Finite Group Databasebeta

← Group #318321

Character table — Group #318321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888444444888888888822444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-11-1-1-1-11-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-111-11111-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-111-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-111-1-11111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111111-1-1-1-1
χ91111111111111111-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-111-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1111-1-11111-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111-1-111111-1-1-1-1-1-111
χ172222222222-2-2-22-2222-2-2-2-200002-222-2-200000000000020000-2000000000000
χ182222222222-2-2-22-2222-2-2-2-200002-2-2-222000000000000-200002000000000000
χ192222222222-2-2-22-22-2-222-2-20000-2222-2-2000000000000-200002000000000000
χ202222222222-2-2-22-22-2-222-2-20000-22-2-22200000000000020000-2000000000000
χ2122222222-2-2222-22-22222-2-22222-2-2000022-2-2-2-2000000000000000000000000
χ2222222222-2-2222-22-22222-2-2-2-2-2-2-2-20000-2-22222000000000000000000000000
χ2322222222-2-2222-22-2-2-2-2-2-2-22222220000-2-222-2-2000000000000000000000000
χ2422222222-2-2222-22-2-2-2-2-2-2-2-2-2-2-222000022-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220000-2200000000002i2i−2i−2i0000000000002i−2i000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000-220000000000−2i−2i2i2i000000000000−2i2i000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200002-200000000002i2i−2i−2i000000000000−2i2i000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200002-20000000000−2i−2i2i2i0000000000002i−2i000000
χ29222-22-2-2-2002-2-20202-22-2002i2i−2i−2i0000002i−2i000000000000000000i2−i200i2−i22−22−2
χ30222-22-2-2-2002-2-20202-22-2002i2i−2i−2i0000002i−2i000000000000000000−i2i200−i2i2−22−22
χ31222-22-2-2-2002-2-20202-22-200−2i−2i2i2i000000−2i2i000000000000000000i2−i200i2−i2−22−22
χ32222-22-2-2-2002-2-20202-22-200−2i−2i2i2i000000−2i2i000000000000000000−i2i200−i2i22−22−2
χ33222-22-2-2-2002-2-2020-22-22002i2i−2i−2i000000−2i2i000000000000000000i2−i200−i2i22−2−22
χ34222-22-2-2-2002-2-2020-22-22002i2i−2i−2i000000−2i2i000000000000000000−i2i200i2−i2−222−2
χ35222-22-2-2-2002-2-2020-22-2200−2i−2i2i2i0000002i−2i000000000000000000i2−i200−i2i2−222−2
χ36222-22-2-2-2002-2-2020-22-2200−2i−2i2i2i0000002i−2i000000000000000000−i2i200i2−i22−2−22
χ3722-2-2-22-2222-22-2-22-200002-22-22-200000000002-200000002i−2i2i−2i0000000000000
χ3822-2-2-22-2222-22-2-22-200002-22-22-200000000002-20000000−2i2i−2i2i0000000000000
χ3922-2-2-22-2222-22-2-22-200002-2-22-220000000000-2200000002i−2i−2i2i0000000000000
χ4022-2-2-22-2222-22-2-22-200002-2-22-220000000000-220000000−2i2i2i−2i0000000000000
χ4122-2-2-22-22-2-2-22-22220000-222-22-20000000000-2200002-20000002-20000000000
χ4222-2-2-22-22-2-2-22-22220000-222-22-20000000000-220000-22000000-220000000000
χ4322-2-2-22-22-2-2-22-22220000-22-22-2200000000002-200002-2000000-220000000000
χ4422-2-2-22-22-2-2-22-22220000-22-22-2200000000002-20000-220000002-20000000000
χ45444-44-4-4-400-4440-404-4-44000000000000000000000000000000000000000000
χ46444-44-4-4-400-4440-40-444-4000000000000000000000000000000000000000000
χ4744-44-4-44-40044-40-400000000000000000004-400000000000000000000000000
χ4844-44-4-44-40044-40-40000000000000000000-4400000000000000000000000000
χ4944-44-4-44-400-4-440400000004i−4i−4i4i000000000000000000000000000000000000
χ5044-44-4-44-400-4-44040000000−4i4i4i−4i000000000000000000000000000000000000
χ5144-4-4-44-44444-44-4-4-40000-440000000000000000000000000000000000000000
χ5244-4-4-44-44-4-44-444-4400004-40000000000000000000000000000000000000000
χ534-444-44-4-44-400040-40000000000004-400000000000000000000000000000000
χ544-444-44-4-44-400040-4000000000000-4400000000000000000000000000000000
χ554-444-44-4-4-44000-404000000000000004i−4i000000000000000000000000000000
χ564-444-44-4-4-44000-40400000000000000−4i4i000000000000000000000000000000
χ574-4-4-4444-44-4000-404000000000000000000000022−2222−2200000000000000000000
χ584-4-4-4444-44-4000-4040000000000000000000000−2222−222200000000000000000000
χ594-4-4-4444-4-4400040-400000000000000000000002i2−2i2−2i22i200000000000000000000
χ604-4-4-4444-4-4400040-40000000000000000000000−2i22i22i2−2i200000000000000000000
χ618-88-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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