Finite Group Databasebeta

← Group #304006

Character table — Group #304006

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444444444444444488888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ3111111111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-111
χ511111111111111111111111111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ611111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11-1
χ10111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-11
χ11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-11
χ12111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11111-1
χ13111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1111-1
χ14111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-111-11
χ15111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-11
χ16111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11-1
χ172222222222-2-2222222-2-222-2-2-2-200002222-200000000000000000000000000000-20-20000
χ182222222222-2-2222222-2-222-2-2-2-20000-2-2-2-2-2000000000000000000000000000002020000
χ192222222222-2-2-2-2-2-222-2-2-2-222-2-2000022-2-2200000000000000000000000000000-2020000
χ202222222222-2-2-2-2-2-222-2-2-2-222-2-20000-2-22220000000000000000000000000000020-20000
χ2122222222-2-2222222-2-222-2-222-2-222220000-20000000000000000000000000000-20-200000
χ2222222222-2-2222222-2-222-2-222-2-2-2-2-2-20000-2000000000000000000000000000020200000
χ2322222222-2-222-2-2-2-2-2-22222-2-2-2-222-2-2000020000000000000000000000000000-20200000
χ2422222222-2-222-2-2-2-2-2-22222-2-2-2-2-2-22200002000000000000000000000000000020-200000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-22200000000222-2-200000000000000000000000000002-200
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-222000000002-2-2220000000000000000000000000000-2200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-222-2-20000000000000000000000000000-2200
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-2-2-22200000000000000000000000000002-200
χ2922-22-2-22-2002-22i2i−2i−2i002-2002i−2i002i−2i2-2000000000i2i2−i2−i222−2−20000000022−2−2i2i2−i2−i200000000
χ3022-22-2-22-2002-22i2i−2i−2i002-2002i−2i002i−2i2-2000000000−i2−i2i2i2−2−22200000000−2−222−i2−i2i2i200000000
χ3122-22-2-22-2002-22i2i−2i−2i002-2002i−2i00−2i2i-22000000000i2i2−i2−i222−2−200000000−2−222−i2−i2i2i200000000
χ3222-22-2-22-2002-22i2i−2i−2i002-2002i−2i00−2i2i-22000000000−i2−i2i2i2−2−2220000000022−2−2i2i2−i2−i200000000
χ3322-22-2-22-2002-2−2i−2i2i2i002-200−2i2i002i−2i-22000000000i2i2−i2−i2−2−2220000000022−2−2−i2−i2i2i200000000
χ3422-22-2-22-2002-2−2i−2i2i2i002-200−2i2i002i−2i-22000000000−i2−i2i2i222−2−200000000−2−222i2i2−i2−i200000000
χ3522-22-2-22-2002-2−2i−2i2i2i002-200−2i2i00−2i2i2-2000000000i2i2−i2−i2−2−22200000000−2−222i2i2−i2−i200000000
χ3622-22-2-22-2002-2−2i−2i2i2i002-200−2i2i00−2i2i2-2000000000−i2−i2i2i222−2−20000000022−2−2−i2−i2i2i200000000
χ372-22-22-22-22-2002i−2i2i−2i2-2002i−2i000000002i−2i2-20000000000000i2i2−i2−i222−2−22−22−2i2−i2i2−i200000000
χ382-22-22-22-22-2002i−2i2i−2i2-2002i−2i000000002i−2i2-20000000000000−i2−i2i2i2−2−222−22−22−i2i2−i2i200000000
χ392-22-22-22-22-2002i−2i2i−2i2-2002i−2i00000000−2i2i-220000000000000i2i2−i2−i222−2−2−22−22−i2i2−i2i200000000
χ402-22-22-22-22-2002i−2i2i−2i2-2002i−2i00000000−2i2i-220000000000000−i2−i2i2i2−2−2222−22−2i2−i2i2−i200000000
χ412-22-22-22-22-200−2i2i−2i2i2-200−2i2i000000002i−2i-220000000000000i2i2−i2−i2−2−2222−22−2−i2i2−i2i200000000
χ422-22-22-22-22-200−2i2i−2i2i2-200−2i2i000000002i−2i-220000000000000−i2−i2i2i222−2−2−22−22i2−i2i2−i200000000
χ432-22-22-22-22-200−2i2i−2i2i2-200−2i2i00000000−2i2i2-20000000000000i2i2−i2−i2−2−222−22−22i2−i2i2−i200000000
χ442-22-22-22-22-200−2i2i−2i2i2-200−2i2i00000000−2i2i2-20000000000000−i2−i2i2i222−2−22−22−2−i2i2−i2i200000000
χ452-2-222-2-222-22-20000-22-2200002-20000000002-22-22i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ462-2-222-2-222-22-20000-22-2200002-20000000002-22-2−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ472-2-222-2-222-22-20000-22-2200002-2000000000-22-222i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ482-2-222-2-222-22-20000-22-2200002-2000000000-22-22−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ492-2-222-2-22-22-2200002-22-200002-20000000002-2-2200002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ502-2-222-2-22-22-2200002-22-200002-20000000002-2-220000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ512-2-222-2-22-22-2200002-22-200002-2000000000-222-200002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ522-2-222-2-22-22-2200002-22-200002-2000000000-222-20000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ5344-44-4-44-400-444i4i−4i−4i00-4400−4i4i00000000000000000000000000000000000000000000000
χ5444-44-4-44-400-44−4i−4i4i4i00-44004i−4i00000000000000000000000000000000000000000000000
χ5544-4-444-4-444000000-4-40000000000000000000000000000022−22−222200000000000000000000
χ5644-4-444-4-444000000-4-400000000000000000000000000000−222222−2200000000000000000000
χ5744-4-444-4-4-4-4000000440000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ5844-4-444-4-4-4-400000044000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ594-444-44-4-40044000000-4-4000000000000000000022−22−22220000000000000000000000000000
χ604-444-44-4-40044000000-4-40000000000000000000−222222−220000000000000000000000000000
χ614-444-44-4-400-4-400000044000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ624-444-44-4-400-4-40000004400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ634-44-44-44-4-44004i−4i4i−4i-4400−4i4i0000000000000000000000000000000000000000000000000
χ644-44-44-44-4-4400−4i4i−4i4i-44004i−4i0000000000000000000000000000000000000000000000000
χ654-4-444-4-444-4-440000-444-40000-44000000000000000000000000000000000000000000000
χ664-4-444-4-44-444-400004-4-440000-44000000000000000000000000000000000000000000000
χ674-4-4-4-444400004-4-440000000000000000000000000000000000000002-2-222-2-2200000000
χ684-4-4-4-444400004-4-44000000000000000000000000000000000000000-222-2-222-200000000
χ694-4-4-4-44440000-444-40000000000000000000000000000000000000002-2-22-222-200000000
χ704-4-4-4-44440000-444-4000000000000000000000000000000000000000-222-22-2-2200000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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