Finite Group Databasebeta

← Group #328021

Character table — Group #328021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444224444444444444444444448888888844448888888824
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ9111111111111-1-1-1-11111-1-1-1-111-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ10111111111111-1-1-1-11111-1-1-1-111-111-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-11
χ11111111111111-1-1-1-11111-1-1-1-111-111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-11
χ12111111111111-1-1-1-11111-1-1-1-111-111-1-111-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ13111111111111-1-1-1-11111-1-1-1-111-1-1-111-1-111-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-11
χ14111111111111-1-1-1-11111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1111-1
χ15111111111111-1-1-1-11111-1-1-1-111-1-1-111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111-1-1111-1
χ16111111111111-1-1-1-11111-1-1-1-111-1-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-111-1-111-1-1-11
χ172222222222-2-2222222-2-222-2-2-2-2-22222-2-20000-2-200000000000000000000000000
χ182222222222-2-2222222-2-222-2-2-2-2-2-2-2-2-22200002200000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-222-2-2222-2-2-2-200002200000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-222-2-22-2-222220000-2-200000000000000000000000000
χ2122222222-2-2222222-2-222-2-222-2-2-200000022-2-200-2-2220000000000000000000000
χ2222222222-2-2222222-2-222-2-222-2-2-2000000-2-2220022-2-20000000000000000000000
χ2322222222-2-222-2-2-2-2-2-22222-2-2-2-22000000222200-2-2-2-20000000000000000000000
χ2422222222-2-222-2-2-2-2-2-22222-2-2-2-22000000-2-2-2-20022220000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-22220000000000000000000000002-22-20000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-2222000000000000000000000000-22-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000000000000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000000000000000000000-222-20000000000
χ29222-2-2-22-2002-22i2i−2i−2i002-2002i−2i0000000002-20000002i−2i22−2−2i2i2−i2−i2000000002−2i2−i200
χ30222-2-2-22-2002-22i2i−2i−2i002-2002i−2i0000000002-20000002i−2i−2−222−i2−i2i2i200000000−22−i2i200
χ31222-2-2-22-2002-22i2i−2i−2i002-2002i−2i000000000-22000000−2i2i22−2−2i2i2−i2−i200000000−22−i2i200
χ32222-2-2-22-2002-22i2i−2i−2i002-2002i−2i000000000-22000000−2i2i−2−222−i2−i2i2i2000000002−2i2−i200
χ33222-2-2-22-2002-2−2i−2i2i2i002-200−2i2i0000000002-2000000−2i2i22−2−2−i2−i2i2i2000000002−2−i2i200
χ34222-2-2-22-2002-2−2i−2i2i2i002-200−2i2i0000000002-2000000−2i2i−2−222i2i2−i2−i200000000−22i2−i200
χ35222-2-2-22-2002-2−2i−2i2i2i002-200−2i2i000000000-220000002i−2i22−2−2−i2−i2i2i200000000−22i2−i200
χ36222-2-2-22-2002-2−2i−2i2i2i002-200−2i2i000000000-220000002i−2i−2−222i2i2−i2−i2000000002−2−i2i200
χ372-2-22-2-222-2-2002-22-222002-20000000002-200002-200002−22−22−22−200002−22−2000000
χ382-2-22-2-222-2-2002-22-222002-20000000002-200002-20000−22−22−22−220000−22−22000000
χ392-2-22-2-222-2-2002-22-222002-2000000000-220000-2200002−22−22−22−20000−22−22000000
χ402-2-22-2-222-2-2002-22-222002-2000000000-220000-220000−22−22−22−2200002−22−2000000
χ412-2-22-2-222-2-200-22-222200-220000000002-20000-2200002−22−2−22−2200002−2−22000000
χ422-2-22-2-222-2-200-22-222200-220000000002-20000-220000−22−222−22−20000−222−2000000
χ432-2-22-2-222-2-200-22-222200-22000000000-2200002-200002−22−2−22−220000−222−2000000
χ442-2-22-2-222-2-200-22-222200-22000000000-2200002-20000−22−222−22−200002−2−22000000
χ45444-4-4-44-400-444i4i−4i−4i00-4400−4i4i00000000000000000000000000000000000000000
χ46444-4-4-44-400-44−4i−4i4i4i00-44004i−4i00000000000000000000000000000000000000000
χ4744-444-4-4-44-40000004-4000000000004-40000000000000000000000000000000000
χ4844-444-4-4-44-40000004-400000000000-440000000000000000000000000000000000
χ4944-444-4-4-4-44000000-440000000004-4000000000000000000000000000000000000
χ5044-444-4-4-4-44000000-44000000000-44000000000000000000000000000000000000
χ514-444-44-4-44-44-40000-44-4400004-4000000000000000000000000000000000000000
χ524-444-44-4-44-4-440000-444-40000-44000000000000000000000000000000000000000
χ534-444-44-4-4-444-400004-4-440000-44000000000000000000000000000000000000000
χ544-444-44-4-4-44-4400004-44-400004-4000000000000000000000000000000000000000
χ554-44-44-4-440044000000-4-40000000000000004i−4i0000000000000000000000000000
χ564-44-44-4-440044000000-4-4000000000000000−4i4i0000000000000000000000000000
χ574-44-44-4-4400-4-40000004400000000000000000004-4000000000000000000000000
χ584-44-44-4-4400-4-4000000440000000000000000000-44000000000000000000000000
χ594-4-44-4-44444004-44-4-4-400-440000000000000000000000000000000000000000000
χ604-4-44-4-4444400-44-44-4-4004-40000000000000000000000000000000000000000000
χ614-4-4-4444-400004i−4i−4i4i0000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ624-4-4-4444-400004i−4i−4i4i000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ634-4-4-4444-40000−4i4i4i−4i0000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ644-4-4-4444-40000−4i4i4i−4i000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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