Finite Group Databasebeta

← Group #324821

Character table — Group #324821

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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222-2-2-2-2222222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-20000000000000000000000000000
χ2122222222-2-2-22222-200000000-2-222-2-2-2-2220000000000002222-2-2-2-200000000000000000000
χ2222222222-2-2-22222-200000000-2-222-2-2-2-222000000000000-2-2-2-2222200000000000000000000
χ2322222222-2-2-22222-200000000-2-2-2-22222-2-200000000000022-2-2-2-22200000000000000000000
χ2422222222-2-2-22222-200000000-2-2-2-22222-2-2000000000000-2-22222-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-222-2-2-22-2-222-2-222i2i2i2i−2i−2i−2i−2i2-2000000002i2i−2i−2i00000000000000000000000000002i−2i2-20000
χ3022-222-2-2-22-2-222-2-222i2i2i2i−2i−2i−2i−2i2-2000000002i2i−2i−2i0000000000000000000000000000−2i2i-220000
χ3122-222-2-2-22-2-222-2-22−2i−2i−2i−2i2i2i2i2i2-200000000−2i−2i2i2i00000000000000000000000000002i−2i-220000
χ3222-222-2-2-22-2-222-2-22−2i−2i−2i−2i2i2i2i2i2-200000000−2i−2i2i2i0000000000000000000000000000−2i2i2-20000
χ3322-222-2-2-22-2-2-2-22222i2i2i2i−2i−2i−2i−2i-2200000000−2i−2i2i2i0000000000000000000000002i−2i2-200000000
χ3422-222-2-2-22-2-2-2-22222i2i2i2i−2i−2i−2i−2i-2200000000−2i−2i2i2i000000000000000000000000−2i2i-2200000000
χ3522-222-2-2-22-2-2-2-2222−2i−2i−2i−2i2i2i2i2i-22000000002i2i−2i−2i0000000000000000000000002i−2i-2200000000
χ3622-222-2-2-22-2-2-2-2222−2i−2i−2i−2i2i2i2i2i-22000000002i2i−2i−2i000000000000000000000000−2i2i2-200000000
χ372-222-2-2-220002-22-2022−2−222−2−200002i−2i2i−2i002−22−2i2i2−i2−i2i2i2−i2−i2002i−2i2-2002−22−2i2−i2i2−i2000000000000
χ382-222-2-2-220002-22-2022−2−222−2−200002i−2i2i−2i002−22−2i2i2−i2−i2i2i2−i2−i200−2i2i-2200−22−22−i2i2−i2i2000000000000
χ392-222-2-2-220002-22-2022−2−222−2−20000−2i2i−2i2i002−22−2−i2−i2i2i2−i2−i2i2i2002i−2i-2200−22−22i2−i2i2−i2000000000000
χ402-222-2-2-220002-22-2022−2−222−2−20000−2i2i−2i2i002−22−2−i2−i2i2i2−i2−i2i2i200−2i2i2-2002−22−2−i2i2−i2i2000000000000
χ412-222-2-2-220002-22-20−2−222−2−22200002i−2i2i−2i00−22−22−i2−i2i2i2−i2−i2i2i2002i−2i2-200−22−22−i2i2−i2i2000000000000
χ422-222-2-2-220002-22-20−2−222−2−22200002i−2i2i−2i00−22−22−i2−i2i2i2−i2−i2i2i200−2i2i-22002−22−2i2−i2i2−i2000000000000
χ432-222-2-2-220002-22-20−2−222−2−2220000−2i2i−2i2i00−22−22i2i2−i2−i2i2i2−i2−i2002i−2i-22002−22−2−i2i2−i2i2000000000000
χ442-222-2-2-220002-22-20−2−222−2−2220000−2i2i−2i2i00−22−22i2i2−i2−i2i2i2−i2−i200−2i2i2-200−22−22i2−i2i2−i2000000000000
χ452-222-2-2-22000-22-22022−2−222−2−200002i−2i−2i2i00−22−22i2i2−i2−i2−i2−i2i2i22i−2i00002-2i2−i2−i2i22−2−22000000000000
χ462-222-2-2-22000-22-22022−2−222−2−200002i−2i−2i2i00−22−22i2i2−i2−i2−i2−i2i2i2−2i2i0000-22−i2i2i2−i2−222−2000000000000
