Finite Group Databasebeta

← Group #418089

Character table — Group #418089

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12222222222244444444888822224444444444444444888888888822444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-11-1-1-1-11111
χ5111111111111111111111111-1-11111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-111-111-1-1-1-1-1-1
χ911111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111
χ1111111111111111111111-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-111-1-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1-111111-1-111
χ1722222222-2-2-2-222-22-2-2-222222220000-2-20000000000000000-2-2000000-200200000000
χ1822222222-2-2-2-222-22-2-2-222222-2-20000220000000000000000-2-2000000200-200000000
χ1922222222-2-2-2-222-22-2-2-22-2-2-2-2220000-2-2000000000000000022000000200-200000000
χ2022222222-2-2-2-222-22-2-2-22-2-2-2-2-2-2000022000000000000000022000000-200200000000
χ2122222222-2-2-2-2-2-22-2222-2000000222200-2-2-2-20000000022-2-200000000000000000000
χ2222222222-2-2-2-2-2-22-2222-200000022-2-200-2-22200000000-2-22200000000000000000000
χ2322222222-2-2-2-2-2-22-2222-2000000-2-2220022-2-200000000-2-22200000000000000000000
χ2422222222-2-2-2-2-2-22-2222-2000000-2-2-2-20022220000000022-2-200000000000000000000
χ25222-2-2-22-222-2-2-2-2222-2-2200000000000000002i2i−2i−2i000000000022-2-20000000000002i−2i
χ26222-2-2-22-222-2-2-2-2222-2-2200000000000000002i2i−2i−2i0000000000-2-222000000000000−2i2i
χ27222-2-2-22-222-2-2-2-2222-2-220000000000000000−2i−2i2i2i000000000022-2-2000000000000−2i2i
χ28222-2-2-22-222-2-2-2-2222-2-220000000000000000−2i−2i2i2i0000000000-2-2220000000000002i−2i
χ292-2-222-22-22-22-22-22-2-22-22000000002i−2i00002i−2i00002i2i−2i−2i0000002-22-200000000000000
χ302-2-222-22-22-22-22-22-2-22-22000000002i−2i00002i−2i0000−2i−2i2i2i000000-22-2200000000000000
χ312-2-222-22-22-22-22-22-2-22-2200000000−2i2i0000−2i2i00002i2i−2i−2i000000-22-2200000000000000
χ322-2-222-22-22-22-22-22-2-22-2200000000−2i2i0000−2i2i0000−2i−2i2i2i0000002-22-200000000000000
χ332-2-222-22-22-22-2-22-222-22-22i2i−2i−2i0000000000002i−2i2i−2i000000002i−2i00000002-2000000000
χ342-2-222-22-22-22-2-22-222-22-22i2i−2i−2i000000000000−2i2i−2i2i000000002i−2i0000000-22000000000
χ352-2-222-22-22-22-2-22-222-22-2−2i−2i2i2i0000000000002i−2i2i−2i00000000−2i2i0000000-22000000000
χ362-2-222-22-22-22-2-22-222-22-2−2i−2i2i2i000000000000−2i2i−2i2i00000000−2i2i00000002-2000000000
χ372-2-222-22-2-22-22-2222-22-2-22i2i−2i−2i00002i−2i0000−2i2i000000000000−2i2i0000000000002-20000
χ382-2-222-22-2-22-22-2222-22-2-22i2i−2i−2i0000−2i2i00002i−2i000000000000−2i2i000000000000-220000
χ392-2-222-22-2-22-22-2222-22-2-2−2i−2i2i2i00002i−2i0000−2i2i0000000000002i−2i000000000000-220000
χ402-2-222-22-2-22-22-2222-22-2-2−2i−2i2i2i0000−2i2i00002i−2i0000000000002i−2i0000000000002-20000
χ412-2-2-2-22222-2-222-2-2222-2-20000002-200002-2002-2-220000000000000000000000002-200
χ422-2-2-2-22222-2-222-2-2222-2-20000002-200002-200-222-2000000000000000000000000-2200
χ432-2-2-2-22222-2-222-2-2222-2-2000000-220000-22002-2-22000000000000000000000000-2200
χ442-2-2-2-22222-2-222-2-2222-2-2000000-220000-2200-222-20000000000000000000000002-200
χ452-2-2-2-22222-2-22-222-2-2-22200002-200002-20000000000000000002-2-222-2000000000000
χ462-2-2-2-22222-2-22-222-2-2-22200002-200002-2000000000000000000-222-2-22000000000000
χ472-2-2-2-22222-2-22-222-2-2-2220000-220000-220000000000000000002-2-22-22000000000000
χ482-2-2-2-22222-2-22-222-2-2-2220000-220000-22000000000000000000-222-22-2000000000000
χ492-2-2-2-2222-222-2-22-2-222-2200002-22-200-22-22000000000000000000000000002-2000000
χ502-2-2-2-2222-222-2-22-2-222-2200002-2-2200-222-200000000000000000000000000-22000000
χ512-2-2-2-2222-222-2-22-2-222-220000-222-2002-2-2200000000000000000000000000-22000000
χ522-2-2-2-2222-222-2-22-2-222-220000-22-22002-22-2000000000000000000000000002-2000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-444-4-4-444-4000000000000000000000000000000000000000000000000
χ55444-4-4-44-4-4-444444-44-4-4-4000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-4-444-4-4-44-4444000000000000000000000000000000000000000000000000
χ5744-4-444-4-40000000000002i2−2i22i2−2i200000000000000002i−2i2i−2i22−220000000000000000000000
χ5844-4-444-4-40000000000002i2−2i22i2−2i20000000000000000−2i2i−2i2i−22220000000000000000000000
χ5944-4-444-4-4000000000000−2i22i2−2i22i200000000000000002i−2i2i−2i−22220000000000000000000000
χ6044-4-444-4-4000000000000−2i22i2−2i22i20000000000000000−2i2i−2i2i22−220000000000000000000000
χ614-44-44-4-4400000000000022−22−222200000000000000002-2-220022−2200000000000000000000
χ624-44-44-4-4400000000000022−22−22220000000000000000-222-200−222200000000000000000000
χ634-44-44-4-44000000000000−222222−2200000000000000002-2-2200−222200000000000000000000
χ644-44-44-4-44000000000000−222222−220000000000000000-222-20022−2200000000000000000000
χ654-4-444-44-4-44-444-4-4-44-444000000000000000000000000000000000000000000000000
χ664-4-4-4-4444-444-44-444-4-44-4000000000000000000000000000000000000000000000000
χ6788-88-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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