Finite Group Databasebeta

← Group #256937

Character table — Group #256937

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444444444442444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ5111111111111111111111111-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ91111111111111111-1-11-1-11-1-1111111-1-1-1-1111111-1-1-1-1-11-1111-1-1-1-111-1-111-1-1
χ101111111111111111-1-11-1-11-1-1111111-1-1-1-111-1-1-1-11111-11-11-1-1-1-111-1-111-1-111
χ111111111111111111-1-11-1-11-1-11111-1-11111-1-11111-1-1-1-11-11-111-1-1-1-1-1-111-1-111
χ121111111111111111-1-11-1-11-1-11111-1-11111-1-1-1-1-1-111111-11-1-1-1-1-11111-1-111-1-1
χ131111111111111111-1-11-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1111111-1-1-1-111
χ141111111111111111-1-11-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11111-1-1
χ151111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11-1-11111-1-11111-1-1
χ161111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111111-1-111-1-1-1-111
χ172222222222-2-222-2-222-222-2-2-20000002200220000000000-2-200000000000000
χ182222222222-2-222-2-222-222-2-2-2000000-2-200-2-200000000002200000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-2220000002200-2-20000000000-2200000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-222000000-2-2002200000000002-200000000000000
χ2122222222-2-222-2-22222-2-2-2-22-200002200-2-200000000002-20000000000000000
χ2222222222-2-222-2-22222-2-2-2-22-20000-2-200220000000000-220000000000000000
χ2322222222-2-222-2-222-2-2-222-2-2200002200220000000000-2-20000000000000000
χ2422222222-2-222-2-222-2-2-222-2-220000-2-200-2-20000000000220000000000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-22-2222-2-200000000000000000000002-20000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-22-22-2-2220000000000000000000000-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-222-2-20000000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-2-2-22200000000000000000000002-20000000000
χ29222-2-2-2-222-2002-2002i−2i02i−2i0000000002i−2i002-222−2−2i2i2−i2−i2000000000000002−2i2−i2
χ30222-2-2-2-222-2002-2002i−2i02i−2i0000000002i−2i002-2−2−222−i2−i2i2i200000000000000−22−i2i2
χ31222-2-2-2-222-2002-2002i−2i02i−2i000000000−2i2i00-2222−2−2i2i2−i2−i200000000000000−22−i2i2
χ32222-2-2-2-222-2002-2002i−2i02i−2i000000000−2i2i00-22−2−222−i2−i2i2i2000000000000002−2i2−i2
χ33222-2-2-2-222-2002-200−2i2i0−2i2i0000000002i−2i00-2222−2−2−i2−i2i2i200000000000000−22i2−i2
χ34222-2-2-2-222-2002-200−2i2i0−2i2i0000000002i−2i00-22−2−222i2i2−i2−i2000000000000002−2−i2i2
χ35222-2-2-2-222-2002-200−2i2i0−2i2i000000000−2i2i002-222−2−2−i2−i2i2i2000000000000002−2−i2i2
χ36222-2-2-2-222-2002-200−2i2i0−2i2i000000000−2i2i002-2−2−222i2i2−i2−i200000000000000−22i2−i2
χ372-222-22-2-22-22-2-222-200-2002002i−2i2i−2i000000002-22-2000000002i−2i000000000000
χ382-222-22-2-22-22-2-222-200-2002002i−2i2i−2i00000000-22-2200000000−2i2i000000000000
χ392-222-22-2-22-22-2-222-200-200200−2i2i−2i2i000000002-22-200000000−2i2i000000000000
χ402-222-22-2-22-22-2-222-200-200200−2i2i−2i2i00000000-22-22000000002i−2i000000000000
χ412-222-22-2-2-22-222-2-2200-2002002i−2i−2i2i0000000000002-22-2000000002i−2i00000000
χ422-222-22-2-2-22-222-2-2200-2002002i−2i−2i2i000000000000-22-2200000000−2i2i00000000
χ432-222-22-2-2-22-222-2-2200-200200−2i2i2i−2i0000000000002-22-200000000−2i2i00000000
χ442-222-22-2-2-22-222-2-2200-200200−2i2i2i−2i000000000000-22-22000000002i−2i00000000
χ45444-4-4-4-44-4400-44004i−4i0−4i4i00000000000000000000000000000000000000000
χ46444-4-4-4-44-4400-4400−4i4i04i−4i00000000000000000000000000000000000000000
χ4744-444-4-4-4004-400-440000000000000000000000000000000000000022−22000000
χ4844-444-4-4-4004-400-4400000000000000000000000000000000000000−2222000000
χ4944-444-4-4-400-44004-4000000000000000000000000000000000000000022−220000
χ5044-444-4-4-400-44004-40000000000000000000000000000000000000000−22220000
χ514-444-44-4-44-4-44-44-4400400-40000000000000000000000000000000000000000
χ524-444-44-4-4-444-44-44-400400-40000000000000000000000000000000000000000
χ534-44-44-44-44400-4-4000000000000000000000022−22−22220000000000000000000000
χ544-44-44-44-44400-4-40000000000000000000000−222222−220000000000000000000000
χ554-44-44-44-4-4-40044000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ564-44-44-44-4-4-4004400000000000000000000000000−2i22i22i2−2i2000000000000000000
χ574-4-44-4-444004400-4-40000000000004i−4i00000000000000000000000000000000
χ584-4-44-4-444004400-4-4000000000000−4i4i00000000000000000000000000000000
χ594-4-44-4-44400-4-4004400000000000000004-40000000000000000000000000000
χ604-4-44-4-44400-4-400440000000000000000-440000000000000000000000000000
χ6188-8-8-888-8000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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