Finite Group Databasebeta

← Group #278324

Character table — Group #278324

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444444888888888888888888888161616161616161632323232
order12222244444422444444444888888888888888888888888888244488884488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11-11-1
χ611111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-11-11
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-11-11
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1111-11-1
χ9111111111111-1-1-1-1111-1-1-1-11111111-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1
χ10111111111111-1-1-1-1111-1-1-1-11111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ11111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-111
χ12111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-11111-1-1-1-1-111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-11
χ1722222222-222-22222-2-2-2-2-2-2-222-2-2-2-22220000-2-2000000000000000000000000
χ1822222222-222-22222-2-2-2-2-2-2-2-2-22222-2-2-2000022000000000000000000000000
χ1922222222-222-2-2-2-2-2-2-2-2222222-2-2-2-22-2-2000022000000000000000000000000
χ2022222222-222-2-2-2-2-2-2-2-22222-2-22222-2220000-2-2000000000000000000000000
χ212222-2-22-222-2200002-2-200002222-2-2-200222200-2-20000-2-20000000000000000
χ222222-2-22-222-2200002-2-200002222-2-2-200-2-2-2-200220000220000000000000000
χ232222-2-22-222-2200002-2-20000-2-2-2-22220022-2-200-2-20000220000000000000000
χ242222-2-22-222-2200002-2-20000-2-2-2-222200-2-22200220000-2-20000000000000000
χ252222-2-22-2-22-2-20000-222000022-2-222-200000000002i2i−2i−2i002i2i−2i−2i000000000000
χ262222-2-22-2-22-2-20000-222000022-2-222-20000000000−2i−2i2i2i00−2i−2i2i2i000000000000
χ272222-2-22-2-22-2-20000-2220000-2-222-2-2200000000002i2i−2i−2i00−2i−2i2i2i000000000000
χ282222-2-22-2-22-2-20000-2220000-2-222-2-220000000000−2i−2i2i2i002i2i−2i−2i000000000000
χ292222-2-2-222-22222-2-2-22-222-2-20000000000000000000000000002-2002-2000000
χ302222-2-2-222-22222-2-2-22-222-2-2000000000000000000000000000-2200-22000000
χ312222-2-2-222-222-2-222-22-2-2-2220000000000000000000000000002-200-22000000
χ322222-2-2-222-222-2-222-22-2-2-222000000000000000000000000000-22002-2000000
χ332222-2-2-22-2-22-222-2-22-22-2-222000000000000000000000000000002i−2i002i−2i0000
χ342222-2-2-22-2-22-222-2-22-22-2-22200000000000000000000000000000−2i2i00−2i2i0000
χ352222-2-2-22-2-22-2-2-2222-2222-2-2000000000000000000000000000002i−2i00−2i2i0000
χ362222-2-2-22-2-22-2-2-2222-2222-2-200000000000000000000000000000−2i2i002i−2i0000
χ3722-2-22-2-2-2022000000002i−2i2i−2i002-22-202i−2ii2−i2i2−i200i2−i22−22−2i2−i22−22−2000000000000
χ3822-2-22-2-2-2022000000002i−2i2i−2i002-22-202i−2i−i2i2−i2i200−i2i2−22−22−i2i2−22−22000000000000
χ3922-2-22-2-2-2022000000002i−2i2i−2i00-22-220−2i2ii2−i2−i2i200i2−i22−22−2−i2i2−22−22000000000000
χ4022-2-22-2-2-2022000000002i−2i2i−2i00-22-220−2i2i−i2i2i2−i200−i2i2−22−22i2−i22−22−2000000000000
χ4122-2-22-2-2-202200000000−2i2i−2i2i002-22-20−2i2ii2−i2i2−i200i2−i2−22−22i2−i2−22−22000000000000
χ4222-2-22-2-2-202200000000−2i2i−2i2i002-22-20−2i2i−i2i2−i2i200−i2i22−22−2−i2i22−22−2000000000000
χ4322-2-22-2-2-202200000000−2i2i−2i2i00-22-2202i−2ii2−i2−i2i200i2−i2−22−22−i2i22−22−2000000000000
χ4422-2-22-2-2-202200000000−2i2i−2i2i00-22-2202i−2i−i2i2i2−i200−i2i22−22−2i2−i2−22−22000000000000
χ4522-2-2-22-2202-202-22-20000000002-2-22000i2−i2i2−i22-2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2000000000000
χ4622-2-2-22-2202-202-22-20000000002-2-22000−i2i2−i2i22-2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2000000000000
χ4722-2-2-22-2202-202-22-2000000000-222-2000i2−i2−i2i2-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ4822-2-2-22-2202-202-22-2000000000-222-2000−i2i2i2−i2-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ4922-2-2-22-2202-20-22-220000000002-2-22000i2−i2i2−i2-22−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ5022-2-2-22-2202-20-22-220000000002-2-22000−i2i2−i2i2-22i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ5122-2-2-22-2202-20-22-22000000000-222-2000i2−i2−i2i22-2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2000000000000
χ5222-2-2-22-2202-20-22-22000000000-222-2000−i2i2i2−i22-2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2000000000000
χ53444444-4-44-4-440000-4-440000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000000000
χ5544-4-44-4440-4-404-4-440000000000000000000000000000000000000000000000
χ5644-4-44-4440-4-40-444-40000000000000000000000000000000000000000000000
χ5744-4-4-444-40-44000000004i−4i−4i4i000000000000000000000000000000000000000
χ5844-4-4-444-40-4400000000−4i4i4i−4i000000000000000000000000000000000000000
χ598-88-800000000000000000004i2−4i20000000000000000000000000000000000000
χ608-88-80000000000000000000−4i24i20000000000000000000000000000000000000
χ618-8-880000800-800000000000000000000000000000000000000000000000000
χ628-8-880000-800800000000000000000000000000000000000000000000000000

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