Finite Group Databasebeta

← Group #252848

Character table — Group #252848

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444448888888888888888888161616161616161616161616161616161616
order12222222444444442244444444442244444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-11-1-111111111-1-1-1-11-1-11-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111111111111-111-111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111
χ91111111111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-11111-1-1-1-111-1-11-1-1-11111-1-111-1-1
χ101111111111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-11111-1-1-1-1-1-111-1111-1-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1111111-1-1-1-1-1-111111-1-1-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-1111111-1-1111-1-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1111111-1-1-1-111-1-1-1-1-1111-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-111-1-1-1-11111-1-111-1-1-111111-1-111-1-1
χ172222222222-2-2-222-22222-2-20000-2-222220000-200000000000000-200-20000000000
χ182222222222-2-2-222-22222-2-20000-2-2-2-2-2-20000-20000000000000020020000000000
χ192222222222-2-2-222-2-2-2-2-2220000-2-222-2-20000200000000000000-20020000000000
χ202222222222-2-2-222-2-2-2-2-2220000-2-2-2-2220000200000000000000200-20000000000
χ2122222222-2-2222-2-2222-2-2222222-2-20000-2-2-2-2-22200000000000000000000000000
χ2222222222-2-2222-2-2222-2-222-2-2-2-2-2-200002222-2-2-200000000000000000000000000
χ2322222222-2-2222-2-22-2-222-2-22222-2-20000-2-2222-2-200000000000000000000000000
χ2422222222-2-2222-2-22-2-222-2-2-2-2-2-2-2-2000022-2-222200000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-20000220000000020000000000000002-202-200000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2000022000000002000000000000000-220-2200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200002200000000-20000000000000002-20-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200002200000000-2000000000000000-2202-200000000
χ292-22-2-2-2220022-200-22-2002-222-2-2000000000002-2i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i20000
χ302-22-2-2-2220022-200-22-2002-222-2-2000000000002-2−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i20000
χ312-22-2-2-2220022-200-22-2002-2-2-22200000000000-22i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i20000
χ322-22-2-2-2220022-200-22-2002-2-2-22200000000000-22−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i20000
χ332-22-2-2-2220022-200-2-2200-2222-2-200000000000-22i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i20000
χ342-22-2-2-2220022-200-2-2200-2222-2-200000000000-22−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i20000
χ352-22-2-2-2220022-200-2-2200-22-2-222000000000002-2i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i20000
χ362-22-2-2-2220022-200-2-2200-22-2-222000000000002-2−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i20000
χ372-2-2-2222-22-22-222-2-20000002i−2i2i−2i2-200002i−2i0000000000000002-20000000000002i−2i
χ382-2-2-2222-22-22-222-2-20000002i−2i2i−2i2-200002i−2i000000000000000-22000000000000−2i2i
χ392-2-2-2222-22-22-222-2-2000000−2i2i−2i2i2-20000−2i2i0000000000000002-2000000000000−2i2i
χ402-2-2-2222-22-22-222-2-2000000−2i2i−2i2i2-20000−2i2i000000000000000-220000000000002i−2i
χ412-2-2-2222-2-222-22-22-20000002i−2i2i−2i-220000−2i2i00000000000002-20000000000002i−2i00
χ422-2-2-2222-2-222-22-22-20000002i−2i2i−2i-220000−2i2i0000000000000-22000000000000−2i2i00
χ432-2-2-2222-2-222-22-22-2000000−2i2i−2i2i-2200002i−2i00000000000002-2000000000000−2i2i00
χ442-2-2-2222-2-222-22-22-2000000−2i2i−2i2i-2200002i−2i0000000000000-220000000000002i−2i00
χ45444-44-4-4-44-4000-440000000000000004-4000000000000000000000000000000000
χ46444-44-4-4-44-4000-44000000000000000-44000000000000000000000000000000000
χ47444-44-4-4-4-440004-400000000000004-400000000000000000000000000000000000
χ48444-44-4-4-4-440004-40000000000000-4400000000000000000000000000000000000
χ4944-44-4-44-4004-4-40040000004i−4i−4i4i000000000000000000000000000000000000000
χ5044-44-4-44-4004-4-4004000000−4i4i4i−4i000000000000000000000000000000000000000
χ5144-44-4-44-400-44400-40000000000000000004-400000000000000000000000000000
χ5244-44-4-44-400-44400-4000000000000000000-4400000000000000000000000000000
χ5344-4-4-44-4400000000004i−4i00000000000000000002-22-22i−2i2i−2i000000000000000000
χ5444-4-4-44-4400000000004i−4i0000000000000000000-22-22−2i2i−2i2i000000000000000000
χ5544-4-4-44-440000000000−4i4i00000000000000000002-22-2−2i2i−2i2i000000000000000000
χ5644-4-4-44-440000000000−4i4i0000000000000000000-22-222i−2i2i−2i000000000000000000
χ574-44-4-4-44400-4-440044-400-440000000000000000000000000000000000000000000
χ584-44-4-4-44400-4-44004-44004-40000000000000000000000000000000000000000000
χ594-4-444-4-4444000-4-40000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-4-444-4-4444000-4-4000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ614-4-444-4-44-4-400044000000000000000000000000000022−22−2222000000000000000000
χ624-4-444-4-44-4-4000440000000000000000000000000000−222222−22000000000000000000
χ634-4-4-4444-44-4-44-44-440000000000-440000000000000000000000000000000000000
χ644-4-4-4444-4-44-44-4-44400000000004-40000000000000000000000000000000000000
χ658-888-88-8-8000000000000000000000000000000000000000000000000000000000

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