Finite Group Databasebeta

← Group #285811

Character table — Group #285811

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444488888888888888884444444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ91111111111111111-1-111-1-1-1-11111-1-1-1-111111111-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-111-1-1-1-11111-1-1-1-111111111-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111-11
χ111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1111-1
χ121111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-111-1-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-111-1-1-1-111-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-11111-1-11-1
χ17222222222-2-2-2222-222-2-222-2-20000000000000000-222-2-222-2-20000000000000000000000
χ18222222222-2-2-2222-222-2-222-2-20000000000000000-2-2-222-2-2220000000000000000000000
χ19222222222-2-2-2222-2-2-2-2-2-2-2220000000000000000222-2-2-2-2220000000000000000000000
χ20222222222-2-2-2222-2-2-2-2-2-2-22200000000000000002-2-22222-2-20000000000000000000000
χ2122222222-2222-2-2-2222-2-2-2-2222222222200000000-200000000-2-2-2-2000000000000000000
χ2222222222-2222-2-2-2222-2-2-2-222-2-2-2-2-2-2-2-200000000-2000000002222000000000000000000
χ2322222222-2222-2-2-22-2-2-2-222-2-22222-2-2-2-20000000020000000022-2-2000000000000000000
χ2422222222-2222-2-2-22-2-2-2-222-2-2-2-2-2-2222200000000200000000-2-222000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i20000000000002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i2000000000000−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i-2000000000000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i-20000000000002i2i−2i−2i00000000000000
χ292-222-22-2-22000-2-2202-2002-200i2i2−i2−i2i2i2−i2−i222−2−222−2−20002i−2i002i−2ii2−i2i2−i22−22−200000000000000
χ302-222-22-2-22000-2-2202-2002-200i2i2−i2−i2i2i2−i2−i2−2−222−2−222000−2i2i00−2i2ii2−i2i2−i2−22−2200000000000000
χ312-222-22-2-22000-2-2202-2002-200−i2−i2i2i2−i2−i2i2i222−2−222−2−2000−2i2i00−2i2i−i2i2−i2i22−22−200000000000000
χ322-222-22-2-22000-2-2202-2002-200−i2−i2i2i2−i2−i2i2i2−2−222−2−2220002i−2i002i−2i−i2i2−i2i2−22−2200000000000000
χ332-222-22-2-22000-2-220-2200-2200i2i2−i2−i2−i2−i2i2i222−2−222−2−20002i−2i00−2i2i−i2i2i2−i2−22−2200000000000000
χ342-222-22-2-22000-2-220-2200-2200i2i2−i2−i2−i2−i2i2i2−2−222−2−222000−2i2i002i−2i−i2i2i2−i22−22−200000000000000
χ352-222-22-2-22000-2-220-2200-2200−i2−i2i2i2i2i2−i2−i222−2−222−2−2000−2i2i002i−2ii2−i2−i2i2−22−2200000000000000
χ362-222-22-2-22000-2-220-2200-2200−i2−i2i2i2i2i2−i2−i2−2−222−2−2220002i−2i00−2i2ii2−i2−i2i22−22−200000000000000
χ372-222-22-2-2-200022-202-200-2200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i202-2002-200−i2i2−i2i2i2−i2−i2i200000000000000
χ382-222-22-2-2-200022-202-200-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20-2200-2200−i2i2−i2i2−i2i2i2−i200000000000000
χ392-222-22-2-2-200022-202-200-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20-2200-2200i2−i2i2−i2i2−i2−i2i200000000000000
χ402-222-22-2-2-200022-202-200-2200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i202-2002-200i2−i2i2−i2−i2i2i2−i200000000000000
χ412-222-22-2-2-200022-20-22002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i202-200-2200i2−i2−i2i2−i2i2i2−i200000000000000
χ422-222-22-2-2-200022-20-22002-200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20-22002-200i2−i2−i2i2i2−i2−i2i200000000000000
χ432-222-22-2-2-200022-20-22002-200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20-22002-200−i2i2i2−i2−i2i2i2−i200000000000000
χ442-222-22-2-2-200022-20-22002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i202-200-2200−i2i2i2−i2i2−i2−i2i200000000000000
χ452-22-22-22-222-2-22-2-22002-20000000000002-22-22-22-200000000000000000002i−2i0000002i−2i00
χ462-22-22-22-222-2-22-2-22002-20000000000002-22-22-22-20000000000000000000−2i2i000000−2i2i00
χ472-22-22-22-222-2-22-2-22002-2000000000000-22-22-22-2200000000000000000002i−2i000000−2i2i00
χ482-22-22-22-222-2-22-2-22002-2000000000000-22-22-22-220000000000000000000−2i2i0000002i−2i00
χ492-22-22-22-2-2-222-222-2002-20000000000002i−2i2i−2i−2i2i−2i2i000000000000000002i−2i0000002-20000
χ502-22-22-22-2-2-222-222-2002-20000000000002i−2i2i−2i−2i2i−2i2i00000000000000000−2i2i000000-220000
χ512-22-22-22-2-2-222-222-2002-2000000000000−2i2i−2i2i2i−2i2i−2i000000000000000002i−2i000000-220000
χ522-22-22-22-2-2-222-222-2002-2000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000−2i2i0000002-20000
χ53444-4-4-4-444000-44-40000000000000000022−22−222222−22−22220000000000000000000000000000000
χ54444-4-4-4-444000-44-400000000000000000−222222−22−222222−220000000000000000000000000000000
χ55444-4-4-4-44-40004-44000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ56444-4-4-4-44-40004-4400000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ5744-44-4-44-4044-4000-4000000004-44-40000000000000000000000000000000000000000000
χ5844-44-4-44-4044-4000-400000000-44-440000000000000000000000000000000000000000000
χ5944-44-4-44-40-4-4400040000000000004i−4i4i−4i000000000000000000000000000000000000000
χ6044-44-4-44-40-4-440004000000000000−4i4i−4i4i000000000000000000000000000000000000000
χ614-44-44-44-44-4444-4-4-400-44000000000000000000000000000000000000000000000000000
χ624-44-44-44-4-44-4-4-444400-44000000000000000000000000000000000000000000000000000
χ634-4-444-4-44000000000000004i−4i2i2−2i2−2i22i222−22−2222000000000000000000000000000000000000000
χ644-4-444-4-44000000000000004i−4i−2i22i22i2−2i2−222222−22000000000000000000000000000000000000000
χ654-4-444-4-4400000000000000−4i4i2i2−2i2−2i22i2−222222−22000000000000000000000000000000000000000
χ664-4-444-4-4400000000000000−4i4i−2i22i22i2−2i222−22−2222000000000000000000000000000000000000000
χ674-4-4-4-444404-44000-4000000000000000000000000000000000000000000000002i2−2i2000000
χ684-4-4-4-444404-44000-400000000000000000000000000000000000000000000000−2i22i2000000
χ694-4-4-4-44440-44-4000400000000000000000000000000000000000000000000022−2200000000
χ704-4-4-4-44440-44-40004000000000000000000000000000000000000000000000−222200000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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