Finite Group Databasebeta

← Group #288385

Character table — Group #288385

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444222444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1111111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-11-1-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-11111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11-1-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1111-1-1-1-1-1-111-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11-111-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-1-11-111111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-111-1-111-1-111-1-1-11
χ172222222222-22-2-2-22-2-2000022220000-2-2-2-20000000022-2-2000020000-2000000000000
χ182222222222-22-2-2-22-2-2000022220000-2-2-2-200000000-2-2220000-200002000000000000
χ192222222222-22-2-2-22-2-20000-2-2-2-2000022220000000022-2-20000-200002000000000000
χ202222222222-22-2-2-22-2-20000-2-2-2-20000222200000000-2-222000020000-2000000000000
χ2122222222-2-22-2222-2-2-222220000-2-2-2-2000000000000000022-2-2000-220000000000000
χ2222222222-2-22-2222-2-2-222220000-2-2-2-20000000000000000-2-2220002-20000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-20000222200000000000000002222000-2-20000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2000022220000000000000000-2-2-2-2000220000000000000
χ2522-22-2-2-220020-2-220000000i2i2−i2−i222-2-2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200002i−2i2i−2i0000000000002−22−200
χ2622-22-2-2-220020-2-220000000i2i2−i2−i222-2-2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i20000−2i2i−2i2i000000000000−22−2200
χ2722-22-2-2-220020-2-220000000i2i2−i2−i2-2-222i2i2−i2−i2−i2−i2−i2−i2i2i2i2i200002i−2i−2i2i0000000000002−2−2200
χ2822-22-2-2-220020-2-220000000i2i2−i2−i2-2-222i2i2−i2−i2−i2−i2−i2−i2i2i2i2i20000−2i2i2i−2i000000000000−222−200
χ2922-22-2-2-220020-2-220000000−i2−i2i2i222-2-2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200002i−2i2i−2i000000000000−22−2200
χ3022-22-2-2-220020-2-220000000−i2−i2i2i222-2-2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i20000−2i2i−2i2i0000000000002−22−200
χ3122-22-2-2-220020-2-220000000−i2−i2i2i2-2-222−i2−i2i2i2i2i2i2i2−i2−i2−i2−i200002i−2i−2i2i000000000000−222−200
χ3222-22-2-2-220020-2-220000000−i2−i2i2i2-2-222−i2−i2i2i2i2i2i2i2−i2−i2−i2−i20000−2i2i2i−2i0000000000002−2−2200
χ332-2-2-222-22222-2-22-2-2-22000000000000000022-2-222-2-22i−2i2i−2i000000000000002i−2i000000
χ342-2-2-222-22222-2-22-2-2-22000000000000000022-2-222-2-2−2i2i−2i2i00000000000000−2i2i000000
χ352-2-2-222-22222-2-22-2-2-220000000000000000-2-222-2-2222i−2i2i−2i00000000000000−2i2i000000
χ362-2-2-222-22222-2-22-2-2-220000000000000000-2-222-2-222−2i2i−2i2i000000000000002i−2i000000
χ372-2-2-222-2222-2-22-22-22-222-2-200002-22-20000000000002i−2i−2i2i0000000000002i−2i00000000
χ382-2-2-222-2222-2-22-22-22-222-2-200002-22-2000000000000−2i2i2i−2i000000000000−2i2i00000000
χ392-2-2-222-2222-2-22-22-22-2-2-2220000-22-220000000000002i−2i−2i2i000000000000−2i2i00000000
χ402-2-2-222-2222-2-22-22-22-2-2-2220000-22-22000000000000−2i2i2i−2i0000000000002i−2i00000000
χ412-2-2-222-22-2-2-222-222-2222-2-20000-22-220000000000000000000002-20002-20000000000
χ422-2-2-222-22-2-2-222-222-2222-2-20000-22-22000000000000000000000-22000-220000000000
χ432-2-2-222-22-2-2-222-222-22-2-22200002-22-20000000000000000000002-2000-220000000000
χ442-2-2-222-22-2-2-222-222-22-2-22200002-22-2000000000000000000000-220002-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-44-404000-40000004-44-4000000000000000000000000000000000000000000
χ47444-44-4-4-44-404000-4000000-44-44000000000000000000000000000000000000000000
χ48444-44-4-4-4-440-400040000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000
χ49444-44-4-4-4-440-40004000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000
χ5044-44-4-4-4400-4044-400000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ5144-44-4-4-4400-4044-40000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ5244-4-4-444-400000000002i2−2i22i2−2i22i2−2i2−2i22i2000000002-22-2-22-2200000000000000000000000000
χ5344-4-4-444-400000000002i2−2i22i2−2i2−2i22i22i2−2i200000000-22-222-22-200000000000000000000000000
χ5444-4-4-444-40000000000−2i22i2−2i22i22i2−2i2−2i22i200000000-22-222-22-200000000000000000000000000
χ5544-4-4-444-40000000000−2i22i2−2i22i2−2i22i22i2−2i2000000002-22-2-22-2200000000000000000000000000
χ564-444-44-4-400000000002i2−2i2−2i22i2000000002i2−2i22i2−2i22-2-22-222-200000000000000000000000000
χ574-444-44-4-400000000002i2−2i2−2i22i200000000−2i22i2−2i22i2-222-22-2-2200000000000000000000000000
χ584-444-44-4-40000000000−2i22i22i2−2i2000000002i2−2i22i2−2i2-222-22-2-2200000000000000000000000000
χ594-444-44-4-40000000000−2i22i22i2−2i200000000−2i22i2−2i22i22-2-22-222-200000000000000000000000000
χ604-44-4-4-44400404-4-400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ614-44-4-4-44400404-4-40000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ624-44-4-4-44400-40-444000000000004-4-4400000000000000000000000000000000000000
χ634-44-4-4-44400-40-44400000000000-444-400000000000000000000000000000000000000
χ644-4-444-44-44-40-40004000000000000004-4-440000000000000000000000000000000000
χ654-4-444-44-44-40-4000400000000000000-444-40000000000000000000000000000000000
χ664-4-444-44-4-4404000-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ674-4-444-44-4-4404000-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ684-4-4-444-44-4-444-44-444-400000000000000000000000000000000000000000000000000

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