Finite Group Databasebeta

← Group #278161

Character table — Group #278161

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888822444444448888888888882244444488888888888888882444
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
χ5111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11-11-1
χ6111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-11
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-11-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-11111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1111111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-11111-1-11-1-11
χ17222222222-2-2-2222-22222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ18222222222-2-2-2222-222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ19222222222-2-2-2222-2-2-2-2-2-2-2-2-222-2-2-2-222-2-222222222-2-2-2-20000000000000000000000000000
χ20222222222-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-222220000000000000000000000000000
χ2122222222-2222-2-2-220000000022-2-2-2-2-2-22200000000000022-2-2-2-22200000000000000000000
χ2222222222-2222-2-2-220000000022-2-2-2-2-2-222000000000000-2-22222-2-200000000000000000000
χ2322222222-2222-2-2-2200000000-2-2-2-22222-2-20000000000002222-2-2-2-200000000000000000000
χ2422222222-2222-2-2-2200000000-2-2-2-22222-2-2000000000000-2-2-2-2222200000000000000000000
χ2522222222-2-2-2-2-2-2-2-200000000222222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-200000000222222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-222-2-22222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-222-2-2222200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292-22-22-22-2-222-22-22-22222-2-2-2-2002-200000022-2-200000000000000000000000000002i−2i2i−2i0000
χ302-22-22-22-2-222-22-22-22222-2-2-2-2002-200000022-2-20000000000000000000000000000−2i2i−2i2i0000
χ312-22-22-22-2-222-22-22-2-2-2-2-22222002-2000000-2-22200000000000000000000000000002i−2i−2i2i0000
χ322-22-22-22-2-222-22-22-2-2-2-2-22222002-2000000-2-2220000000000000000000000000000−2i2i2i−2i0000
χ332-22-22-22-2-2-2-222-2222222-2-2-2-200-22000000-2-2220000000000000000000000002-22-200000000
χ342-22-22-22-2-2-2-222-2222222-2-2-2-200-22000000-2-222000000000000000000000000-22-2200000000
χ352-22-22-22-2-2-2-222-222-2-2-2-2222200-2200000022-2-20000000000000000000000002-2-2200000000
χ362-22-22-22-2-2-2-222-222-2-2-2-2222200-2200000022-2-2000000000000000000000000-222-200000000
χ372-2-2-2-222202-22000-222−2−222−2−22-20000002-22−22−222−2−222−2−2002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i2000000000000
χ382-2-2-2-222202-22000-222−2−222−2−22-20000002-22−22−222−2−222−2−200−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2000000000000
χ392-2-2-2-222202-22000-222−2−222−2−2-22000000-222−22−2−2−222−2−222002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i2000000000000
χ402-2-2-2-222202-22000-222−2−222−2−2-22000000-222−22−2−2−222−2−22200−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i2000000000000
χ412-2-2-2-222202-22000-2−2−222−2−2222-20000002-2−22−22−2−222−2−222002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2000000000000
χ422-2-2-2-222202-22000-2−2−222−2−2222-20000002-2−22−22−2−222−2−22200−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2000000000000
χ432-2-2-2-222202-22000-2−2−222−2−222-22000000-22−22−2222−2−222−2−2002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i2000000000000
χ442-2-2-2-222202-22000-2−2−222−2−222-22000000-22−22−2222−2−222−2−200−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i2000000000000
χ452-2-2-2-22220-22-2000222−2−222−2−22-2000000-22−22−22−2−22222−2−22-200002-22−2−222−2−22000000000000
χ462-2-2-2-22220-22-2000222−2−222−2−22-2000000-22−22−22−2−22222−2−2-220000-22−222−2−222−2000000000000
χ472-2-2-2-22220-22-2000222−2−222−2−2-220000002-2−22−2222−2−2−2−2222-20000-22−222−22−2−22000000000000
χ482-2-2-2-22220-22-2000222−2−222−2−2-220000002-2−22−2222−2−2−2−222-2200002-22−2−22−222−2000000000000
χ492-2-2-2-22220-22-20002−2−222−2−2222-2000000-222−22−222−2−2−2−2222-200002-2−222−2−222−2000000000000
χ502-2-2-2-22220-22-20002−2−222−2−2222-2000000-222−22−222−2−2−2−222-220000-222−2−222−2−22000000000000
χ512-2-2-2-22220-22-20002−2−222−2−222-220000002-22−22−2−2−22222−2−22-20000-222−2−22−222−2000000000000
χ522-2-2-2-22220-22-20002−2−222−2−222-220000002-22−22−2−2−22222−2−2-2200002-2−222−22−2−22000000000000
χ53444-4-4-4-44000000002i2−2i22i2−2i22i2−2i22i2−2i20000004i−4i000000000022−2222−220000000000000000000000000000
χ54444-4-4-4-44000000002i2−2i22i2−2i22i2−2i22i2−2i2000000−4i4i0000000000−2222−22220000000000000000000000000000
χ55444-4-4-4-4400000000−2i22i2−2i22i2−2i22i2−2i22i20000004i−4i0000000000−2222−22220000000000000000000000000000
χ56444-4-4-4-4400000000−2i22i2−2i22i2−2i22i2−2i22i2000000−4i4i000000000022−2222−220000000000000000000000000000
χ5744-44-4-44-404-4-400042222−22−22−22−222222000000000022−22−2222000000000000000000000000000000000000
χ5844-44-4-44-404-4-40004−22−2222222222−22−220000000000−222222−22000000000000000000000000000000000000
χ5944-44-4-44-40-444000-42222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000
χ6044-44-4-44-40-444000-4−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000
χ6144-4-444-4-44000-4-44000000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ6244-4-444-4-44000-4-4400000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ6344-4-444-4-4-400044-404i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6444-4-444-4-4-400044-40−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ654-444-44-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i200004-4000000002i2−2i2−2i22i200000000000000000000000000000000
χ664-444-44-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000-4400000000−2i22i22i2−2i200000000000000000000000000000000
χ674-444-44-4-400000000−2i22i2−2i22i22i2−2i22i2−2i200004-400000000−2i22i22i2−2i200000000000000000000000000000000
χ684-444-44-4-400000000−2i22i2−2i22i22i2−2i22i2−2i20000-44000000002i2−2i2−2i22i200000000000000000000000000000000
χ694-44-44-44-4444-4-44-4-40000000000-440000000000000000000000000000000000000000000000
χ704-44-44-44-44-4-44-44-4400000000004-40000000000000000000000000000000000000000000000
χ714-4-444-4-4440004-4-404i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ724-4-444-4-4440004-4-40−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ734-4-444-4-44-4000-4440000000000000000000000000004-4-440000000000000000000000000000
χ744-4-444-4-44-4000-444000000000000000000000000000-444-40000000000000000000000000000

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