Finite Group Databasebeta

← Group #258337

Character table — Group #258337

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888824444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111111
χ71111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111
χ81111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ91111111111-1-1-1-1111111-1-111111-1-11-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111-111-1-1-1-111-1-1
χ101111111111-1-1-1-1111111-1-111111-1-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-111-1-111
χ111111111111-1-1-1-1111111-1-111111-1-11-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-111
χ121111111111-1-1-1-1111111-1-111111-1-11-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-11-1-1111111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-11-1-11-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-11111-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-11-1-11-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-11-1-11-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-11-1-11-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-111111-1-1-1-1-1-111
χ1722222222222222-2-2-222-2222222-2-2-2-2-2-2-222-2-20000000000000000000000000000000000
χ1822222222222222-2-2-222-222-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-222-2-2-22222-222-22-2-2-2-2220000000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-222222-2-20000000000000000000000000000000000
χ2122222222-2-22222222-2-22-2-20000-222-2-200000022220000000000000000-200-20000000000
χ2222222222-2-22222222-2-22-2-20000-222-2-2000000-2-2-2-2000000000000000020020000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-200002-2-2220000000000000000000000000002-20002-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-200002-2-222000000000000000000000000000-22000-22000000
χ2522222222-2-2-2-2-2-2222-2-22220000-2-2-2-2200000022-2-20000000000000000-20020000000000
χ2622222222-2-2-2-2-2-2222-2-22220000-2-2-2-22000000-2-2220000000000000000200-20000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200002222-20000000000000000000000000002-2000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002222-2000000000000000000000000000-220002-2000000
χ2922-22-2-2-222-22i2i−2i−2i0002-202i−2i2i2i−2i−2i00000002-20000000000000022−2−2i2i2−i2−i20000000000i2−i22−2
χ3022-22-2-2-222-22i2i−2i−2i0002-202i−2i2i2i−2i−2i00000002-200000000000000−2−222−i2−i2i2i20000000000−i2i2−22
χ3122-22-2-2-222-22i2i−2i−2i0002-202i−2i−2i−2i2i2i0000000-220000000000000022−2−2i2i2−i2−i20000000000−i2i2−22
χ3222-22-2-2-222-22i2i−2i−2i0002-202i−2i−2i−2i2i2i0000000-2200000000000000−2−222−i2−i2i2i20000000000i2−i22−2
χ3322-22-2-2-222-2−2i−2i2i2i0002-20−2i2i2i2i−2i−2i0000000-220000000000000022−2−2−i2−i2i2i20000000000i2−i2−22
χ3422-22-2-2-222-2−2i−2i2i2i0002-20−2i2i2i2i−2i−2i0000000-2200000000000000−2−222i2i2−i2−i20000000000−i2i22−2
χ3522-22-2-2-222-2−2i−2i2i2i0002-20−2i2i−2i−2i2i2i00000002-20000000000000022−2−2−i2−i2i2i20000000000−i2i22−2
χ3622-22-2-2-222-2−2i−2i2i2i0002-20−2i2i−2i−2i2i2i00000002-200000000000000−2−222i2i2−i2−i20000000000i2−i2−22
χ372-2-222-22-22-2000022-2-22-2002i−2i2i−2i-200202i−2i00000000000022-2-200000000000000002i−2i0000
χ382-2-222-22-22-2000022-2-22-2002i−2i2i−2i-200202i−2i000000000000-2-2220000000000000000−2i2i0000
χ392-2-222-22-22-2000022-2-22-200−2i2i−2i2i-20020−2i2i00000000000022-2-20000000000000000−2i2i0000
χ402-2-222-22-22-2000022-2-22-200−2i2i−2i2i-20020−2i2i000000000000-2-22200000000000000002i−2i0000
χ412-2-222-22-22-20000-2-22-222002i−2i2i−2i200-20−2i2i000000002i2i−2i−2i00000000000000002-200000000
χ422-2-222-22-22-20000-2-22-222002i−2i2i−2i200-20−2i2i00000000−2i−2i2i2i0000000000000000-2200000000
χ432-2-222-22-22-20000-2-22-22200−2i2i−2i2i200-202i−2i000000002i2i−2i−2i0000000000000000-2200000000
χ442-2-222-22-22-20000-2-22-22200−2i2i−2i2i200-202i−2i00000000−2i−2i2i2i00000000000000002-200000000
χ452-2-2-2-2222002-22-22-2200-200000002-2000000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000
χ462-2-2-2-2222002-22-22-2200-200000002-2000000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000
χ472-2-2-2-2222002-22-22-2200-200000002-200000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000
χ482-2-2-2-2222002-22-22-2200-200000002-200000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000
χ492-2-2-2-222200-22-222-2200-20000000-22000000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000000000
χ502-2-2-2-222200-22-222-2200-20000000-22000000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000000000
χ512-2-2-2-222200-22-222-2200-20000000-2200000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−200000000000000
χ522-2-2-2-222200-22-222-2200-20000000-2200000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000000000
χ53444-4-4-44-40000004-4-400400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ54444-4-4-44-40000004-4-40040000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ55444-4-4-44-4000000-44400-400000000000000000000022−22−222200000000000000000000000000
χ56444-4-4-44-4000000-44400-4000000000000000000000−222222−2200000000000000000000000000
χ5744-44-4-4-44-444i4i−4i−4i000-440−4i4i0000000000000000000000000000000000000000000000000
χ5844-44-4-4-44-44−4i−4i4i4i000-4404i−4i0000000000000000000000000000000000000000000000000
χ594-444-44-4-4440000000-4-40004-4-44000000000000000000000000000000000000000000000
χ604-444-44-4-4440000000-4-4000-444-4000000000000000000000000000000000000000000000
χ614-444-44-4-4-4-400000004400000000000000004i−4i0000000000000000000000000000000000
χ624-444-44-4-4-4-40000000440000000000000000−4i4i0000000000000000000000000000000000
χ634-44-44-4-44004i−4i−4i4i000000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ644-44-44-4-44004i−4i−4i4i00000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ654-44-44-4-4400−4i4i4i−4i000000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ664-44-44-4-4400−4i4i4i−4i00000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ674-4-444-44-4-44000044-44-4-4000000400-400000000000000000000000000000000000000000
χ684-4-444-44-4-440000-4-444-44000000-400400000000000000000000000000000000000000000
χ694-4-4-4-4444004-44-4-44-40040000000-44000000000000000000000000000000000000000000
χ704-4-4-4-444400-44-44-44-400400000004-4000000000000000000000000000000000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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