Finite Group Databasebeta

← Group #419563

Character table — Group #419563

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444224444444444444444444444444488888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ911111111111111111111-1-11111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-111-1-111-1-1
χ1722222222-2-2-2-222-2-22-22-200000000000022-2-2000022-2-20000000022-2-2000000000000
χ1822222222-2-2-2-222-2-22-22-200000000000022-2-20000-2-22200000000-2-222000000000000
χ1922222222-2-2-2-222-2-22-22-2000000000000-2-222000022-2-200000000-2-222000000000000
χ2022222222-2-2-2-222-2-22-22-2000000000000-2-2220000-2-2220000000022-2-2000000000000
χ2122222222-2-2-2-2-2-222-22-222222-2-2-2-20000000000000000000022-2-20000000000000000
χ2222222222-2-2-2-2-2-222-22-2222-2-222-2-200000000000000000000-2-2220000000000000000
χ2322222222-2-2-2-2-2-222-22-22-2-222-2-22200000000000000000000-2-2220000000000000000
χ2422222222-2-2-2-2-2-222-22-22-2-2-2-222220000000000000000000022-2-20000000000000000
χ2522-2-222-2-222-2-22-2-2-222-220000000022-2-200002i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ2622-2-222-2-222-2-22-2-2-222-220000000022-2-20000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ2722-2-222-2-222-2-22-2-2-222-2200000000-2-22200002i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ2822-2-222-2-222-2-22-2-2-222-2200000000-2-2220000−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ292-2222-2-2-22-22-22-22-2-2-222002-22-2000000000000002i−2i2i−2i000000000000002i−2i00000000
χ302-2222-2-2-22-22-22-22-2-2-222002-22-200000000000000−2i2i−2i2i00000000000000−2i2i00000000
χ312-2222-2-2-22-22-22-22-2-2-22200-22-22000000000000002i−2i2i−2i00000000000000−2i2i00000000
χ322-2222-2-2-22-22-22-22-2-2-22200-22-2200000000000000−2i2i−2i2i000000000000002i−2i00000000
χ332-2222-2-2-2-22-222-2-22-222-2000000002i−2i2i−2i000000002i−2i−2i2i00000000000000000000002-2
χ342-2222-2-2-2-22-222-2-22-222-2000000002i−2i2i−2i00000000−2i2i2i−2i0000000000000000000000-22
χ352-2222-2-2-2-22-222-2-22-222-200000000−2i2i−2i2i000000002i−2i−2i2i0000000000000000000000-22
χ362-2222-2-2-2-22-222-2-22-222-200000000−2i2i−2i2i00000000−2i2i2i−2i00000000000000000000002-2
χ372-2222-2-2-2-22-22-222-22-2-22002-2-2200000000002i−2i2i−2i000000000000000000002i−2i000000
χ382-2222-2-2-2-22-22-222-22-2-22002-2-220000000000−2i2i−2i2i00000000000000000000−2i2i000000
χ392-2222-2-2-2-22-22-222-22-2-2200-222-200000000002i−2i2i−2i00000000000000000000−2i2i000000
χ402-2222-2-2-2-22-22-222-22-2-2200-222-20000000000−2i2i−2i2i000000000000000000002i−2i000000
χ412-2-2-22-2222-2-22-2-22-2222-22-200002-200002-22-2000000000000000000002-20000000000
χ422-2-2-22-2222-2-22-2-22-2222-22-200002-20000-22-2200000000000000000000-220000000000
χ432-2-2-22-2222-2-22-2-22-2222-2-220000-2200002-22-200000000000000000000-220000000000
χ442-2-2-22-2222-2-22-2-22-2222-2-220000-220000-22-22000000000000000000002-20000000000
χ452-2-2-22-222-222-2222-2-22-2-22-20000-222i−2i−2i2i000000000000000000000000000000002i−2i00
χ462-2-2-22-222-222-2222-2-22-2-22-20000-22−2i2i2i−2i00000000000000000000000000000000−2i2i00
χ472-2-2-22-222-222-2222-2-22-2-2-2200002-22i−2i−2i2i00000000000000000000000000000000−2i2i00
χ482-2-2-22-222-222-2222-2-22-2-2-2200002-2−2i2i2i−2i000000000000000000000000000000002i−2i00
χ492-2-2-22-222-222-2-2-2-222-2220000000000002-2-222-2-2200000000000000000000002-20000
χ502-2-2-22-222-222-2-2-2-222-2220000000000002-2-22-222-20000000000000000000000-220000
χ512-2-2-22-222-222-2-2-2-222-222000000000000-222-22-2-220000000000000000000000-220000
χ522-2-2-22-222-222-2-2-2-222-222000000000000-222-2-222-200000000000000000000002-20000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-4-4-44-40000000000000000000000000000000000002i−2i2i−2i002i2−2i222−2200000000000000
χ55444-4-4-44-40000000000000000000000000000000000002i−2i2i−2i00−2i22i2−222200000000000000
χ56444-4-4-44-4000000000000000000000000000000000000−2i2i−2i2i002i2−2i2−222200000000000000
χ57444-4-4-44-4000000000000000000000000000000000000−2i2i−2i2i00−2i22i222−2200000000000000
χ5844-44-4-4-440000000000000000000000000000000000002-2-222i2−2i200002i2−2i2000000000000
χ5944-44-4-4-440000000000000000000000000000000000002-2-22−2i22i20000−2i22i2000000000000
χ6044-44-4-4-44000000000000000000000000000000000000-222-22i2−2i20000−2i22i2000000000000
χ6144-44-4-4-44000000000000000000000000000000000000-222-2−2i22i200002i2−2i2000000000000
χ6244-4-444-4-444-4-4-4444-4-44-4000000000000000000000000000000000000000000000000
χ6344-4-444-4-4-4-4444-4444-4-4-4000000000000000000000000000000000000000000000000
χ6444-4-444-4-4-4-444-44-4-4-4444000000000000000000000000000000000000000000000000
χ654-4444-4-4-44-44-4-44-4444-4-4000000000000000000000000000000000000000000000000
χ664-4-4-44-4444-4-4444-44-4-4-44000000000000000000000000000000000000000000000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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