Finite Group Databasebeta

← Group #286751

Character table — Group #286751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444488888888888888884444444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ9111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ11111111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-111-1-111-1-111-1-1-1-111-1-111-1-1-1-111-11
χ12111111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111-1-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-111111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-11111-1-1111111-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-1-1-1111111-1-11111-1-1-1-1111-1
χ17222222222-222-2-22-2-2-222-2-2-2-2000000002222-2-2-2-2200000000-2-222000000000000000000
χ18222222222-222-2-22-2-2-222-2-2-2-200000000-2-2-2-2222220000000022-2-2000000000000000000
χ19222222222-222-2-22-2-2-2-2-222220000000022222222-200000000-2-2-2-2000000000000000000
χ20222222222-222-2-22-2-2-2-2-2222200000000-2-2-2-2-2-2-2-2-2000000002222000000000000000000
χ2122222222-22-2-222-22-2-222-2-2220000000000000000-222-2-2-2-2220000000000000000000000
χ2222222222-22-2-222-22-2-222-2-2220000000000000000-2-2-22222-2-20000000000000000000000
χ2322222222-22-2-222-22-2-2-2-222-2-2000000000000000022222-2-2-2-20000000000000000000000
χ2422222222-22-2-222-22-2-2-2-222-2-200000000000000002-2-2-2-222220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-22i2i2i2i−2i−2i−2i−2i00000000-20000000000002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i00000000-2000000000000−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i000000002000000000000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000020000000000002i2i−2i−2i00000000000000
χ2922-2-22-22-20200-2-202002i−2i002i−2i22−2−222−2−222−2−2i2i2−i2−i202-200002i−2i2−2i2−i2i2−i2i2−i200000000000000
χ3022-2-22-22-20200-2-202002i−2i002i−2i22−2−222−2−2−2−222−i2−i2i2i20-220000−2i2i−22−i2i2i2−i2i2−i200000000000000
χ3122-2-22-22-20200-2-202002i−2i002i−2i−2−222−2−22222−2−2i2i2−i2−i20-220000−2i2i2−2i2−i2−i2i2−i2i200000000000000
χ3222-2-22-22-20200-2-202002i−2i002i−2i−2−222−2−222−2−222−i2−i2i2i202-200002i−2i−22−i2i2−i2i2−i2i200000000000000
χ3322-2-22-22-20200-2-20200−2i2i00−2i2i22−2−222−2−222−2−2−i2−i2i2i202-20000−2i2i2−2−i2i2−i2i2−i2i200000000000000
χ3422-2-22-22-20200-2-20200−2i2i00−2i2i22−2−222−2−2−2−222i2i2−i2−i20-2200002i−2i−22i2−i2−i2i2−i2i200000000000000
χ3522-2-22-22-20200-2-20200−2i2i00−2i2i−2−222−2−22222−2−2−i2−i2i2i20-2200002i−2i2−2−i2i2i2−i2i2−i200000000000000
χ3622-2-22-22-20200-2-20200−2i2i00−2i2i−2−222−2−222−2−222i2i2−i2−i202-20000−2i2i−22i2−i2i2−i2i2−i200000000000000
χ3722-2-22-22-20-200220-2002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−i2−i2i2i20002-22i−2i00−22i2−i2−222−200000000000000
χ3822-2-22-22-20-200220-2002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i2−2−222i2i2−i2−i2000-22−2i2i002−2−i2i2−222−200000000000000
χ3922-2-22-22-20-200220-2002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−i2−i2i2i2000-22−2i2i00−22i2−i22−2−2200000000000000
χ4022-2-22-22-20-200220-2002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i2−2−222i2i2−i2−i20002-22i−2i002−2−i2i22−2−2200000000000000
χ4122-2-22-22-20-200220-200−2i2i002i−2ii2i2−i2−i2−i2−i2i2i222−2−2i2i2−i2−i2000-222i−2i00−22−i2i22−2−2200000000000000
χ4222-2-22-22-20-200220-200−2i2i002i−2ii2i2−i2−i2−i2−i2i2i2−2−222−i2−i2i2i20002-2−2i2i002−2i2−i22−2−2200000000000000
χ4322-2-22-22-20-200220-200−2i2i002i−2i−i2−i2i2i2i2i2−i2−i222−2−2i2i2−i2−i20002-2−2i2i00−22−i2i2−222−200000000000000
χ4422-2-22-22-20-200220-200−2i2i002i−2i−i2−i2i2i2i2i2−i2−i2−2−222−i2−i2i2i2000-222i−2i002−2i2−i2−222−200000000000000
χ452-22-2-222-22-22-22-2-222-20000002-22-22-22-200000000000000000000000002i−2i002i−2i00000000
χ462-22-2-222-22-22-22-2-222-20000002-22-22-22-20000000000000000000000000−2i2i00−2i2i00000000
χ472-22-2-222-22-22-22-2-222-2000000-22-22-22-2200000000000000000000000002i−2i00−2i2i00000000
χ482-22-2-222-22-22-22-2-222-2000000-22-22-22-220000000000000000000000000−2i2i002i−2i00000000
χ492-22-2-222-2-22-22-222-22-20000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000002-200002i−2i0000
χ502-22-2-222-2-22-22-222-22-20000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000-220000−2i2i0000
χ512-22-2-222-2-22-22-222-22-2000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000002-20000−2i2i0000
χ522-22-2-222-2-22-22-222-22-2000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000-2200002i−2i0000
χ5344-44-44-4-440-4-4004000000000000000000000000000000000000000000000000000022−2200
χ5444-44-44-4-440-4-40040000000000000000000000000000000000000000000000000000−222200
χ5544-44-44-4-4-404400-400000000000000000000000000000000000000000000000022−22000000
χ5644-44-44-4-4-404400-4000000000000000000000000000000000000000000000000−2222000000
χ574-4444-4-4-40000000000004-4000000000022−2222−2222−2222−220000000000000000000000000000000
χ584-4444-4-4-40000000000004-40000000000−2222−2222−2222−22220000000000000000000000000000000
χ594-4444-4-4-4000000000000-44000000000022−2222−22−2222−22220000000000000000000000000000000
χ604-4444-4-4-4000000000000-440000000000−2222−222222−2222−220000000000000000000000000000000
χ614-44-4-444-4444-4-44-4-4-4400000000000000000000000000000000000000000000000000000
χ624-44-4-444-4-4-4-444-444-4400000000000000000000000000000000000000000000000000000
χ634-4-44-4-44404004-40-4000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ644-4-44-4-44404004-40-400000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ654-4-44-4-4440-400-44040000000022−22−222222−22−2222000000000000000000000000000000000000000
χ664-4-44-4-4440-400-440400000000−222222−22−222222−22000000000000000000000000000000000000000
χ674-4-4-444-4440-4400-40000000000000000000004i−4i−4i4i0000000000000000000000000000000
χ684-4-4-444-4440-4400-4000000000000000000000−4i4i4i−4i0000000000000000000000000000000
χ694-4-4-444-44-404-4004000000000000000004-4-4400000000000000000000000000000000000
χ704-4-4-444-44-404-400400000000000000000-444-400000000000000000000000000000000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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