Finite Group Databasebeta

← Group #291715

Character table — Group #291715

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444488888888888888888888888888888161616161616161616163232
order12222222444444442244444444444444444448888888888888888224444888824
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-11-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111111
χ5111111111111111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1
χ7111111111111111111111111-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ8111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ91111111111111111-1-1-1-1-1-11111-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-11111-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-11
χ121111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-11-1
χ131111111111111111-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-11
χ151111111111111111-1-1-1-1-1-111-1-1-111-1-11111111111-1-1-1-1-1-1-1-111111-1-11-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1111-1
χ1722222222222-2-2-2-2222-2-222-2-222-222000000000000000000000000-20-2000000000
χ1822222222222-2-2-2-2222-2-222-2-2-2-2-2-2-2000000000000000000000000202000000000
χ1922222222222-2-2-2-22-2-222-2-2-2-2222-2-200000000000000000000000020-2000000000
χ2022222222222-2-2-2-22-2-222-2-2-2-2-2-2222000000000000000000000000-202000000000
χ2122222222-2-2-22222-222-2-2-2-2-2-2002002222000000000000000000000-20-200000000
χ2222222222-2-2-22222-222-2-2-2-2-2-200200-2-2-2-200000000000000000000020200000000
χ2322222222-2-2-22222-2-2-22222-2-200-20022-2-2000000000000000000000-20200000000
χ2422222222-2-2-22222-2-2-22222-2-200-200-2-22200000000000000000000020-200000000
χ2522222222-2-2-2-2-2-2-2-22222-2-22200-200000022-2-2000000000000000000002-2000000
χ2622222222-2-2-2-2-2-2-2-22222-2-22200-2000000-2-22200000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200200000022-2-200000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222002000000-2-222000000000000000000002-2000000
χ2922-222-2-2-222-2-2-222-20000002-20000000002i−2i2i−2i22-2-20000000000000000002i−2i0000
χ3022-222-2-2-222-2-2-222-20000002-20000000002i−2i2i−2i-2-222000000000000000000−2i2i0000
χ3122-222-2-2-222-2-2-222-20000002-2000000000−2i2i−2i2i22-2-2000000000000000000−2i2i0000
χ3222-222-2-2-222-2-2-222-20000002-2000000000−2i2i−2i2i-2-2220000000000000000002i−2i0000
χ3322-222-2-2-2-2-2222-2-220000002-20000000002i−2i−2i2i00002i2i−2i−2i00000000000000002-200
χ3422-222-2-2-2-2-2222-2-220000002-20000000002i−2i−2i2i0000−2i−2i2i2i0000000000000000-2200
χ3522-222-2-2-2-2-2222-2-220000002-2000000000−2i2i2i−2i00002i2i−2i−2i0000000000000000-2200
χ3622-222-2-2-2-2-2222-2-220000002-2000000000−2i2i2i−2i0000−2i−2i2i2i00000000000000002-200
χ372-2-22-222-22-220000-22-2002-2002i−2i02i−2i000000002−22−22−22−2i2i2−i2−i2i2i2−i2−i2000000000000
χ382-2-22-222-22-220000-22-2002-2002i−2i02i−2i00000000−22−22−22−22−i2−i2i2i2−i2−i2i2i2000000000000
χ392-2-22-222-22-220000-22-2002-200−2i2i0−2i2i000000002−22−22−22−2−i2−i2i2i2−i2−i2i2i2000000000000
χ402-2-22-222-22-220000-22-2002-200−2i2i0−2i2i00000000−22−22−22−22i2i2−i2−i2i2i2−i2−i2000000000000
χ412-2-22-222-22-220000-2-2200-22002i−2i0−2i2i000000002−22−2−22−22i2i2−i2−i2−i2−i2i2i2000000000000
χ422-2-22-222-22-220000-2-2200-22002i−2i0−2i2i00000000−22−222−22−2−i2−i2i2i2i2i2−i2−i2000000000000
χ432-2-22-222-22-220000-2-2200-2200−2i2i02i−2i000000002−22−2−22−22−i2−i2i2i2i2i2−i2−i2000000000000
χ442-2-22-222-22-220000-2-2200-2200−2i2i02i−2i00000000−22−222−22−2i2i2−i2−i2−i2−i2i2i2000000000000
χ45444-4-4-44-400000000004-400000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ46444-4-4-44-400000000004-40000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ47444-4-4-44-40000000000-4400000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ48444-4-4-44-40000000000-440000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ4944-444-4-4-444-444-4-4-4000000-4400000000000000000000000000000000000000000
χ5044-444-4-4-4-4-44-4-4444000000-4400000000000000000000000000000000000000000
χ514-444-4-4-444-4-40000400000000000000000000022−22−2222000000000000000000000000
χ524-444-4-4-444-4-400004000000000000000000000−222222−22000000000000000000000000
χ534-444-4-4-44-4440000-400000000000000000000000002i2−2i2−2i22i200000000000000000000
χ544-444-4-4-44-4440000-40000000000000000000000000−2i22i22i2−2i200000000000000000000
χ554-44-444-4-40004-44-400000000000000004i−4i00000000000000000000000000000000
χ564-44-444-4-40004-44-40000000000000000−4i4i00000000000000000000000000000000
χ574-44-444-4-4000-44-44000000000000004i−4i0000000000000000000000000000000000
χ584-44-444-4-4000-44-4400000000000000−4i4i0000000000000000000000000000000000
χ594-4-44-444-4-44-4000044-400-440000000000000000000000000000000000000000000
χ604-4-44-444-4-44-400004-44004-40000000000000000000000000000000000000000000
χ614-4-4-44-4440004-4-4400000000000000000000000000000022−22−22220000000000000000
χ624-4-4-44-4440004-4-44000000000000000000000000000000−222222−220000000000000000
χ634-4-4-44-444000-444-4000000000000000000000000000000000022−22−2222000000000000
χ644-4-4-44-444000-444-40000000000000000000000000000000000−222222−22000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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