Finite Group Databasebeta

← Group #350933

Character table — Group #350933

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844444444448888888888884444444488888888888888884444
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
χ5111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-11-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1-11
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-111-1
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-1
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-11
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-1
χ172222222222-2-2-2-2222222222222-2-222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222-2-2-2-22222222222-2-222-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-20000000000000000000000000000
χ2122222222-2-22222-2-2000000002222-2-2-2-2-2-200000000000022-2-2-2-22200000000000000000000
χ2222222222-2-22222-2-2000000002222-2-2-2-2-2-2000000000000-2-22222-2-200000000000000000000
χ2322222222-2-22222-2-200000000-2-2-2-222-2-2220000000000002222-2-2-2-200000000000000000000
χ2422222222-2-22222-2-200000000-2-2-2-222-2-222000000000000-2-2-2-2222200000000000000000000
χ2522222222-2-2-2-2-2-2-2-20000000022-2-2-2-22222000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-20000000022-2-2-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-2222222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-2222222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292-22-22-22-22-200002-22222-2-2-2-22i−2i002i−2i00002i2i−2i−2i000000000000000000000000i2−i2i2−i22−22−20000
χ302-22-22-22-22-200002-22222-2-2-2-22i−2i002i−2i00002i2i−2i−2i000000000000000000000000−i2i2−i2i2−22−220000
χ312-22-22-22-22-200002-22222-2-2-2-2−2i2i00−2i2i0000−2i−2i2i2i000000000000000000000000i2−i2i2−i2−22−220000
χ322-22-22-22-22-200002-22222-2-2-2-2−2i2i00−2i2i0000−2i−2i2i2i000000000000000000000000−i2i2−i2i22−22−20000
χ332-22-22-22-22-200002-2-2-2-2-222222i−2i002i−2i0000−2i−2i2i2i000000000000000000000000i2−i2−i2i22−2−220000
χ342-22-22-22-22-200002-2-2-2-2-222222i−2i002i−2i0000−2i−2i2i2i000000000000000000000000−i2i2i2−i2−222−20000
χ352-22-22-22-22-200002-2-2-2-2-22222−2i2i00−2i2i00002i2i−2i−2i000000000000000000000000i2−i2−i2i2−222−20000
χ362-22-22-22-22-200002-2-2-2-2-22222−2i2i00−2i2i00002i2i−2i−2i000000000000000000000000−i2i2i2−i22−2−220000
χ372-2-222-2-222-222-2-2-22000000000000002-2002i−2i2i−2i00002i2i−2i−2i002-2002-22i−2i2i−2i0000000000000000
χ382-2-222-2-222-222-2-2-22000000000000002-2002i−2i2i−2i00002i2i−2i−2i00-2200-22−2i2i−2i2i0000000000000000
χ392-2-222-2-222-222-2-2-22000000000000002-200−2i2i−2i2i0000−2i−2i2i2i002-2002-2−2i2i−2i2i0000000000000000
χ402-2-222-2-222-222-2-2-22000000000000002-200−2i2i−2i2i0000−2i−2i2i2i00-2200-222i−2i2i−2i0000000000000000
χ412-2-222-2-222-2-2-222-2200000000000000-22002i−2i2i−2i0000−2i−2i2i2i2i−2i002i−2i0000002-22-2000000000000
χ422-2-222-2-222-2-2-222-2200000000000000-22002i−2i2i−2i0000−2i−2i2i2i−2i2i00−2i2i000000-22-22000000000000
χ432-2-222-2-222-2-2-222-2200000000000000-2200−2i2i−2i2i00002i2i−2i−2i2i−2i002i−2i000000-22-22000000000000
χ442-2-222-2-222-2-2-222-2200000000000000-2200−2i2i−2i2i00002i2i−2i−2i−2i2i00−2i2i0000002-22-2000000000000
