000000-22000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-200-2-222000000220000000000002-2000000000000
χ2122222222-222-2-2-222-2-20000220000-2-222-2-200000022-2-2000000000000000000
χ2222222222-222-2-2-222-2-20000220000-2-2-2-222000000-2-222000000000000000000
χ2322222222-222-2-2-222-2-20000-2-200002222-2-2000000-2-222000000000000000000
χ2422222222-222-2-2-222-2-20000-2-2000022-2-22200000022-2-2000000000000000000
χ252-222-22-2-2-20022-2000022-2-2002i−2i2i−2i000000000000i2−i2i2−i2i2i2−i2−i2000000002−22−200
χ262-222-22-2-2-20022-2000022-2-2002i−2i2i−2i000000000000−i2i2−i2i2−i2−i2i2i200000000−22−2200
χ272-222-22-2-2-20022-2000022-2-200−2i2i−2i2i000000000000i2−i2i2−i2i2i2−i2−i200000000−22−2200
χ282-222-22-2-2-20022-2000022-2-200−2i2i−2i2i000000000000−i2i2−i2i2−i2−i2i2i2000000002−22−200
χ292-222-22-2-2-20022-20000-2-222002i−2i−2i2i000000000000i2−i2i2−i2−i2−i2i2i2000000002−2−2200
χ302-222-22-2-2-20022-20000-2-222002i−2i−2i2i000000000000−i2i2−i2i2i2i2−i2−i200000000−222−200
χ312-222-22-2-2-20022-20000-2-22200−2i2i2i−2i000000000000i2−i2i2−i2−i2−i2i2i200000000−222−200
χ322-222-22-2-2-20022-20000-2-22200−2i2i2i−2i000000000000−i2i2−i2i2i2i2−i2−i2000000002−2−2200
χ332-22-2-2-222222-22-2-2-2-2200002i−2i00002i−2i0000002i2i−2i−2i00002-22-200000000000000
χ342-22-2-2-222222-22-2-2-2-2200002i−2i00002i−2i000000−2i−2i2i2i0000-22-2200000000000000
χ352-22-2-2-222222-22-2-2-2-220000−2i2i0000−2i2i0000002i2i−2i−2i0000-22-2200000000000000
χ362-22-2-2-222222-22-2-2-2-220000−2i2i0000−2i2i000000−2i−2i2i2i00002-22-200000000000000
χ372-22-2-2-222-2222-22-2-22-22-22-22i−2i0000−2i2i00002-20000000000000000002i−2i000000
χ382-22-2-2-222-2222-22-2-22-22-22-2−2i2i00002i−2i00002-2000000000000000000−2i2i000000
χ392-22-2-2-222-2222-22-2-22-2-22-222i−2i0000−2i2i0000-22000000000000000000−2i2i000000
χ402-22-2-2-222-2222-22-2-22-2-22-22−2i2i00002i−2i0000-220000000000000000002i−2i000000
χ412-22-2-2-222-2-2-22-2222-222-22-2000000000000-22000000000000002-22-200000000
χ422-22-2-2-222-2-2-22-2222-222-22-2000000000000-2200000000000000-22-2200000000
χ432-22-2-2-222-2-2-22-2222-22-22-220000000000002-2000000000000002-2-2200000000
χ442-22-2-2-222-2-2-22-2222-22-22-220000000000002-200000000000000-222-200000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-44-4-4-44004-4-400004-4-440000000000000000000000000000000000000000
χ47444-44-4-4-44004-4-40000-444-40000000000000000000000000000000000000000
χ48444-44-4-4-4-400-4440000000000000000000000000000002i2−2i2−2i22i200000000000000
χ49444-44-4-4-4-400-444000000000000000000000000000000−2i22i22i2−2i200000000000000
χ5044-44-4-44-404-40004-4000000000000000000002i2−2i22i2−2i20000000000000000000000
χ5144-44-4-44-404-40004-400000000000000000000−2i22i2−2i22i20000000000000000000000
χ5244-44-4-44-40-44000-4400000000000000004i−4i0000000000000000000000000000
χ5344-44-4-44-40-44000-440000000000000000−4i4i0000000000000000000000000000
χ544-444-44-4-4400-4-44000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ554-444-44-4-4400-4-4400000000000000000000000000−2i22i22i2−2i2000000000000000000
χ564-44-4-4-4444-4-4-44-4444-400000000000000000000000000000000000000000000
χ574-4-4-4444-404-4000-440000000000000000000022−22−22220000000000000000000000
χ584-4-4-4444-404-4000-4400000000000000000000−222222−220000000000000000000000
χ594-4-4-4444-40-440004-4000000000000004-4000000000000000000000000000000
χ604-4-4-4444-40-440004-400000000000000-44000000000000000000000000000000
χ6188-8-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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