Finite Group Databasebeta

← Group #243985

Character table — Group #243985

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888888888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222-2-22222-2-222-2-2-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ1822222222222222-2-22222-2-222-2-2-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ19222222222222-2-222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ20222222222222-2-222-2-2-2-2-2-2-2-222-2-222-2-20000000000000000-2-222-2-222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000022-2-2-2-2220000000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000-2-22222-2-20000000000000000
χ2522222222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-222000000000000000022-2-2-2-222000000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2220000000000000000-2-22222-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ292-222-2-2-2222-2-2222222-2-222-2-2-2-2-2-22-22-2000000000000000000000000000000000000000000002-22-2
χ302-222-2-2-2222-2-2222222-2-222-2-2-2-2-2-22-22-200000000000000000000000000000000000000000000-22-22
χ312-222-2-2-2222-2-222-2-222-2-2-2-2-2-22222-22-22000000000000000000000000000000002i−2i2i−2i000000000000
χ322-222-2-2-2222-2-222-2-222-2-2-2-2-2-22222-22-2200000000000000000000000000000000−2i2i−2i2i000000000000
χ332-222-2-2-2222-2-2-2-222-2-222-2-222-2-2222-2-220000000000000000000000000000000000002i−2i2i−2i00000000
χ342-222-2-2-2222-2-2-2-222-2-222-2-222-2-2222-2-22000000000000000000000000000000000000−2i2i−2i2i00000000
χ352-222-2-2-2222-2-2-2-2-2-2-2-222222222-2-2-222-200000000000000000000000000000000000000002i−2i2i−2i0000
χ362-222-2-2-2222-2-2-2-2-2-2-2-222222222-2-2-222-20000000000000000000000000000000000000000−2i2i−2i2i0000
χ372-222-2-2-22-2-2222222-2-22222-2-2-2-2-2-2-22-22000000000000000000000000000000000000000000002-2-22
χ382-222-2-2-22-2-2222222-2-22222-2-2-2-2-2-2-22-2200000000000000000000000000000000000000000000-222-2
χ392-222-2-2-22-2-22222-2-2-2-222-2-2-2-222222-22-2000000000000000000000000000000002i−2i−2i2i000000000000
χ402-222-2-2-22-2-22222-2-2-2-222-2-2-2-222222-22-200000000000000000000000000000000−2i2i2i−2i000000000000
χ412-222-2-2-22-2-222-2-22222-2-2-2-222-2-222-222-20000000000000000000000000000000000002i−2i−2i2i00000000
χ422-222-2-2-22-2-222-2-22222-2-2-2-222-2-222-222-2000000000000000000000000000000000000−2i2i2i−2i00000000
χ432-222-2-2-22-2-222-2-2-2-222-2-2222222-2-22-2-2200000000000000000000000000000000000000002i−2i−2i2i0000
χ442-222-2-2-22-2-222-2-2-2-222-2-2222222-2-22-2-220000000000000000000000000000000000000000−2i2i2i−2i0000
χ452-22-222-2-22-22-22-2002-22-2002-20000000022−2−222−2−222−2−222−2−2i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i0000000000000000
χ462-22-222-2-22-22-22-2002-22-2002-20000000022−2−222−2−222−2−222−2−2−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i0000000000000000
χ472-22-222-2-22-22-22-2002-22-2002-200000000−2−222−2−222−2−222−2−222i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i0000000000000000
χ482-22-222-2-22-22-22-2002-22-2002-200000000−2−222−2−222−2−222−2−222−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i0000000000000000
χ492-22-222-2-22-22-2-2200-22-2200-220000000022−2−2−2−22222−2−2−2−222i2−i2−i2i2i2−i2−i2i22i−2i002i−2i000000000000000000
