Finite Group Databasebeta

← Group #349889

Character table — Group #349889

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222444444444444444444448888888888888888888816161616161616161616161616161616
order12222222222222222222444444444444224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000000000-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000002200000000000000000000
χ19222222222222-2-2-2-2222222222222-2-2-2-2-2-2000000000000-2-200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2220000000000002200000000000000000000
χ2122222222-2-2-2-222-2-2000022-2-2000022-2-20000000022-2-2220000-2-20000000000000000
χ2222222222-2-2-2-222-2-2000022-2-2000022-2-200000000-2-222-2-20000220000000000000000
χ2322222222-2-2-2-222-2-20000-2-2220000-2-2220022-2-22200000000-2-2000000000000000000
χ2422222222-2-2-2-222-2-20000-2-2220000-2-22200-2-222-2-20000000022000000000000000000
χ2522222222-2-2-2-2-2-222000022-2-20000-2-2220022-2-2-2-20000000022000000000000000000
χ2622222222-2-2-2-2-2-222000022-2-20000-2-22200-2-2222200000000-2-2000000000000000000
χ2722222222-2-2-2-2-2-2220000-2-222000022-2-20000000022-2-2-2-20000220000000000000000
χ2822222222-2-2-2-2-2-2220000-2-222000022-2-200000000-2-222220000-2-20000000000000000
χ29222-2-2-22-22-22-200000000000022-2-22-22-22-200002i−2i2i−2i2i−2i00002i−2i000000000000000000
χ30222-2-2-22-22-22-200000000000022-2-22-22-22-20000−2i2i−2i2i−2i2i0000−2i2i000000000000000000
χ31222-2-2-22-22-22-200000000000022-2-2-22-22-222i−2i2i−2i0000002i−2i00002i−2i0000000000000000
χ32222-2-2-22-22-22-200000000000022-2-2-22-22-22−2i2i−2i2i000000−2i2i0000−2i2i0000000000000000
χ33222-2-2-22-22-22-2000000000000-2-2222-22-2-2200002i−2i−2i2i−2i2i00002i−2i000000000000000000
χ34222-2-2-22-22-22-2000000000000-2-2222-22-2-220000−2i2i2i−2i2i−2i0000−2i2i000000000000000000
χ35222-2-2-22-22-22-2000000000000-2-222-22-222-22i−2i2i−2i000000−2i2i0000−2i2i0000000000000000
χ36222-2-2-22-22-22-2000000000000-2-222-22-222-2−2i2i−2i2i0000002i−2i00002i−2i0000000000000000
χ37222-2-2-22-2-22-22000022-2-2000000002-2-22002i−2i−2i2i002i−2i−2i2i002-200000000000000000000
χ38222-2-2-22-2-22-22000022-2-2000000002-2-2200−2i2i2i−2i00−2i2i2i−2i002-200000000000000000000
χ39222-2-2-22-2-22-22000022-2-200000000-222-20000002i−2i0000−2i2i-22−2i2i2i−2i0000000000000000
χ40222-2-2-22-2-22-22000022-2-200000000-222-2000000−2i2i00002i−2i-222i−2i−2i2i0000000000000000
χ41222-2-2-22-2-22-220000-2-222000000002-2-22002i−2i−2i2i00−2i2i2i−2i00-2200000000000000000000
χ42222-2-2-22-2-22-220000-2-222000000002-2-2200−2i2i2i−2i002i−2i−2i2i00-2200000000000000000000
χ43222-2-2-22-2-22-220000-2-22200000000-222-20000002i−2i00002i−2i2-2−2i2i−2i2i0000000000000000
χ44222-2-2-22-2-22-220000-2-22200000000-222-2000000−2i2i0000−2i2i2-22i−2i2i−2i0000000000000000
χ4522-22-2-2-22-222-200002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000002−2i2−i22−2i2−i2
χ4622-22-2-2-22-222-200002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000−22−i2i2−22−i2i2
χ4722-22-2-2-22-222-200002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000002−2−i2i22−2−i2i2
χ4822-22-2-2-22-222-200002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000−22i2−i2−22i2−i2
χ4922-22-2-2-22-222-20000-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000002−2i2−i2−22−i2i2
χ5022-22-2-2-22-222-20000-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000−22−i2i22−2i2−i2
χ5122-22-2-2-22-222-20000-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002−2−i2i2−22i2−i2
χ5222-22-2-2-22-222-20000-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000−22i2−i22−2−i2i2
χ5344-44-4-4-444-4-44000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ5444-44-4-4-444-4-4400000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5544-4-444-4-444-4-400004-4-44000000000000000000000000000000000000000000000000
χ5644-4-444-4-444-4-40000-444-4000000000000000000000000000000000000000000000000
χ5744-4-444-4-4-4-4440000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ5844-4-444-4-4-4-444000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ594-4444-4-4-40000004-40000000000000000000000000000000000002i−2i2i−2i000000000000
χ604-4444-4-4-40000004-4000000000000000000000000000000000000−2i2i−2i2i000000000000
χ614-4444-4-4-4000000-440000000000000000000000000000000000002i−2i−2i2i000000000000
χ624-4444-4-4-4000000-44000000000000000000000000000000000000−2i2i2i−2i000000000000
χ634-4-4-44-44400004-40000000000000000000000000000000000000000002-22-200000000
χ644-4-4-44-44400004-4000000000000000000000000000000000000000000-22-2200000000
χ654-4-4-44-4440000-440000000000000000000000000000000000000000002-2-2200000000
χ664-4-4-44-4440000-44000000000000000000000000000000000000000000-222-200000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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