Finite Group Databasebeta

← Group #347883

Character table — Group #347883

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244448888444444448888882224444444888888888888888888882244
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-11111-1-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-11111-1-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111-1-1-1-111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111-1-1-1-111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111-1-1-1-111-1-1-1-111-1-11111-111-111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111-1-1-1-111-1-1-1-111-1-11111-111-111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ151111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222-2-22222-2-2222222-200-2000000-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-22002000000-2-22200000000000000000000
χ192222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-200-2000000222200000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222200200000022-2-200000000000000000000
χ21222222-2-2-2-200002222-2-2-2-2000000200-200000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222-2-2-2-200002222-2-2-2-2000000200-20000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ23222222-2-2-2-2000022-2-222-2-2000000-200200000000002i2i−2i−2i−2i−2i2i2i000000000000
χ24222222-2-2-2-2000022-2-222-2-2000000-20020000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ25222222-2-2-2-20000-2-222-2-222000000-22-222-222-2-2000000000000000000000000
χ26222222-2-2-2-20000-2-222-2-222000000-2-222-22-2-222000000000000000000000000
χ27222222-2-2-2-20000-2-2-2-2222200000022-2-22-2-2-222000000000000000000000000
χ28222222-2-2-2-20000-2-2-2-222220000002-22-2-2222-2-2000000000000000000000000
χ292222-2-222-2-200002-200002-2002i2i−2i−2i0000002-22-2002i−2i2i−2i2i−2i0000000000000000
χ302222-2-222-2-200002-200002-2002i2i−2i−2i000000-22-22002i−2i−2i2i−2i2i0000000000000000
χ312222-2-222-2-200002-200002-200−2i−2i2i2i0000002-22-200−2i2i−2i2i−2i2i0000000000000000
χ322222-2-222-2-200002-200002-200−2i−2i2i2i000000-22-2200−2i2i2i−2i2i−2i0000000000000000
χ332222-2-222-2-20000-220000-22002i2i−2i−2i0220-2-2000000−2i2i00002i−2i2i−2i000000000000
χ342222-2-222-2-20000-220000-22002i2i−2i−2i0-2-2022000000−2i2i0000−2i2i−2i2i000000000000
χ352222-2-222-2-20000-220000-2200−2i−2i2i2i0220-2-20000002i−2i0000−2i2i−2i2i000000000000
χ362222-2-222-2-20000-220000-2200−2i−2i2i2i0-2-20220000002i−2i00002i−2i2i−2i000000000000
χ372222-2-2-2-22222222-20000-22-2-2000002-20-2200002-2002-2-220000000000000000
χ382222-2-2-2-22222222-20000-22-2-200000-2202-200002-200-222-20000000000000000
χ392222-2-2-2-2222222-2200002-2-2-200000000002-2-22-220000002-2-22000000000000
χ402222-2-2-2-2222222-2200002-2-2-20000000000-222-2-22000000-222-2000000000000
χ412222-2-2-2-222-2-2-2-22-20000-2222000002-20-220000-2200-222-20000000000000000
χ422222-2-2-2-222-2-2-2-22-20000-222200000-2202-20000-22002-2-220000000000000000
χ432222-2-2-2-222-2-2-2-2-2200002-22200000000002-2-222-2000000-222-2000000000000
χ442222-2-2-2-222-2-2-2-2-2200002-2220000000000-222-22-20000002-2-22000000000000
χ4522-2-22-22-22-222-2-2002i−2i2i−2i002-22i−2i2i−2i00000000000000000000002−22−2i2−i2i2−i20000
χ4622-2-22-22-22-222-2-2002i−2i2i−2i002-22i−2i2i−2i0000000000000000000000−22−22−i2i2−i2i20000
χ4722-2-22-22-22-222-2-200−2i2i−2i2i002-2−2i2i−2i2i00000000000000000000002−22−2−i2i2−i2i20000
χ4822-2-22-22-22-222-2-200−2i2i−2i2i002-2−2i2i−2i2i0000000000000000000000−22−22i2−i2i2−i20000
χ4922-2-22-22-22-2-2-222002i−2i2i−2i00-22−2i2i−2i2i00000000000000000000002−2−22i2−i2−i2i20000
χ5022-2-22-22-22-2-2-222002i−2i2i−2i00-22−2i2i−2i2i0000000000000000000000−222−2−i2i2i2−i20000
χ5122-2-22-22-22-2-2-22200−2i2i−2i2i00-222i−2i2i−2i00000000000000000000002−2−22−i2i2i2−i20000
χ5222-2-22-22-22-2-2-22200−2i2i−2i2i00-222i−2i2i−2i0000000000000000000000−222−2i2−i2−i2i20000
χ5344-4-44-4-44-440000004i−4i−4i4i000000000000000000000000000000000000000000
χ5444-4-44-4-44-44000000−4i4i4i−4i000000000000000000000000000000000000000000
χ5544-4-4-444-4-44000000000000004-4-440000000000000000000000000000000000
χ5644-4-4-444-4-4400000000000000-444-40000000000000000000000000000000000
χ5744-4-4-44-444-444-4-400000000-4400000000000000000000000000000000000000
χ5844-4-4-44-444-4-4-444000000004-400000000000000000000000000000000000000
χ598-88-800000042−4242−42000000000000000000000000000000000000000000000000
χ608-88-8000000−4242−4242000000000000000000000000000000000000000000000000
χ618-8-8800000042−42−4242000000000000000000000000000000000000000000000000
χ628-8-88000000−424242−42000000000000000000000000000000000000000000000000

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