Finite Group Databasebeta

← Group #285707

Character table — Group #285707

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444888888888888888822444444488888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-11
χ1011111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-1
χ1111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-111111111-1-1-1-1-1-11111-1-11-1
χ1211111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-111-11
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111-1
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-11
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-111-1-111-11
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1111111-1-111-1-11-1
χ1722222222222222-2-2-22-22-2-2-2-222000000000000000022-2-2-2-2-22200000000000000000000000000
χ1822222222222222-2-2-22-22-2-2-2-2220000000000000000-2-2-22222-2-200000000000000000000000000
χ19222222222222-2-2222-22-2-2-222-2-2222222220000000000-2000000-2-2-2-20000000000000000000000
χ20222222222222-2-2222-22-2-2-222-2-2-2-2-2-2-2-2-2-20000000000-200000022220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i00200000000002i2i−2i−2i000000000000000000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i0020000000000−2i−2i2i2i000000000000000000
χ2322222222-2-2-2-222-2-2-22-22-2-222-2-2000000000000000022222-2-2-2-200000000000000000000000000
χ2422222222-2-2-2-222-2-2-22-22-2-222-2-20000000000000000-2-22-2-2222200000000000000000000000000
χ2522222222-2-2-2-2-2-2222-22-2-2-2-2-2222222-2-2-2-200000000002000000-2-2220000000000000000000000
χ2622222222-2-2-2-2-2-2222-22-2-2-2-2-222-2-2-2-222220000000000200000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i00-20000000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i00-200000000002i2i−2i−2i000000000000000000
χ292-22-22-22-200002-222-2-2-222-20000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000022-2-2002i−2i000000
χ302-22-22-22-200002-222-2-2-222-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000-2-22200−2i2i000000
χ312-22-22-22-200002-222-2-2-222-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000022-2-200−2i2i000000
χ322-22-22-22-200002-222-2-2-222-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000-2-222002i−2i000000
χ332-22-22-22-20000-22-2-2222-22-200000000000022-2-2-2-222000000000000000002i2i−2i−2i00002i−2i00000000
χ342-22-22-22-20000-22-2-2222-22-200000000000022-2-2-2-22200000000000000000−2i−2i2i2i0000−2i2i00000000
χ352-22-22-22-20000-22-2-2222-22-2000000000000-2-22222-2-2000000000000000002i2i−2i−2i0000−2i2i00000000
χ362-22-22-22-20000-22-2-2222-22-2000000000000-2-22222-2-200000000000000000−2i−2i2i2i00002i−2i00000000
χ372-2-222-2-2222-2-2002-220-20002-2002i2i−2i−2i2i2i−2i−2i0000000000000000000000000i2−i2i2−i2i2−i2i2−i200002−22−200
χ382-2-222-2-2222-2-2002-220-20002-2002i2i−2i−2i2i2i−2i−2i0000000000000000000000000−i2i2−i2i2−i2i2−i2i20000−22−2200
χ392-2-222-2-2222-2-2002-220-20002-200−2i−2i2i2i−2i−2i2i2i0000000000000000000000000i2−i2i2−i2i2−i2i2−i20000−22−2200
χ402-2-222-2-2222-2-2002-220-20002-200−2i−2i2i2i−2i−2i2i2i0000000000000000000000000−i2i2−i2i2−i2i2−i2i200002−22−200
χ412-2-222-2-22-2-222002-220-2000-22002i2i−2i−2i−2i−2i2i2i0000000000000000000000000i2−i2i2−i2−i2i2−i2i200002−2−2200
χ422-2-222-2-22-2-222002-220-2000-22002i2i−2i−2i−2i−2i2i2i0000000000000000000000000−i2i2−i2i2i2−i2i2−i20000−222−200
χ432-2-222-2-22-2-222002-220-2000-2200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000i2−i2i2−i2−i2i2−i2i20000−222−200