χ452-2-222-2-22-2222-2-22-22i2i−2i−2i2i2i−2i−2i000000-220000002i2i−2i−2i0000002-200-2200002i−2i−2i2i000000000000
χ462-2-222-2-22-2222-2-22-22i2i−2i−2i2i2i−2i−2i000000-220000002i2i−2i−2i000000-22002-20000−2i2i2i−2i000000000000
χ472-2-222-2-22-2222-2-22-2−2i−2i2i2i−2i−2i2i2i000000-22000000−2i−2i2i2i0000002-200-220000−2i2i2i−2i000000000000
χ482-2-222-2-22-2222-2-22-2−2i−2i2i2i−2i−2i2i2i000000-22000000−2i−2i2i2i000000-22002-200002i−2i−2i2i000000000000
χ492-2-222-2-22-22-2-2222-22i2i−2i−2i2i2i−2i−2i0000002-2000000−2i−2i2i2i00002i−2i00−2i2i002-2-220000000000000000
χ502-2-222-2-22-22-2-2222-22i2i−2i−2i2i2i−2i−2i0000002-2000000−2i−2i2i2i0000−2i2i002i−2i00-222-20000000000000000
χ512-2-222-2-22-22-2-2222-2−2i−2i2i2i−2i−2i2i2i0000002-20000002i2i−2i−2i00002i−2i00−2i2i00-222-20000000000000000
χ522-2-222-2-22-22-2-2222-2−2i−2i2i2i−2i−2i2i2i0000002-20000002i2i−2i−2i0000−2i2i002i−2i002-2-220000000000000000
χ534444-4-4-4-4004-44-40022−2222−2222−2222−220000000000000022−2222−2200000000000000000000000000000000
χ544444-4-4-4-4004-44-400−2222−2222−2222−222200000000000000−2222−222200000000000000000000000000000000
χ554444-4-4-4-400-44-440022−2222−2222−2222−2200000000000000−2222−222200000000000000000000000000000000
χ564444-4-4-4-400-44-4400−2222−2222−2222−22220000000000000022−2222−2200000000000000000000000000000000
χ5744-4-444-4-4440000-4-40000000000000000004-4-44000000000000000000000000000000000000
χ5844-4-444-4-4440000-4-4000000000000000000-444-4000000000000000000000000000000000000
χ5944-4-444-4-4-4-40000444i4i−4i−4i−4i−4i4i4i00000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-4-4000044−4i−4i4i4i4i4i−4i−4i00000000000000000000000000000000000000000000000000
χ6144-4-4-4-444000000002i2−2i2−2i22i2−2i22i22i2−2i2004i−4i0000000000000022−2222−220000000000000000000000000000
χ6244-4-4-4-444000000002i2−2i2−2i22i2−2i22i22i2−2i200−4i4i00000000000000−2222−22220000000000000000000000000000
χ6344-4-4-4-44400000000−2i22i22i2−2i22i2−2i2−2i22i2004i−4i00000000000000−2222−22220000000000000000000000000000
χ6444-4-4-4-44400000000−2i22i22i2−2i22i2−2i2−2i22i200−4i4i0000000000000022−2222−220000000000000000000000000000
χ654-44-44-44-4-440000-44000000004i−4i00−4i4i00000000000000000000000000000000000000000000
χ664-44-44-44-4-440000-4400000000−4i4i004i−4i00000000000000000000000000000000000000000000
χ674-44-4-44-440000000022−2222−22−2222−2222000000004i−4i000000002i2−2i2−2i22i20000000000000000000000000000
χ684-44-4-44-440000000022−2222−22−2222−222200000000−4i4i00000000−2i22i22i2−2i20000000000000000000000000000
χ694-44-4-44-4400000000−2222−222222−2222−22000000004i−4i00000000−2i22i22i2−2i20000000000000000000000000000
χ704-44-4-44-4400000000−2222−222222−2222−2200000000−4i4i000000002i2−2i2−2i22i20000000000000000000000000000
χ714-4-44-444-4004-4-44002i2−2i2−2i22i22i2−2i2−2i22i2000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ724-4-44-444-4004-4-4400−2i22i22i2−2i2−2i22i22i2−2i200000000000000−2i22i22i2−2i200000000000000000000000000000000
χ734-4-44-444-400-444-4002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−2i22i22i2−2i200000000000000000000000000000000
χ744-4-44-444-400-444-400−2i22i22i2−2i2−2i22i22i2−2i2000000000000002i2−2i2−2i22i200000000000000000000000000000000

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