χ502-22-222-2-22-22-2-2200-22-2200-220000000022−2−2−2−22222−2−2−2−222−i2i2i2−i2−i2i2i2−i2−2i2i00−2i2i000000000000000000
χ512-22-222-2-22-22-2-2200-22-2200-2200000000−2−22222−2−2−2−22222−2−2i2−i2−i2i2i2−i2−i2i2−2i2i00−2i2i000000000000000000
χ522-22-222-2-22-22-2-2200-22-2200-2200000000−2−22222−2−2−2−22222−2−2−i2i2i2−i2−i2i2i2−i22i−2i002i−2i000000000000000000
χ532-22-222-2-2-22-222-200-22-22002-20000000022−2−222−2−2−2−222−2−222i2−i2i2−i2−i2i2−i2i2002i−2i00−2i2i0000000000000000
χ542-22-222-2-2-22-222-200-22-22002-20000000022−2−222−2−2−2−222−2−222−i2i2−i2i2i2−i2i2−i200−2i2i002i−2i0000000000000000
χ552-22-222-2-2-22-222-200-22-22002-200000000−2−222−2−22222−2−222−2−2i2−i2i2−i2−i2i2−i2i200−2i2i002i−2i0000000000000000
χ562-22-222-2-2-22-222-200-22-22002-200000000−2−222−2−22222−2−222−2−2−i2i2−i2i2i2−i2i2−i2002i−2i00−2i2i0000000000000000
χ572-22-222-2-2-22-22-22002-22-200-220000000022−2−2−2−222−2−22222−2−2i2−i2−i2i2−i2i2i2−i22i−2i00−2i2i000000000000000000
χ582-22-222-2-2-22-22-22002-22-200-220000000022−2−2−2−222−2−22222−2−2−i2i2i2−i2i2−i2−i2i2−2i2i002i−2i000000000000000000
χ592-22-222-2-2-22-22-22002-22-200-2200000000−2−22222−2−222−2−2−2−222i2−i2−i2i2−i2i2i2−i2−2i2i002i−2i000000000000000000
χ602-22-222-2-2-22-22-22002-22-200-2200000000−2−22222−2−222−2−2−2−222−i2i2i2−i2i2−i2−i2i22i−2i00−2i2i000000000000000000
χ61444-4-4-44-44-4-444-4004-4-4400-4400000000000000000000000000000000000000000000000000000000
χ62444-4-4-44-44-4-44-4400-444-4004-400000000000000000000000000000000000000000000000000000000
χ63444-4-4-44-4-444-44-400-444-400-4400000000000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-444-4-44004-4-44004-400000000000000000000000000000000000000000000000000000000
χ6544-444-4-4-40000004-4000000004-40000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ6644-444-4-4-40000004-4000000004-400000000000000−2222−2222−2222−222200000000000000000000000000000000
χ6744-444-4-4-4000000-4400000000-440000000000000022−2222−22−2222−222200000000000000000000000000000000
χ6844-444-4-4-4000000-4400000000-4400000000000000−2222−222222−2222−2200000000000000000000000000000000
χ6944-4-4-44-440000000000004-400004-4000000004i−4i4i−4i0000000000000000000000000000000000000000
χ7044-4-4-44-440000000000004-400004-400000000−4i4i−4i4i0000000000000000000000000000000000000000
χ7144-4-4-44-44000000000000-440000-4400004i−4i4i−4i00000000000000000000000000000000000000000000
χ7244-4-4-44-44000000000000-440000-440000−4i4i−4i4i00000000000000000000000000000000000000000000
χ734-4-44-444-40000004-400000000-440000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ744-4-44-444-40000004-400000000-44000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ754-4-44-444-4000000-44000000004-40000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ764-4-44-444-4000000-44000000004-4000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ774-4-4-44-4440000000000004-40000-4400000000000000004-4-4400000000000000000000000000000000
χ784-4-4-44-4440000000000004-40000-440000000000000000-444-400000000000000000000000000000000
χ794-4-4-44-444000000000000-4400004-40000000000004-4-44000000000000000000000000000000000000
χ804-4-4-44-444000000000000-4400004-4000000000000-444-4000000000000000000000000000000000000

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