Finite Group Databasebeta

← Group #307655

Character table — Group #307655

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888822444488888822
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-11
χ11111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-111111-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-111-1-1-1-111-1-1-11
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-11-1-11111-1-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-11111-1-111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1111-1-1-1-111111-1
χ1722222222222-2-2-2-22-2-22222000000002222-2-2000000000000-2-2000000000000
χ1822222222222-2-2-2-22-2-2222200000000-2-2-2-2-2-200000000000022000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-20000000022-2-222000000000000-22000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-200000000-2-222220000000000002-2000000000000
χ2122222222-2-2-22222-2-2-2000022-2-222-2-200000022-2-20000000000000000000000
χ2222222222-2-2-22222-2-2-2000022-2-2-2-222000000-2-2220000000000000000000000
χ2322222222-2-2-22222-2-2-20000-2-22222-2-2000000-2-2220000000000000000000000
χ2422222222-2-2-22222-2-2-20000-2-222-2-22200000022-2-20000000000000000000000
χ25222-2-2-2-222-2-222-2-222-2000000002i−2i2i−2i000000000022-2-22i2i−2i−2i00000000000000
χ26222-2-2-2-222-2-222-2-222-2000000002i−2i2i−2i0000000000-2-222−2i−2i2i2i00000000000000
χ27222-2-2-2-222-2-222-2-222-200000000−2i2i−2i2i000000000022-2-2−2i−2i2i2i00000000000000
χ28222-2-2-2-222-2-222-2-222-200000000−2i2i−2i2i0000000000-2-2222i2i−2i−2i00000000000000
χ29222-2-2-2-22-22222-2-2-2-2222-2-200002i−2i−2i2i00002-200000000000000000000002i−2i00
χ30222-2-2-2-22-22222-2-2-2-2222-2-20000−2i2i2i−2i00002-20000000000000000000000−2i2i00
χ31222-2-2-2-22-22222-2-2-2-22-2-22200002i−2i−2i2i0000-220000000000000000000000−2i2i00
χ32222-2-2-2-22-22222-2-2-2-22-2-2220000−2i2i2i−2i0000-2200000000000000000000002i−2i00
χ33222-2-2-2-22-222-2-222-22-222-2-2000000000000-22000000000000002i−2i2i−2i00000000
χ34222-2-2-2-22-222-2-222-22-222-2-2000000000000-2200000000000000−2i2i−2i2i00000000
χ35222-2-2-2-22-222-2-222-22-2-2-2220000000000002-2000000000000002i−2i−2i2i00000000
χ36222-2-2-2-22-222-2-222-22-2-2-2220000000000002-200000000000000−2i2i2i−2i00000000
χ3722-222-2-2-222-20000-2002-22-2000000002i−2i2i−2i002−22−200002−22−2000000i2−i2i2−i20000
χ3822-222-2-2-222-20000-2002-22-2000000002i−2i2i−2i00−22−220000−22−22000000−i2i2−i2i20000
χ3922-222-2-2-222-20000-2002-22-200000000−2i2i−2i2i002−22−200002−22−2000000−i2i2−i2i20000
χ4022-222-2-2-222-20000-2002-22-200000000−2i2i−2i2i00−22−220000−22−22000000i2−i2i2−i20000
χ4122-222-2-2-222-20000-200-22-22000000002i−2i−2i2i002−22−20000−22−22000000i2−i2−i2i20000
χ4222-222-2-2-222-20000-200-22-22000000002i−2i−2i2i00−22−2200002−22−2000000−i2i2i2−i20000
χ4322-222-2-2-222-20000-200-22-2200000000−2i2i2i−2i002−22−20000−22−22000000−i2i2i2−i20000
χ4422-222-2-2-222-20000-200-22-2200000000−2i2i2i−2i00−22−2200002−22−2000000i2−i2−i2i20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-4-444-4-4-4-4444-4400000000000000000000000000000000000000000000
χ4744-444-4-4-4-4-44000040000000000000000000022−22−22220000000000000000000000
χ4844-444-4-4-4-4-440000400000000000000000000−222222−220000000000000000000000
χ4944-4-4-444-44-440000-400000000000000000000000000002i2−2i2−2i22i200000000000000
χ5044-4-4-444-44-440000-40000000000000000000000000000−2i22i22i2−2i200000000000000
χ5144-4-4-444-4-44-400004004-4-440000000000000000000000000000000000000000
χ5244-4-4-444-4-44-40000400-444-40000000000000000000000000000000000000000
χ534-4-44-44-440004-44-4000000000000000000000000022−2222−22000000000000000000
χ544-4-44-44-440004-44-40000000000000000000000000−2222−2222000000000000000000
χ554-4-44-44-44000-44-4400000004-400000000000000000000000000000000000000
χ564-4-44-44-44000-44-440000000-4400000000000000000000000000000000000000
χ574-4-4-44-4440004-4-44000000000000000000000000022−22−2222000000000000000000
χ584-4-4-44-4440004-4-440000000000000000000000000−222222−22000000000000000000
χ594-4-4-44-444000-444-40000000004-4000000000000000000000000000000000000
χ604-4-4-44-444000-444-4000000000-44000000000000000000000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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