χ472-222-2-2-22000-22-22022−2−222−2−20000−2i2i2i−2i00−22−22−i2−i2i2i2i2i2−i2−i22i−2i0000-22i2−i2−i2i2−222−2000000000000
χ482-222-2-2-22000-22-22022−2−222−2−20000−2i2i2i−2i00−22−22−i2−i2i2i2i2i2−i2−i2−2i2i00002-2−i2i2i2−i22−2−22000000000000
χ492-222-2-2-22000-22-220−2−222−2−22200002i−2i−2i2i002−22−2−i2−i2i2i2i2i2−i2−i22i−2i00002-2−i2i2i2−i2−222−2000000000000
χ502-222-2-2-22000-22-220−2−222−2−22200002i−2i−2i2i002−22−2−i2−i2i2i2i2i2−i2−i2−2i2i0000-22i2−i2−i2i22−2−22000000000000
χ512-222-2-2-22000-22-220−2−222−2−2220000−2i2i2i−2i002−22−2i2i2−i2−i2−i2−i2i2i22i−2i0000-22−i2i2i2−i22−2−22000000000000
χ522-222-2-2-22000-22-220−2−222−2−2220000−2i2i2i−2i002−22−2i2i2−i2−i2−i2−i2i2i2−2i2i00002-2i2−i2−i2i2−222−2000000000000
χ53444-4-44-4-40000000022−2222−2222−2222−22004-4000000000022−2222−2200000000000000000000000000000000
χ54444-4-44-4-40000000022−2222−2222−2222−2200-440000000000−2222−222200000000000000000000000000000000
χ55444-4-44-4-400000000−2222−2222−2222−2222004-40000000000−2222−222200000000000000000000000000000000
χ56444-4-44-4-400000000−2222−2222−2222−222200-44000000000022−2222−2200000000000000000000000000000000
χ5744-444-4-4-4-44444-4-4-400000000-44000000000000000000000000000000000000000000000000
χ5844-444-4-4-4-444-4-444-4000000004-4000000000000000000000000000000000000000000000000
χ5944-4-4-4-444000000002i2−2i22i2−2i2−2i22i2−2i22i2000000004-4000000002i2−2i22i2−2i20000000000000000000000000000
χ6044-4-4-4-444000000002i2−2i22i2−2i2−2i22i2−2i22i200000000-4400000000−2i22i2−2i22i20000000000000000000000000000
χ6144-4-4-4-44400000000−2i22i2−2i22i22i2−2i22i2−2i2000000004-400000000−2i22i2−2i22i20000000000000000000000000000
χ6244-4-4-4-44400000000−2i22i2−2i22i22i2−2i22i2−2i200000000-44000000002i2−2i22i2−2i20000000000000000000000000000
χ634-44-44-44-444-40000-44-4-444-4-4400000000000000000000000000000000000000000000000000
χ644-44-44-44-444-40000-4-444-4-444-400000000000000000000000000000000000000000000000000
χ654-44-44-44-4-4-440000400000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ664-44-44-44-4-4-44000040000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ674-4-44-444-40004-4-4402i22i2−2i2−2i2−2i2−2i22i22i200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ684-4-44-444-40004-4-440−2i2−2i22i22i22i22i2−2i2−2i20000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ694-4-44-444-4000-444-402i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ704-4-44-444-4000-444-40−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ714-4-4-444-444-440000-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ724-4-4-444-444-440000-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ734-4-4-444-44-44-400004000000000000000000000000004-4-440000000000000000000000000000
χ744-4-4-444-44-44-40000400000000000000000000000000-444-40000000000000000000000000000

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