Finite Group Databasebeta

← Group #427893

Character table — Group #427893

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422222244444444444444444488882444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111
χ51111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111
χ61111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111
χ10111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ11111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ14111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111
χ1722222-2-22-2-22222-2-2-2-20000002200-2-2000000002i2i−2i−2i000000000000002i−2i0000
χ1822222-2-22-2-22222-2-2-2-20000002200-2-200000000−2i−2i2i2i00000000000000−2i2i0000
χ1922222-2-22-2-22222-2-2-2-2000000-2-20022000000002i2i−2i−2i00000000000000−2i2i0000
χ2022222-2-22-2-22222-2-2-2-2000000-2-2002200000000−2i−2i2i2i000000000000002i−2i0000
χ2122222-2-22-2-2-2-2-2-2222222-2-22200-2-20000000000000000000000002-200000000
χ2222222-2-22-2-2-2-2-2-2222222-2-2-2-20022000000000000000000000000-2200000000
χ2322222-2-22-2-2-2-2-2-22222-2-2222200-2-2000000000000000000000000-2200000000
χ2422222-2-22-2-2-2-2-2-22222-2-222-2-200220000000000000000000000002-200000000
χ252222-22-2-2-222-2-222-2-2200000000000022-2-222-2-2000000002-200000000000000
χ262222-22-2-2-222-2-222-2-2200000000000022-2-2-2-22200000000-2200000000000000
χ272222-22-2-2-222-2-222-2-22000000000000-2-22222-2-200000000-2200000000000000
χ282222-22-2-2-222-2-222-2-22000000000000-2-222-2-222000000002-200000000000000
χ292-22-222-2-22-222-2-2-22-220000002i−2i002i−2i00002i−2i2i−2i00000000000000000000002-2
χ302-22-222-2-22-222-2-2-22-220000002i−2i002i−2i0000−2i2i−2i2i0000000000000000000000-22
χ312-22-222-2-22-222-2-2-22-22000000−2i2i00−2i2i00002i−2i2i−2i0000000000000000000000-22
χ322-22-222-2-22-222-2-2-22-22000000−2i2i00−2i2i0000−2i2i−2i2i00000000000000000000002-2
χ332-22-222-2-22-2-2-2222-22-22-22-2000000002i−2i2i−2i000000002i2i−2i−2i0000000000000000
χ342-22-222-2-22-2-2-2222-22-22-22-200000000−2i2i−2i2i00000000−2i−2i2i2i0000000000000000
χ352-22-222-2-22-2-2-2222-22-2-22-22000000002i−2i2i−2i00000000−2i−2i2i2i0000000000000000
χ362-22-222-2-22-2-2-2222-22-2-22-2200000000−2i2i−2i2i000000002i2i−2i−2i0000000000000000
χ372-22-22-22-2-2222-2-22-22-22-2-22002i−2i00−2i2i0000000000000000002i−2i000000000000
χ382-22-22-22-2-2222-2-22-22-22-2-2200−2i2i002i−2i000000000000000000−2i2i000000000000
χ392-22-22-22-2-2222-2-22-22-2-222-2002i−2i00−2i2i000000000000000000−2i2i000000000000
χ402-22-22-22-2-2222-2-22-22-2-222-200−2i2i002i−2i0000000000000000002i−2i000000000000
χ412-22-2-2222-2-22-22-2-2-22200002-2002-20000002i−2i−2i2i00000000000000002i−2i000000
χ422-22-2-2222-2-22-22-2-2-22200002-2002-2000000−2i2i2i−2i0000000000000000−2i2i000000
χ432-22-2-2222-2-22-22-2-2-2220000-2200-220000002i−2i−2i2i0000000000000000−2i2i000000
χ442-22-2-2222-2-22-22-2-2-2220000-2200-22000000−2i2i2i−2i00000000000000002i−2i000000
χ452-22-2-2222-2-2-22-2222-2-20000000000002i−2i−2i2i00002i−2i2i−2i00000000000000002-200
χ462-22-2-2222-2-2-22-2222-2-20000000000002i−2i−2i2i0000−2i2i−2i2i0000000000000000-2200
χ472-22-2-2222-2-2-22-2222-2-2000000000000−2i2i2i−2i00002i−2i2i−2i0000000000000000-2200
χ482-22-2-2222-2-2-22-2222-2-2000000000000−2i2i2i−2i0000−2i2i−2i2i00000000000000002-200
χ492-22-2-2-2-2222-22-22-2-22200002-200-2200000000002-2-22000000002-20000000000
χ502-22-2-2-2-2222-22-22-2-22200002-200-220000000000-222-200000000-220000000000
χ512-22-2-2-2-2222-22-22-2-2220000-22002-200000000002-2-2200000000-220000000000
χ522-22-2-2-2-2222-22-22-2-2220000-22002-20000000000-222-2000000002-20000000000
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ544444-44-4-4-44-444-4-444-400000000000000000000000000000000000000000000
χ554444-4-44-44-44-4-44-444-400000000000000000000000000000000000000000000
χ564444-4-44-44-4-444-44-4-4400000000000000000000000000000000000000000000
χ574-44-44-44-4-44-4-444-44-4400000000000000000000000000000000000000000000
χ584-44-4-4-4-44444-44-444-4-400000000000000000000000000000000000000000000
χ5988-8-8000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ6088-8-800000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ618-8-880000000000000000000000000000000000000022−22−22220000000000000000
χ628-8-8800000000000000000000000000000000000000−222222−220000000000000000

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