Finite Group Databasebeta

← Group #448647

Character table — Group #448647

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444444444444444444448888888888882244448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ10111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1111111-1-111-1-1-1-1
χ172222222222-2-2-2-2-2-2-2-20000000022-2-2000000002i2i−2i−2i0000000000000000002i−2i
χ182222222222-2-2-2-2-2-2-2-20000000022-2-200000000−2i−2i2i2i000000000000000000−2i2i
χ192222222222-2-2-2-2-2-2-2-200000000-2-222000000002i2i−2i−2i000000000000000000−2i2i
χ202222222222-2-2-2-2-2-2-2-200000000-2-22200000000−2i−2i2i2i0000000000000000002i−2i
χ21222222-2-2-2-22-2222-2-2-222-2-2000000002i2i−2i−2i0000000000000000000000002i−2i00
χ22222222-2-2-2-22-2222-2-2-222-2-200000000−2i−2i2i2i000000000000000000000000−2i2i00
χ23222222-2-2-2-22-2222-2-2-2-2-222000000002i2i−2i−2i000000000000000000000000−2i2i00
χ24222222-2-2-2-22-2222-2-2-2-2-22200000000−2i−2i2i2i0000000000000000000000002i−2i00
χ252222-2-22-2-22-2-222-222-2000022-2-20000000022-2-200000000002-2000000000000
χ262222-2-22-2-22-2-222-222-2000022-2-200000000-2-2220000000000-22000000000000
χ272222-2-22-2-22-2-222-222-20000-2-2220000000022-2-20000000000-22000000000000
χ282222-2-22-2-22-2-222-222-20000-2-22200000000-2-22200000000002-2000000000000
χ292-2-222-222-2-22-22-2-2-2220000000000002i−2i2i−2i2i−2i2i−2i000000002-200000000000000
χ302-2-222-222-2-22-22-2-2-2220000000000002i−2i2i−2i−2i2i−2i2i00000000-2200000000000000
χ312-2-222-222-2-22-22-2-2-222000000000000−2i2i−2i2i2i−2i2i−2i00000000-2200000000000000
χ322-2-222-222-2-22-22-2-2-222000000000000−2i2i−2i2i−2i2i−2i2i000000002-200000000000000
χ332-2-222-2-2-222222-2-22-2-20000000000002-2-2200002i−2i2i−2i000000000000002i−2i0000
χ342-2-222-2-2-222222-2-22-2-20000000000002-2-220000−2i2i−2i2i00000000000000−2i2i0000
χ352-2-222-2-2-222222-2-22-2-2000000000000-222-200002i−2i2i−2i00000000000000−2i2i0000
χ362-2-222-2-2-222222-2-22-2-2000000000000-222-20000−2i2i−2i2i000000000000002i−2i0000
χ372-2-222-2-2-222-2-2-222-22200002-22-20000000000002-2-220000000000002-2000000
χ382-2-222-2-2-222-2-2-222-22200002-22-2000000000000-222-2000000000000-22000000
χ392-2-222-2-2-222-2-2-222-2220000-22-220000000000002-2-22000000000000-22000000
χ402-2-222-2-2-222-2-2-222-2220000-22-22000000000000-222-20000000000002-2000000
χ412-2-22-222-22-22-2-22-22-222i−2i2i−2i00002i−2i2i−2i000000000000000000002-20000000000
χ422-2-22-222-22-22-2-22-22-222i−2i2i−2i0000−2i2i−2i2i00000000000000000000-220000000000
χ432-2-22-222-22-22-2-22-22-22−2i2i−2i2i00002i−2i2i−2i00000000000000000000-220000000000
χ442-2-22-222-22-22-2-22-22-22−2i2i−2i2i0000−2i2i−2i2i000000000000000000002-20000000000
χ452-2-22-222-22-2-222-22-22-2000000002i−2i−2i2i00002i−2i−2i2i000022-2-20000000000000000
χ462-2-22-222-22-2-222-22-22-2000000002i−2i−2i2i0000−2i2i2i−2i0000-2-2220000000000000000
χ472-2-22-222-22-2-222-22-22-200000000−2i2i2i−2i00002i−2i−2i2i0000-2-2220000000000000000
χ482-2-22-222-22-2-222-22-22-200000000−2i2i2i−2i0000−2i2i2i−2i000022-2-20000000000000000
χ492-2-22-22-22-2222-22-2-22-22i−2i−2i2i2-2-22000000000000000000000000002i−2i00000000
χ502-2-22-22-22-2222-22-2-22-22i−2i−2i2i-222-200000000000000000000000000−2i2i00000000
χ512-2-22-22-22-2222-22-2-22-2−2i2i2i−2i2-2-2200000000000000000000000000−2i2i00000000
χ522-2-22-22-22-2222-22-2-22-2−2i2i2i−2i-222-2000000000000000000000000002i−2i00000000
χ53444444-4-4-4-4-44-4-4-444400000000000000000000000000000000000000000000
χ544444-4-44-4-4444-4-44-4-4400000000000000000000000000000000000000000000
χ554444-4-4-444-44-4-4-4444-400000000000000000000000000000000000000000000
χ564444-4-4-444-4-4444-4-4-4400000000000000000000000000000000000000000000
χ574-4-444-444-4-4-44-4444-4-400000000000000000000000000000000000000000000
χ584-4-44-44-44-44-4-44-444-4400000000000000000000000000000000000000000000
χ5988-8-8000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ6088-8-800000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ618-88-8000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ628-88-800000000000000000000000000000000000000−2i22i22i2−2i20000000000000000

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