χ442-2-222-2-22-2-222002-220-2000-2200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000−i2i2−i2i2i2−i2i2−i200002−2−2200
χ452-2-2-2-22222-22-222000-20-200002-22−22−22−22−2i2−i2i2−i2i2−i2i2−i20002i−2i2i−2i002−22−2i2−i2i2−i2000000000000000000
χ462-2-2-2-22222-22-222000-20-200002-22−22−22−22−2−i2i2−i2i2−i2i2−i2i2000−2i2i−2i2i002−22−2−i2i2−i2i2000000000000000000
χ472-2-2-2-22222-22-222000-20-200002-2−22−22−22−22i2−i2i2−i2i2−i2i2−i2000−2i2i−2i2i00−22−22i2−i2i2−i2000000000000000000
χ482-2-2-2-22222-22-222000-20-200002-2−22−22−22−22−i2i2−i2i2−i2i2−i2i20002i−2i2i−2i00−22−22−i2i2−i2i2000000000000000000
χ492-2-2-2-22222-22-2-2-20002020000-222−22−22−22−22−22−2−22−222-2000002-2−22−222−2−22000000000000000000
χ502-2-2-2-22222-22-2-2-20002020000-222−22−22−22−2−22−222−22−2-2200000-22−22−22−222−2000000000000000000
χ512-2-2-2-22222-22-2-2-20002020000-22−22−22−22−222−22−2−22−22-2200000-222−22−22−2−22000000000000000000
χ522-2-2-2-22222-22-2-2-20002020000-22−22−22−22−22−22−222−22−22-2000002-22−22−2−222−2000000000000000000
χ532-2-2-2-2222-22-2222000-20-20000-222−22−2−22−22i2−i2i2−i2i2−i2i2−i20002i−2i−2i2i002−2−22−i2i2−i2i2000000000000000000
χ542-2-2-2-2222-22-2222000-20-20000-222−22−2−22−22−i2i2−i2i2−i2i2−i2i2000−2i2i2i−2i002−2−22i2−i2i2−i2000000000000000000
χ552-2-2-2-2222-22-2222000-20-20000-22−22−222−22−2i2−i2i2−i2i2−i2i2−i2000−2i2i2i−2i00−222−2−i2i2−i2i2000000000000000000
χ562-2-2-2-2222-22-2222000-20-20000-22−22−222−22−2−i2i2−i2i2−i2i2−i2i20002i−2i−2i2i00−222−2i2−i2i2−i2000000000000000000
χ572-2-2-2-2222-22-22-2-200020200002-22−22−2−22−222−22−2−22−22-22000002-2−222−2−222−2000000000000000000
χ582-2-2-2-2222-22-22-2-200020200002-22−22−2−22−22−22−222−22−22-200000-22−222−22−2−22000000000000000000
χ592-2-2-2-2222-22-22-2-200020200002-2−22−222−22−22−22−2−22−222-200000-222−2−22−222−2000000000000000000
χ602-2-2-2-2222-22-22-2-200020200002-2−22−222−22−2−22−222−22−2-22000002-22−2−222−2−22000000000000000000
χ61444-4-4-4-444-4-44000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ62444-4-4-4-444-4-4400000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ63444-4-4-4-44-444-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ64444-4-4-4-44-444-400000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ6544-44-4-44-400004-400040-40000000000000022−22−222222−22−222200000000000000000000000000000000000
χ6644-44-4-44-400004-400040-400000000000000−222222−22−222222−2200000000000000000000000000000000000
χ6744-44-4-44-40000-44000-404000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ6844-44-4-44-40000-44000-40400000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ6944-4-444-4-40000004-4-404000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ7044-4-444-4-40000004-4-40400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ7144-4-444-4-4000000-4440-4000000000000000000000000000000000000000022−22−222200000000000000
χ7244-4-444-4-4000000-4440-40000000000000000000000000000000000000000−222222−2200000000000000
χ734-44-44-44-400004-4-4-44-444-440000000000000000000000000000000000000000000000000000000
χ744-44-44-44-40000-4444-44-4-4-440000000000000000000000000000000000000000000000000000000
χ754-4-444-4-4444-4-400-44-404000-4400000000000000000000000000000000000000000000000000000
χ764-4-444-4-44-4-44400-44-4040004-400000000000000000000000000000000000000000000000000000
χ778-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000

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