Finite Group Databasebeta

← Group #427951

Character table — Group #427951

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12222222222244444444888822222244444444444444888888888822444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-11111-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1111-1-1-1-111
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-11111-1-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-111-1-1-1111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11-1-1-1-111111-1-1
χ911111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111-1-11-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-111-111-1-111
χ1722222222-2-2-2-2222-2-2-2-22222200000000000022-2-200000000-2-200000020000-2000000
χ1822222222-2-2-2-2222-2-2-2-222222000000000000-2-22200000000-2-2000000-200002000000
χ1922222222-2-2-2-2222-2-2-2-22-2-2-2-200000000000022-2-20000000022000000-200002000000
χ2022222222-2-2-2-2222-2-2-2-22-2-2-2-2000000000000-2-222000000002200000020000-2000000
χ2122222222-2-2-2-2-2-2-22222-20000000022-2-222-2-20000000022-2-200000000000000000000
χ2222222222-2-2-2-2-2-2-22222-20000000022-2-2-2-22200000000-2-22200000000000000000000
χ2322222222-2-2-2-2-2-2-22222-200000000-2-22222-2-200000000-2-22200000000000000000000
χ2422222222-2-2-2-2-2-2-22222-200000000-2-222-2-2220000000022-2-200000000000000000000
χ2522-222-2-2-22-2-2222-2-222-2-2000022-2-200000000000000000000002i2i−2i−2i00000000002i−2i00
χ2622-222-2-2-22-2-2222-2-222-2-2000022-2-20000000000000000000000−2i−2i2i2i0000000000−2i2i00
χ2722-222-2-2-22-2-2222-2-222-2-20000-2-22200000000000000000000002i2i−2i−2i0000000000−2i2i00
χ2822-222-2-2-22-2-2222-2-222-2-20000-2-2220000000000000000000000−2i−2i2i2i00000000002i−2i00
χ292-222-2-2-2222-2-22-22-22-22-2000000002-22-200002i−2i2i−2i000000000000000002i−2i000000000
χ302-222-2-2-2222-2-22-22-22-22-2000000002-22-20000−2i2i−2i2i00000000000000000−2i2i000000000
χ312-222-2-2-2222-2-22-22-22-22-200000000-22-2200002i−2i2i−2i00000000000000000−2i2i000000000
χ322-222-2-2-2222-2-22-22-22-22-200000000-22-220000−2i2i−2i2i000000000000000002i−2i000000000
χ332-222-2-2-22-2-2222-222-22-2-200000000000000002i−2i−2i2i00000000002i−2i2i−2i2-2000000000000
χ342-222-2-2-22-2-2222-222-22-2-200000000000000002i−2i−2i2i0000000000−2i2i−2i2i-22000000000000
χ352-222-2-2-22-2-2222-222-22-2-20000000000000000−2i2i2i−2i00000000002i−2i2i−2i-22000000000000
χ362-222-2-2-22-2-2222-222-22-2-20000000000000000−2i2i2i−2i0000000000−2i2i−2i2i2-2000000000000
χ372-222-2-2-22-2-222-22-2-22-22200002-22-22-2-220000000000000000000000000000002-20000
χ382-222-2-2-22-2-222-22-2-22-22200002-22-2-222-2000000000000000000000000000000-220000
χ392-222-2-2-22-2-222-22-2-22-2220000-22-222-2-22000000000000000000000000000000-220000
χ402-222-2-2-22-2-222-22-2-22-2220000-22-22-222-20000000000000000000000000000002-20000
χ412-2-22-222-22-22-2-222-2-222-22i2i−2i−2i000000002-22-20000000000002i−2i00000000000000002i−2i
χ422-2-22-222-22-22-2-222-2-222-22i2i−2i−2i00000000-22-220000000000002i−2i0000000000000000−2i2i
χ432-2-22-222-22-22-2-222-2-222-2−2i−2i2i2i000000002-22-2000000000000−2i2i0000000000000000−2i2i
χ442-2-22-222-22-22-2-222-2-222-2−2i−2i2i2i00000000-22-22000000000000−2i2i00000000000000002i−2i
χ452-2-22-222-2-22-222-2-2-2-22220000000000002-2-22000022-2-20000002-2-2200000000000000
χ462-2-22-222-2-22-222-2-2-2-22220000000000002-2-220000-2-222000000-222-200000000000000
χ472-2-22-222-2-22-222-2-2-2-2222000000000000-222-2000022-2-2000000-222-200000000000000
χ482-2-22-222-2-22-222-2-2-2-2222000000000000-222-20000-2-2220000002-2-2200000000000000
χ492-2-22-222-2-22-22-22222-2-2-22i2i−2i−2i2-2-2200000000000000000000−2i2i0000000002i−2i0000000
χ502-2-22-222-2-22-22-22222-2-2-22i2i−2i−2i-222-200000000000000000000−2i2i000000000−2i2i0000000
χ512-2-22-222-2-22-22-22222-2-2-2−2i−2i2i2i2-2-22000000000000000000002i−2i000000000−2i2i0000000
χ522-2-22-222-2-22-22-22222-2-2-2−2i−2i2i2i-222-2000000000000000000002i−2i0000000002i−2i0000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-4-44-4-40000000000002i2−2i22i2−2i200000000000000002-22-2002i2−2i200000000000000000000
χ55444-4-44-4-40000000000002i2−2i22i2−2i20000000000000000-22-2200−2i22i200000000000000000000
χ56444-4-44-4-4000000000000−2i22i2−2i22i200000000000000002-22-200−2i22i200000000000000000000
χ57444-4-44-4-4000000000000−2i22i2−2i22i20000000000000000-22-22002i2−2i200000000000000000000
χ5844-444-4-4-44-4-44-4-444-4-444000000000000000000000000000000000000000000000000
χ5944-444-4-4-4-444-444-44-4-44-4000000000000000000000000000000000000000000000000
χ6044-444-4-4-4-444-4-4-44-444-44000000000000000000000000000000000000000000000000
χ614-444-4-4-4444-4-4-44-44-44-44000000000000000000000000000000000000000000000000
χ624-4-44-444-44-44-44-4-444-4-44000000000000000000000000000000000000000000000000
χ634-4-4-444-4400000000000022−22−222200000000000000002-2-2222−220000000000000000000000
χ644-4-4-444-4400000000000022−22−22220000000000000000-222-2−22220000000000000000000000
χ654-4-4-444-44000000000000−222222−2200000000000000002-2-22−22220000000000000000000000
χ664-4-4-444-44000000000000−222222−220000000000000000-222-222−220000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-88-88-88-8000000000000000000000000000000000000000000000000000000000000

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