Finite Group Databasebeta

← Group #324282

Character table — Group #324282

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444442244444444888844448888888888888888888888888824884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111111111111111-1-111-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11
χ101111111111111111-1-111-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111-1
χ111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1
χ121111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1111-11-1
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11-11
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1-11-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-111-1-11-11-1
χ17222222222-222-2-22-222-2-2-2-222-2-2000022-2-2000000000000000000000000002-2000000
χ18222222222-222-2-22-222-2-2-2-222-2-20000-2-22200000000000000000000000000-22000000
χ19222222222-222-2-22-2-2-2-2-222-2-222000022-2-200000000000000000000000000-22000000
χ20222222222-222-2-22-2-2-2-2-222-2-2220000-2-222000000000000000000000000002-2000000
χ2122222222-22-2-222-2222-2-2-2-2-2-22222220000-2-2-2-2000000000000220000000000000000
χ2222222222-22-2-222-2222-2-2-2-2-2-222-2-2-2-200002222000000000000-2-20000000000000000
χ2322222222-22-2-222-22-2-2-2-22222-2-222220000-2-222000000000000-2-20000000000000000
χ2422222222-22-2-222-22-2-2-2-22222-2-2-2-2-2-2000022-2-2000000000000220000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000002i2i−2i−2i000000000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2-2-2000000000000−2i−2i2i2i00000000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-222220000000000002i2i−2i−2i00000000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-22222000000000000−2i−2i2i2i000000000000000000002i−2i0000
χ2922-2-22-2-220200-2-20200002i−2i2i−2i0022-2-20000002i−2i0000i2i2−i2−i222−2−200i2i2−i2−i222−2−200000000
χ3022-2-22-2-220200-2-20200002i−2i2i−2i0022-2-20000002i−2i0000−i2−i2i2i2−2−22200−i2−i2i2i2−2−22200000000
χ3122-2-22-2-220200-2-20200002i−2i2i−2i00-2-222000000−2i2i0000i2i2−i2−i222−2−200−i2−i2i2i2−2−22200000000
χ3222-2-22-2-220200-2-20200002i−2i2i−2i00-2-222000000−2i2i0000−i2−i2i2i2−2−22200i2i2−i2−i222−2−200000000
χ3322-2-22-2-220200-2-2020000−2i2i−2i2i0022-2-2000000−2i2i0000i2i2−i2−i2−2−22200i2i2−i2−i2−2−22200000000
χ3422-2-22-2-220200-2-2020000−2i2i−2i2i0022-2-2000000−2i2i0000−i2−i2i2i222−2−200−i2−i2i2i222−2−200000000
χ3522-2-22-2-220200-2-2020000−2i2i−2i2i00-2-2220000002i−2i0000i2i2−i2−i2−2−22200−i2−i2i2i222−2−200000000
χ3622-2-22-2-220200-2-2020000−2i2i−2i2i00-2-2220000002i−2i0000−i2−i2i2i222−2−200i2i2−i2−i2−2−22200000000
χ372-22-2-22-2202002-20-22-20000002-22i−2i2i−2i000000000000i2−i2i2−i2i2−i2i2−i22i−2i2−22−22−22−200000000
χ382-22-2-22-2202002-20-22-20000002-22i−2i2i−2i000000000000−i2i2−i2i2−i2i2−i2i22i−2i−22−22−22−2200000000
χ392-22-2-22-2202002-20-22-20000002-2−2i2i−2i2i000000000000i2−i2i2−i2i2−i2i2−i2−2i2i−22−22−22−2200000000
χ402-22-2-22-2202002-20-22-20000002-2−2i2i−2i2i000000000000−i2i2−i2i2−i2i2−i2i2−2i2i2−22−22−22−200000000
χ412-22-2-22-2202002-20-2-22000000-222i−2i2i−2i000000000000i2−i2i2−i2−i2i2−i2i2−2i2i2−22−2−22−2200000000
χ422-22-2-22-2202002-20-2-22000000-222i−2i2i−2i000000000000−i2i2−i2i2i2−i2i2−i2−2i2i−22−222−22−200000000
χ432-22-2-22-2202002-20-2-22000000-22−2i2i−2i2i000000000000i2−i2i2−i2−i2i2−i2i22i−2i−22−222−22−200000000
χ442-22-2-22-2202002-20-2-22000000-22−2i2i−2i2i000000000000−i2i2−i2i2i2−i2i2−i22i−2i2−22−2−22−2200000000
χ452-2-22-2-22222-2-2-222-2002-20000002i−2i−2i2i00002i−2i00000000002i−2i−2i2i0000002-2-2200000000
χ462-2-22-2-22222-2-2-222-2002-20000002i−2i−2i2i00002i−2i0000000000−2i2i2i−2i000000-222-200000000
χ472-2-22-2-22222-2-2-222-2002-2000000−2i2i2i−2i0000−2i2i00000000002i−2i−2i2i000000-222-200000000
χ482-2-22-2-22222-2-2-222-2002-2000000−2i2i2i−2i0000−2i2i0000000000−2i2i2i−2i0000002-2-2200000000
χ492-2-22-2-222-2222-22-2-200-220000002i−2i−2i2i0000−2i2i0000002-2-22000000−2i2i2i−2i000000000000
χ502-2-22-2-222-2222-22-2-200-220000002i−2i−2i2i0000−2i2i000000-222-20000002i−2i−2i2i000000000000
χ512-2-22-2-222-2222-22-2-200-22000000−2i2i2i−2i00002i−2i0000002-2-220000002i−2i−2i2i000000000000
χ522-2-22-2-222-2222-22-2-200-22000000−2i2i2i−2i00002i−2i000000-222-2000000−2i2i2i−2i000000000000
χ53444-4-4-44-4404-400-40000000000000004-4000000000000000000000000000000000000
χ54444-4-4-44-4404-400-4000000000000000-44000000000000000000000000000000000000
χ55444-4-4-44-4-40-44004000000000000000004i−4i0000000000000000000000000000000000
χ56444-4-4-44-4-40-4400400000000000000000−4i4i0000000000000000000000000000000000
χ5744-4-44-4-440-400440-400004i−4i−4i4i00000000000000000000000000000000000000000000
χ5844-4-44-4-440-400440-40000−4i4i4i−4i00000000000000000000000000000000000000000000
χ594-44-4-44-440-400-44044-4000000-44000000000000000000000000000000000000000000
χ604-44-4-44-440-400-4404-440000004-4000000000000000000000000000000000000000000
χ614-4-44-4-4444-4-4-44-44400-44000000000000000000000000000000000000000000000000
χ624-4-44-4-444-4-4444-4-44004-4000000000000000000000000000000000000000000000000
χ634-4-4-4444-440-4400-4000000000000000000000002i2−2i22i2−2i200000000000000000000000000
χ644-4-4-4444-440-4400-400000000000000000000000−2i22i2−2i22i200000000000000000000000000
χ654-4-4-4444-4-404-40040000000000000000000000022−22−222200000000000000000000000000
χ664-4-4-4444-4-404-400400000000000000000000000−222222−2200000000000000000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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