Finite Group Databasebeta

← Group #320251

Character table — Group #320251

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888444444444444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ91111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ101111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ121111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ1722222222222222-2-2-2-2-2-222-2-2-2-2-2-22200000000000000000000000022-2-222-2-2000000000000
χ1822222222222222-2-2-2-2-2-222-2-2-2-2-2-222000000000000000000000000-2-222-2-222000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-200000000000000000000000022-2-2-2-222000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2000000000000000000000000-2-22222-2-2000000000000
χ2122222222-2-2222222-2-2-2-2-2-222-2-222-2-2000000000000000022-2-222-2-200000000000000000000
χ2222222222-2-2222222-2-2-2-2-2-222-2-222-2-20000000000000000-2-222-2-22200000000000000000000
χ2322222222-2-22222-2-22222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2422222222-2-22222-2-22222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-222000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2220000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ292-222-2-22-2220000-2-222-2-2-2-2220000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000002i−2i2-20000
χ302-222-2-22-2220000-2-222-2-2-2-2220000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i-220000
χ312-222-2-22-2220000-2-222-2-2-2-222000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i-220000
χ322-222-2-22-2220000-2-222-2-2-2-222000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i2-20000
χ332-222-2-22-2-2-200002222-2-222-2-20000002i2i−2i−2i−2i−2i2i2i0000000000000000000000002-22i−2i00000000
χ342-222-2-22-2-2-200002222-2-222-2-20000002i2i−2i−2i−2i−2i2i2i000000000000000000000000-22−2i2i00000000
χ352-222-2-22-2-2-200002222-2-222-2-2000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000002-2−2i2i00000000
χ362-222-2-22-2-2-200002222-2-222-2-2000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000-222i−2i00000000
χ372-22-22-2-222-222-2-20000002-20000002-2i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i22−22−22−22−2002i−2i002i−2i000000000000
χ382-22-22-2-222-222-2-20000002-20000002-2i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2−22−22−22−2200−2i2i00−2i2i000000000000
χ392-22-22-2-222-222-2-20000002-20000002-2−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i22−22−22−22−200−2i2i00−2i2i000000000000
χ402-22-22-2-222-222-2-20000002-20000002-2−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−22−22−22−22002i−2i002i−2i000000000000
χ412-22-22-2-222-2-2-2220000002-2000000-22i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i22−22−2−22−22002i−2i00−2i2i000000000000
χ422-22-22-2-222-2-2-2220000002-2000000-22i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2−22−222−22−200−2i2i002i−2i000000000000
χ432-22-22-2-222-2-2-2220000002-2000000-22−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i22−22−2−22−2200−2i2i002i−2i000000000000
χ442-22-22-2-222-2-2-2220000002-2000000-22−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2−22−222−22−2002i−2i00−2i2i000000000000
χ452-22-22-2-22-2222-2-2000000-22000000-22i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i22−2−222−2−222i−2i002i−2i00000000000000
χ462-22-22-2-22-2222-2-2000000-22000000-22i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i2−222−2−222−2−2i2i00−2i2i00000000000000
χ472-22-22-2-22-2222-2-2000000-22000000-22−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i22−2−222−2−22−2i2i00−2i2i00000000000000
χ482-22-22-2-22-2222-2-2000000-22000000-22−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i2−222−2−222−22i−2i002i−2i00000000000000
χ492-22-22-2-22-22-2-222000000-220000002-2i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i22−2−22−222−22i−2i00−2i2i00000000000000
χ502-22-22-2-22-22-2-222000000-220000002-2i2−i2i2−i2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2−222−22−2−22−2i2i002i−2i00000000000000
χ512-22-22-2-22-22-2-222000000-220000002-2−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i22−2−22−222−2−2i2i002i−2i00000000000000
χ522-22-22-2-22-22-2-222000000-220000002-2−i2i2−i2i2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2−222−22−2−222i−2i00−2i2i00000000000000
χ53444-4-44-4-44-40000000000-440000000022−22−222222−22−2222000000000000000000000000000000000000
χ54444-4-44-4-44-40000000000-4400000000−222222−22−222222−22000000000000000000000000000000000000
χ55444-4-44-4-4-4400000000004-40000000022−22−2222−222222−22000000000000000000000000000000000000
χ56444-4-44-4-4-4400000000004-400000000−222222−2222−22−2222000000000000000000000000000000000000
χ5744-444-4-4-4000000004-44-40000000000000000004-44-400000000000000000000000000000000
χ5844-444-4-4-4000000004-44-4000000000000000000-44-4400000000000000000000000000000000
χ5944-444-4-4-400000000-44-4400000000000000000000004-44-40000000000000000000000000000
χ6044-444-4-4-400000000-44-440000000000000000000000-44-440000000000000000000000000000
χ6144-4-4-4-444004i−4i4i−4i4-40000004-4004i−4i0000000000000000000000000000000000000000000000
χ6244-4-4-4-444004i−4i4i−4i-44000000-4400−4i4i0000000000000000000000000000000000000000000000
χ6344-4-4-4-44400−4i4i−4i4i4-40000004-400−4i4i0000000000000000000000000000000000000000000000
χ6444-4-4-4-44400−4i4i−4i4i-44000000-44004i−4i0000000000000000000000000000000000000000000000
χ654-444-4-44-444000044-4-444-4-4-4-400000000000000000000000000000000000000000000000000
χ664-444-4-44-4-4-40000-4-4-4-444444400000000000000000000000000000000000000000000000000
χ674-4-44-44-44004i−4i−4i4i004-4-4400004i−4i000000000000000000000000000000000000000000000000
χ684-4-44-44-44004i−4i−4i4i00-444-40000−4i4i000000000000000000000000000000000000000000000000
χ694-4-44-44-4400−4i4i4i−4i004-4-440000−4i4i000000000000000000000000000000000000000000000000
χ704-4-44-44-4400−4i4i4i−4i00-444-400004i−4i000000000000000000000000000000000000000000000000
χ714-4-4-4444-40000004-4000000-44000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ724-4-4-4444-40000004-4000000-4400000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ734-4-4-4444-4000000-440000004-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ744-4-4-4444-4000000-440000004-400000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000

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