Finite Group Databasebeta

← Group #258658

Character table — Group #258658

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111111111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-111111111-1-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-1-1-1111111-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1111-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-111111111-1-1-1-1-1-1-11-1-111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-111-1-111-1-111
χ141111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111111-111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-111111-111-1-11111-1-111-1-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-11-11111-1-111-1-1-1-111
χ172222222222-2-2-222-222-2-222-2-222-2-20000-2000000000000000020-20000000000000
χ182222222222-2-2-222-222-2-222-2-2-2-2220000-20000000000000000-2020000000000000
χ192222222222-2-2-222-2-2-222-2-2-2-222-2-2000020000000000000000-2020000000000000
χ202222222222-2-2-222-2-2-222-2-2-2-2-2-22200002000000000000000020-20000000000000
χ2122222222-2-2222-2-222222-2-2-2-200002222-200000000000000000-20-2000000000000
χ2222222222-2-2222-2-222222-2-2-2-20000-2-2-2-2-200000000000000000202000000000000
χ2322222222-2-2222-2-22-2-2-2-222-2-2000022-2-2200000000000000000-202000000000000
χ2422222222-2-2222-2-22-2-2-2-222-2-20000-2-22220000000000000000020-2000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2220000000020000000000000000000000002-22-20000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222000000002000000000000000000000000-22-220000
χ2722222222-2-2-2-2-2-2-2-2-2-222222200000000-20000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200000000-2000000000000000000000000-222-20000
χ29222-22-2-2-2002-2-20022-22-2000000002i−2i2i−2i0i2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ30222-22-2-2-2002-2-20022-22-2000000002i−2i2i−2i0−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ31222-22-2-2-2002-2-20022-22-200000000−2i2i−2i2i0i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ32222-22-2-2-2002-2-20022-22-200000000−2i2i−2i2i0−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ33222-22-2-2-2002-2-2002-22-22000000002i−2i−2i2i0i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ34222-22-2-2-2002-2-2002-22-22000000002i−2i−2i2i0−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ35222-22-2-2-2002-2-2002-22-2200000000−2i2i2i−2i0i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ36222-22-2-2-2002-2-2002-22-2200000000−2i2i2i−2i0−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ372-2-222-22-22-222-22-2-2000000-222i−2i2i−2i000002-22-200000000000000002i−2i0000000000
χ382-2-222-22-22-222-22-2-2000000-222i−2i2i−2i00000-22-220000000000000000−2i2i0000000000
χ392-2-222-22-22-222-22-2-2000000-22−2i2i−2i2i000002-22-20000000000000000−2i2i0000000000
χ402-2-222-22-22-222-22-2-2000000-22−2i2i−2i2i00000-22-2200000000000000002i−2i0000000000
χ412-2-222-22-22-2-2-222-220000002-22i−2i−2i2i0000000002i−2i2i−2i000000000000002-200000000
χ422-2-222-22-22-2-2-222-220000002-22i−2i−2i2i000000000−2i2i−2i2i00000000000000-2200000000
χ432-2-222-22-22-2-2-222-220000002-2−2i2i2i−2i0000000002i−2i2i−2i00000000000000-2200000000
χ442-2-222-22-22-2-2-222-220000002-2−2i2i2i−2i000000000−2i2i−2i2i000000000000002-200000000
χ45444-44-4-4-400-44400-44-4-44000000000000000000000000000000000000000000000
χ46444-44-4-4-400-44400-4-444-4000000000000000000000000000000000000000000000
χ4744-44-44-4-444000-4-4000000000000000000000000000000000000000000000022−2200
χ4844-44-44-4-444000-4-40000000000000000000000000000000000000000000000−222200
χ4944-44-44-4-4-4-4000440000000000000000000000000000000000000000000000002i2−2i2
χ5044-44-44-4-4-4-400044000000000000000000000000000000000000000000000000−2i22i2
χ514-444-4-4-444-4000-44000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ524-444-4-4-444-4000-4400000000000000000000000000−2i22i2−2i22i200000000000000000000
χ534-444-4-4-44-440004-40000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ544-444-4-4-44-440004-4000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ554-44-4-444-40000000000004-400000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ564-44-4-444-40000000000004-40000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ574-44-4-444-4000000000000-4400000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ584-44-4-444-4000000000000-440000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ594-4-444-44-4-4444-4-44-40000004-400000000000000000000000000000000000000000
χ604-4-444-44-4-44-4-44-444000000-4400000000000000000000000000000000000000000
χ614-4-4-444-44004-4400-4000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ624-4-4-444-44004-4400-400000000000000000−2i22i22i2−2i20000000000000000000000000000
χ634-4-4-444-4400-44-400400000000000000000000022−22−2222000000000000000000000000
χ644-4-4-444-4400-44-4004000000000000000000000−222222−22000000000000000000000000
χ6588-8-8-8-888000000000000000000000000000000000000000000000000000000000

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