Finite Group Databasebeta

← Group #293923

Character table — Group #293923

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444224444444444488888888888888888888888822444444
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
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111
χ511111111111111111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ611111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11-1-11-1-1
χ711111111111111111111111111-1-11-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ811111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ9111111111111-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-111-1
χ10111111111111-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-11-11-11
χ11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-11
χ12111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ13111111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1
χ14111111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-11
χ15111111111111-1-1-1-11111-1-1-1-111-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111-11-1-11
χ16111111111111-1-1-1-11111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-11-11-1
χ172222222222-2-2222222-2-2-2-222-2-222-22200000000000000000000000000000000000-2-2000
χ182222222222-2-2222222-2-2-2-222-2-2-2-2-2-2-20000000000000000000000000000000000022000
χ192222222222-2-2-2-2-2-222-2-222-2-2-2-2222-2-200000000000000000000000000000000000-22000
χ202222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2222000000000000000000000000000000000002-2000
χ2122222222-2-2222222-2-22222-2-2-2-200-2002222000000000000000000000000000000-200-200
χ2222222222-2-2222222-2-22222-2-2-2-200-200-2-2-2-2000000000000000000000000000000200200
χ2322222222-2-222-2-2-2-2-2-222-2-222-2-20020022-2-2000000000000000000000000000000200-200
χ2422222222-2-222-2-2-2-2-2-222-2-222-2-200200-2-222000000000000000000000000000000-200200
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-22200200000022-2-20000000000000000000000002-2000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-222002000000-2-222000000000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200-200000022-2-2000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200-2000000-2-2220000000000000000000000002-2000000
χ2922-2-222-2-2002-22i2i−2i−2i002-22i−2i0000000002-22i−2i00000000000022−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000
χ3022-2-222-2-2002-22i2i−2i−2i002-22i−2i0000000002-22i−2i000000000000−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000
χ3122-2-222-2-2002-22i2i−2i−2i002-22i−2i000000000-22−2i2i00000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000
χ3222-2-222-2-2002-22i2i−2i−2i002-22i−2i000000000-22−2i2i000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000
χ3322-2-222-2-2002-2−2i−2i2i2i002-2−2i2i0000000002-2−2i2i00000000000022−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000
χ3422-2-222-2-2002-2−2i−2i2i2i002-2−2i2i0000000002-2−2i2i000000000000−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000
χ3522-2-222-2-2002-2−2i−2i2i2i002-2−2i2i000000000-222i−2i00000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000
χ3622-2-222-2-2002-2−2i−2i2i2i002-2−2i2i000000000-222i−2i000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000
χ372-2-222-2-2222002-22-2-2-200002-2002-202-200000000i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i2i2−i2i2−i200000000
χ382-2-222-2-2222002-22-2-2-200002-2002-202-200000000−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i2−i2i2−i2i200000000
χ392-2-222-2-2222002-22-2-2-200002-200-220-2200000000i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i2−i2i2−i2i200000000
χ402-2-222-2-2222002-22-2-2-200002-200-220-2200000000−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i2i2−i2i2−i200000000
χ412-2-222-2-222200-22-22-2-20000-22002-20-2200000000i2i2−i2−i2−i2−i2i2i200000000i2−i2i2−i2−i2i2−i2i200000000
χ422-2-222-2-222200-22-22-2-20000-22002-20-2200000000−i2−i2i2i2i2i2−i2−i200000000−i2i2−i2i2i2−i2i2−i200000000
χ432-2-222-2-222200-22-22-2-20000-2200-2202-200000000i2i2−i2−i2−i2−i2i2i200000000−i2i2−i2i2i2−i2i2−i200000000
χ442-2-222-2-222200-22-22-2-20000-2200-2202-200000000−i2−i2i2i2i2i2−i2−i200000000i2−i2i2−i2−i2i2−i2i200000000
χ452-2-22-222-22-22-200002-2-2200002-20000000002i−2i2i−2i2i−2i2i−2i000000002-22-20000000000000000
χ462-2-22-222-22-22-200002-2-2200002-20000000002i−2i2i−2i−2i2i−2i2i00000000-22-220000000000000000
χ472-2-22-222-22-22-200002-2-2200002-2000000000−2i2i−2i2i2i−2i2i−2i00000000-22-220000000000000000
χ482-2-22-222-22-22-200002-2-2200002-2000000000−2i2i−2i2i−2i2i−2i2i000000002-22-20000000000000000
χ492-2-22-222-2-22-220000-222-200002-20000000002i−2i−2i2i00002i−2i2i−2i2-22-200000000000000000000
χ502-2-22-222-2-22-220000-222-200002-20000000002i−2i−2i2i0000−2i2i−2i2i-22-2200000000000000000000
χ512-2-22-222-2-22-220000-222-200002-2000000000−2i2i2i−2i00002i−2i2i−2i-22-2200000000000000000000
χ522-2-22-222-2-22-220000-222-200002-2000000000−2i2i2i−2i0000−2i2i−2i2i2-22-200000000000000000000
χ534444-4-4-4-44-4000000-4400000000000000000000022−22−22220000000000000000000000000000
χ544444-4-4-4-44-4000000-44000000000000000000000−222222−220000000000000000000000000000
χ554444-4-4-4-4-440000004-4000000000000000000000000022−22−2222000000000000000000000000
χ564444-4-4-4-4-440000004-40000000000000000000000000−222222−22000000000000000000000000
χ5744-4-444-4-400-444i4i−4i−4i00-44−4i4i0000000000000000000000000000000000000000000000000
χ5844-4-444-4-400-44−4i−4i4i4i00-444i−4i0000000000000000000000000000000000000000000000000
χ594-44-44-44-400004i−4i−4i4i0000000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ604-44-44-44-400004i−4i−4i4i000000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ614-44-44-44-40000−4i4i4i−4i0000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ624-44-44-44-40000−4i4i4i−4i000000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ634-44-4-44-440044000000-4-400000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ644-44-4-44-440044000000-4-40000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ654-44-4-44-4400-4-40000004400000000000000000000000000022−22−222200000000000000000000
χ664-44-4-44-4400-4-400000044000000000000000000000000000−222222−2200000000000000000000
χ674-4-444-4-44-4-4004-44-4440000-4400000000000000000000000000000000000000000000000
χ684-4-444-4-44-4-400-44-444400004-400000000000000000000000000000000000000000000000
χ694-4-44-444-44-4-4400004-44-40000-44000000000000000000000000000000000000000000000
χ704-4-44-444-4-444-40000-44-440000-44000000000000000000000000000000000000000000000
χ7188-8-8-8-888000000000000000000000000000000000000000000000000000000000000000

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