Finite Group Databasebeta

← Group #501315

Character table — Group #501315

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888224444444488888888888816161616161616161616161616161616224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-1
χ91111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ101111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ111111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ121111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11
χ131111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ141111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ151111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ161111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-222220000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-20000000000000000000000000000
χ2122222222-2-22222-2-200000000-2-222-2-2-2-22200000000000022−2−222−2−222−2−222−2−2000000000000
χ2222222222-2-22222-2-200000000-2-222-2-2-2-222000000000000−2−222−2−222−2−222−2−222000000000000
χ2322222222-2-22222-2-200000000-2-2-2-22222-2-200000000000022−2−222−2−2−2−222−2−222000000000000
χ2422222222-2-22222-2-200000000-2-2-2-22222-2-2000000000000−2−222−2−22222−2−222−2−2000000000000
χ2522222222-2-2-2-2-2-2-2-200000000222222-2-2-2-200000000000022−2−2−2−22222−2−2−2−222000000000000
χ2622222222-2-2-2-2-2-2-2-200000000222222-2-2-2-2000000000000−2−22222−2−2−2−22222−2−2000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-2-2-2222200000000000022−2−2−2−222−2−22222−2−2000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-2-2-22222000000000000−2−22222−2−222−2−2−2−222000000000000
χ2922-22-2-2-222-200002-222-2-222-2-200002i−2i002i−2i000000002i2i−2i−2i00000000000000002-2002i−2i000000
χ3022-22-2-2-222-200002-222-2-222-2-200002i−2i002i−2i000000002i2i−2i−2i0000000000000000-2200−2i2i000000
χ3122-22-2-2-222-200002-222-2-222-2-20000−2i2i00−2i2i00000000−2i−2i2i2i00000000000000002-200−2i2i000000
χ3222-22-2-2-222-200002-222-2-222-2-20000−2i2i00−2i2i00000000−2i−2i2i2i0000000000000000-22002i−2i000000
χ3322-22-2-2-222-200002-2-2-222-2-22200002i−2i002i−2i00000000−2i−2i2i2i0000000000000000002i−2i002-20000
χ3422-22-2-2-222-200002-2-2-222-2-22200002i−2i002i−2i00000000−2i−2i2i2i000000000000000000−2i2i00-220000
χ3522-22-2-2-222-200002-2-2-222-2-2220000−2i2i00−2i2i000000002i2i−2i−2i0000000000000000002i−2i00-220000
χ3622-22-2-2-222-200002-2-2-222-2-2220000−2i2i00−2i2i000000002i2i−2i−2i000000000000000000−2i2i002-20000
χ372-22-2-22-222222-2-2-2-2000000002-20000000000002i2i−2i−2i2i−2i2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ382-22-2-22-222222-2-2-2-2000000002-20000000000002i2i−2i−2i2i−2i2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ392-22-2-22-222222-2-2-2-2000000002-2000000000000−2i−2i2i2i−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ402-22-2-22-222222-2-2-2-2000000002-2000000000000−2i−2i2i2i−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ412-22-2-22-2222-2-222-2-200000000-220000000000002i2i−2i−2i−2i2i−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ422-22-2-22-2222-2-222-2-200000000-220000000000002i2i−2i−2i−2i2i−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ432-22-2-22-2222-2-222-2-200000000-22000000000000−2i−2i2i2i2i−2i2i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ442-22-2-22-2222-2-222-2-200000000-22000000000000−2i−2i2i2i2i−2i2i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ452-22-2-22-22-2-222-2-2222222-2-2-2-2-220000000022-2-2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ462-22-2-22-22-2-222-2-2222222-2-2-2-2-220000000022-2-200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ472-22-2-22-22-2-222-2-222-2-2-2-22222-2200000000-2-22200000000000000002-2-222-2-22000000000000
χ482-22-2-22-22-2-222-2-222-2-2-2-22222-2200000000-2-2220000000000000000-222-2-222-2000000000000
χ492-22-2-22-22-2-2-2-222222222-2-2-2-22-200000000-2-222000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ502-22-2-22-22-2-2-2-222222222-2-2-2-22-200000000-2-22200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ512-22-2-22-22-2-2-2-22222-2-2-2-222222-20000000022-2-200000000000000002-2-22-222-2000000000000
χ522-22-2-22-22-2-2-2-22222-2-2-2-222222-20000000022-2-20000000000000000-222-22-2-22000000000000
χ53444-44-4-4-40000000022−2222−2222−2222−22004-4000000000022−2222−2200000000000000000000000000000000
χ54444-44-4-4-40000000022−2222−2222−2222−2200-440000000000−2222−222200000000000000000000000000000000
χ55444-44-4-4-400000000−2222−2222−2222−2222004-40000000000−2222−222200000000000000000000000000000000
χ56444-44-4-4-400000000−2222−2222−2222−222200-44000000000022−2222−2200000000000000000000000000000000
χ5744-44-4-4-44-440000-440000000000004i−4i00−4i4i0000000000000000000000000000000000000000
χ5844-44-4-4-44-440000-44000000000000−4i4i004i−4i0000000000000000000000000000000000000000
χ5944-4-4-444-4004i−4i4i−4i0022−22−222222−22−222200000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ6044-4-4-444-4004i−4i4i−4i00−222222−22−222222−220000000000−2i22i2−2i22i2000000000000000000000000000000000000
χ6144-4-4-444-400−4i4i−4i4i0022−22−222222−22−22220000000000−2i22i2−2i22i2000000000000000000000000000000000000
χ6244-4-4-444-400−4i4i−4i4i00−222222−22−222222−2200000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ634-444-4-44-40000000022−2222−22−2222−22220000004i−4i0000002i2−2i2−2i22i200000000000000000000000000000000
χ644-444-4-44-40000000022−2222−22−2222−2222000000−4i4i000000−2i22i22i2−2i200000000000000000000000000000000
χ654-444-4-44-400000000−2222−222222−2222−220000004i−4i000000−2i22i22i2−2i200000000000000000000000000000000
χ664-444-4-44-400000000−2222−222222−2222−22000000−4i4i0000002i2−2i2−2i22i200000000000000000000000000000000
χ674-4-4444-4-4004i−4i−4i4i0022−22−2222−222222−2200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ684-4-4444-4-4004i−4i−4i4i00−222222−2222−22−22220000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ694-4-4444-4-400−4i4i4i−4i0022−22−2222−222222−220000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ704-4-4444-4-400−4i4i4i−4i00−222222−2222−22−222200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ714-4-4-44-4444-40000-44000000000000000000000000004-4-440000000000000000000000000000
χ724-4-4-44-4444-40000-4400000000000000000000000000-444-40000000000000000000000000000
χ734-4-4-44-444-4400004-444-4-4-4-44400000000000000000000000000000000000000000000000000
χ744-4-4-44-444-4400004-4-4-44444-4-400000000000000000000000000000000000000000000000000

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