Finite Group Databasebeta

← Group #449592

Character table — Group #449592

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12222222224444444444442222222222444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-11111-1-111111111-1-1-1-111-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ10111111111111111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111
χ13111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-111-1-1
χ172222222222-2-2-2-2-2-2-2-2000022-2-20000000000000022-2-2002-200000000000000
χ182222222222-2-2-2-2-2-2-2-2000022-2-200000000000000-2-22200-2200000000000000
χ192222222222-2-2-2-2-2-2-2-20000-2-2220000000000000022-2-200-2200000000000000
χ202222222222-2-2-2-2-2-2-2-20000-2-22200000000000000-2-222002-200000000000000
χ21222222-2-2-2-222-2-222-2-20000000000220000-2-200002i−2i2i−2i0000002i−2i0000000000
χ22222222-2-2-2-222-2-222-2-20000000000220000-2-20000−2i2i−2i2i000000−2i2i0000000000
χ23222222-2-2-2-222-2-222-2-20000000000-2-200002200002i−2i2i−2i000000−2i2i0000000000
χ24222222-2-2-2-222-2-222-2-20000000000-2-20000220000−2i2i−2i2i0000002i−2i0000000000
χ25222222-2-2-2-2-2-222-2-22200000000220000-2-20000002i−2i−2i2i00002i−2i000000000000
χ26222222-2-2-2-2-2-222-2-22200000000220000-2-2000000−2i2i2i−2i0000−2i2i000000000000
χ27222222-2-2-2-2-2-222-2-22200000000-2-20000220000002i−2i−2i2i0000−2i2i000000000000
χ28222222-2-2-2-2-2-222-2-22200000000-2-2000022000000−2i2i2i−2i00002i−2i000000000000
χ292222-2-22-2-222-22-22-22-200002-22-20000220000-2-2000000000000002-200000000
χ302222-2-22-2-222-22-22-22-200002-22-20000-2-200002200000000000000-2200000000
χ312222-2-22-2-222-22-22-22-20000-22-220000220000-2-200000000000000-2200000000
χ322222-2-22-2-222-22-22-22-20000-22-220000-2-2000022000000000000002-200000000
χ332222-2-22-2-22-22-22-22-2222222-2-22000000000000-2-200002-20000000000000000
χ342222-2-22-2-22-22-22-22-222222-222-2000000000000-2-20000-220000000000000000
χ352222-2-22-2-22-22-22-22-22-2-2-2-22-2-22000000000000220000-220000000000000000
χ362222-2-22-2-22-22-22-22-22-2-2-2-2-222-20000000000002200002-20000000000000000
χ372-2-222-222-2-222-22-2-22-22i2i−2i−2i00002-200002-200002i−2i000000000000002i−2i000000
χ382-2-222-222-2-222-22-2-22-22i2i−2i−2i0000-220000-2200002i−2i00000000000000−2i2i000000
χ392-2-222-222-2-222-22-2-22-2−2i−2i2i2i00002-200002-20000−2i2i00000000000000−2i2i000000
χ402-2-222-222-2-222-22-2-22-2−2i−2i2i2i0000-220000-220000−2i2i000000000000002i−2i000000
χ412-2-222-2-2-222-2-2-22222-2000000002-2002-2-22002-2000000000000000000002-200
χ422-2-222-2-2-222-2-2-22222-2000000002-200-22-2200-2200000000000000000000-2200
χ432-2-222-2-2-222-2-2-22222-200000000-22002-22-2002-200000000000000000000-2200
χ442-2-222-2-2-222-2-2-22222-200000000-2200-222-200-22000000000000000000002-200
χ452-2-22-222-22-2-22222-2-2-22i2i−2i−2i0000002-200002-200−2i2i00000000000000002i−2i0000
χ462-2-22-222-22-2-22222-2-2-22i2i−2i−2i000000-220000-2200−2i2i0000000000000000−2i2i0000
χ472-2-22-222-22-2-22222-2-2-2−2i−2i2i2i0000002-200002-2002i−2i0000000000000000−2i2i0000
χ482-2-22-222-22-2-22222-2-2-2−2i−2i2i2i000000-220000-22002i−2i00000000000000002i−2i0000
χ492-2-22-22-22-22-22-2-22-22200000000002-22-200-22-2200000000000000000000002-2
χ502-2-22-22-22-22-22-2-22-22200000000002-2-2200-222-20000000000000000000000-22
χ512-2-22-22-22-22-22-2-22-2220000000000-222-2002-2-220000000000000000000000-22
χ522-2-22-22-22-22-22-2-22-2220000000000-22-22002-22-200000000000000000000002-2
χ534444-4-4-444-44-4-444-4-4400000000000000000000000000000000000000000000
χ544444-4-4-444-4-444-4-444-400000000000000000000000000000000000000000000
χ554-4-444-444-4-4-4-44-444-4400000000000000000000000000000000000000000000
χ564-4-444-4-4-444444-4-4-4-4400000000000000000000000000000000000000000000
χ574-4-44-444-44-44-4-4-4-444400000000000000000000000000000000000000000000
χ584-4-44-44-44-444-444-44-4-400000000000000000000000000000000000000000000
χ5988-8-8000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ6088-8-800000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ618-88-8000000000000004-4-440000000000000000000000000000000000000000
χ628-88-800000000000000-444-40000000000000000000000000000000000000000

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