Finite Group Databasebeta

← Group #456517

Character table — Group #456517

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222222888888888888888816161616161616161616161616161616161616161616
order12222222224444444422448888888888882244444488888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-1-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1
χ17222222-2-2-2-222-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ18222222-2-2-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ19222222-2-2-2-222-2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ20222222-2-2-2-222-2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ212-2-222-222-2-22-2222-2-2-200002i−2i2i−2i000000000000002i−2i00000000002-200
χ222-2-222-222-2-22-2222-2-2-200002i−2i2i−2i00000000000000−2i2i0000000000-2200
χ232-2-222-222-2-22-2222-2-2-20000−2i2i−2i2i000000000000002i−2i0000000000-2200
χ242-2-222-222-2-22-2222-2-2-20000−2i2i−2i2i00000000000000−2i2i00000000002-200
χ252-2-222-2-2-2222-2-2-22-22200002-2-2200000000002-200000000000000002-2
χ262-2-222-2-2-2222-2-2-22-22200002-2-220000000000-220000000000000000-22
χ272-2-222-2-2-2222-2-2-22-2220000-222-200000000002-20000000000000000-22
χ282-2-222-2-2-2222-2-2-22-2220000-222-20000000000-2200000000000000002-2
χ292-2-22-222-22-2222-2-2-22-2000000002-22-20000000000002i−2i002i−2i00000000
χ302-2-22-222-22-2222-2-2-22-2000000002-22-2000000000000−2i2i00−2i2i00000000
χ312-2-22-222-22-2222-2-2-22-200000000-22-220000000000002i−2i00−2i2i00000000
χ322-2-22-222-22-2222-2-2-22-200000000-22-22000000000000−2i2i002i−2i00000000
χ332-2-22-222-22-2-2-2-2222-222-22-20000000000002-2000000000000002-20000
χ342-2-22-222-22-2-2-2-2222-222-22-2000000000000-2200000000000000-220000
χ352-2-22-222-22-2-2-2-2222-22-22-220000000000002-200000000000000-220000
χ362-2-22-222-22-2-2-2-2222-22-22-22000000000000-22000000000000002-20000
χ372-2-22-22-22-2222-22-2-2-22000000002i−2i−2i2i22-2-2000000000000002i−2i000000
χ382-2-22-22-22-2222-22-2-2-22000000002i−2i−2i2i-2-22200000000000000−2i2i000000
χ392-2-22-22-22-2222-22-2-2-2200000000−2i2i2i−2i22-2-200000000000000−2i2i000000
χ402-2-22-22-22-2222-22-2-2-2200000000−2i2i2i−2i-2-222000000000000002i−2i000000
χ412-2-22-22-22-22-2-22-2222-22-2-2200000000000000002-200002-20000000000
χ422-2-22-22-22-22-2-22-2222-22-2-220000000000000000-220000-220000000000
χ432-2-22-22-22-22-2-22-2222-2-222-200000000000000002-20000-220000000000
χ442-2-22-22-22-22-2-22-2222-2-222-20000000000000000-2200002-20000000000
χ454444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000
χ46444444-4-4-4-4-4-444-4-44400000000000000000000000000000000000000
χ474444-4-44-4-444-44-4-44-4400000000000000000000000000000000000000
χ484444-4-44-4-44-44-444-44-400000000000000000000000000000000000000
χ494444-4-4-444-44-4-44-444-400000000000000000000000000000000000000
χ504444-4-4-444-4-444-44-4-4400000000000000000000000000000000000000
χ514-4-444-444-4-4-44-4-4-444400000000000000000000000000000000000000
χ524-4-444-4-4-444-4444-44-4-400000000000000000000000000000000000000
χ5388-8-8000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ5488-8-800000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ558-88-8000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ568-88-800000000000000000000000000−2i22i22i2−2i20000000000000000000000

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