Finite Group Databasebeta

← Group #307679

Character table — Group #307679

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888824444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-1-1-111
χ3111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-11-1-11111-1-1
χ51111111111111111111111-1-111111111-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-11111-1-1-11111-1-1
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-1-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1111-1
χ11111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-111-1-11-1-1-1-111-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111111-1-1-11
χ13111111111111111111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111111-1-111-1-1-111-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111-1-1-111-1-1111-1
χ172222222222-2-222-2-2-2-22222220000000022-2-2000000000000-20000-200000000
χ182222222222-2-222-2-2-2-22222-2-200000000-2-2-2-200000000000020000200000000
χ192222222222-2-222-2-2-2-2-2-2-2-22200000000-2-22200000000000020000-200000000
χ202222222222-2-222-2-2-2-2-2-2-2-2-2-2000000002222000000000000-20000200000000
χ2122222222-2-222-2-222-2-20000002222-2-2-2-2000022-2-20000000000000000000000
χ2222222222-2-222-2-222-2-200000022-2-2-2-2220000-2-2220000000000000000000000
χ2322222222-2-222-2-222-2-2000000-2-22222-2-20000-2-2220000000000000000000000
χ2422222222-2-222-2-222-2-2000000-2-2-2-22222000022-2-20000000000000000000000
χ25222-2-2-2-222222-2-2-2-2-2222-2-200002i−2i002i−2i002-20000000000000000002i−2i000000
χ26222-2-2-2-222222-2-2-2-2-2222-2-20000−2i2i00−2i2i002-2000000000000000000−2i2i000000
χ27222-2-2-2-222222-2-2-2-2-22-2-22200002i−2i002i−2i00-22000000000000000000−2i2i000000
χ28222-2-2-2-222222-2-2-2-2-22-2-2220000−2i2i00−2i2i00-220000000000000000002i−2i000000
χ29222-2-2-2-2222-2-2-2-2222-222-2-2000000000000-2200000000000002i−2i2i−2i000000000
χ30222-2-2-2-2222-2-2-2-2222-222-2-2000000000000-220000000000000−2i2i−2i2i000000000
χ31222-2-2-2-2222-2-2-2-2222-2-2-2220000000000002-200000000000002i−2i−2i2i000000000
χ32222-2-2-2-2222-2-2-2-2222-2-2-2220000000000002-20000000000000−2i2i2i−2i000000000
χ33222-2-2-2-22-2-22222-2-22-2000000002i−2i00−2i2i0000000022-2-22i2i−2i−2i00000000000000
χ34222-2-2-2-22-2-22222-2-22-2000000002i−2i00−2i2i00000000-2-222−2i−2i2i2i00000000000000
χ35222-2-2-2-22-2-22222-2-22-200000000−2i2i002i−2i0000000022-2-2−2i−2i2i2i00000000000000
χ36222-2-2-2-22-2-22222-2-22-200000000−2i2i002i−2i00000000-2-2222i2i−2i−2i00000000000000
χ3722-22-22-2-22-2002-200002i−2i2i−2i2-2000000002i−2i00i2−i2i2−i200002−22−200000000i2−i22−200
χ3822-22-22-2-22-2002-200002i−2i2i−2i2-2000000002i−2i00−i2i2−i2i20000−22−2200000000−i2i2−2200
χ3922-22-22-2-22-2002-200002i−2i2i−2i-2200000000−2i2i00i2−i2i2−i200002−22−200000000−i2i2−2200
χ4022-22-22-2-22-2002-200002i−2i2i−2i-2200000000−2i2i00−i2i2−i2i20000−22−2200000000i2−i22−200
χ4122-22-22-2-22-2002-20000−2i2i−2i2i2-200000000−2i2i00i2−i2i2−i20000−22−2200000000i2−i2−2200
χ4222-22-22-2-22-2002-20000−2i2i−2i2i2-200000000−2i2i00−i2i2−i2i200002−22−200000000−i2i22−200
χ4322-22-22-2-22-2002-20000−2i2i−2i2i-22000000002i−2i00i2−i2i2−i20000−22−2200000000−i2i22−200
χ4422-22-22-2-22-2002-20000−2i2i−2i2i-22000000002i−2i00−i2i2−i2i200002−22−200000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-4-44-4-4-4-44444-4400000000000000000000000000000000000000000000
χ4744-44-44-4-4-4400-4400000000000000000000002i2−2i2−2i22i20000000000000000000000
χ4844-44-44-4-4-4400-440000000000000000000000−2i22i22i2−2i20000000000000000000000
χ4944-4-44-44-44-400-4400004i−4i−4i4i0000000000000000000000000000000000000000
χ5044-4-44-44-44-400-440000−4i4i4i−4i0000000000000000000000000000000000000000
χ5144-4-44-44-4-44004-40000000000000000000000000000002i2−2i2−2i22i200000000000000
χ5244-4-44-44-4-44004-4000000000000000000000000000000−2i22i22i2−2i200000000000000
χ534-4-44-4-444004-4004-400000000000000000000000022−2222−22000000000000000000
χ544-4-44-4-444004-4004-4000000000000000000000000−2222−2222000000000000000000
χ554-4-44-4-44400-4400-44000000004-4000000000000000000000000000000000000
χ564-4-44-4-44400-4400-4400000000-44000000000000000000000000000000000000
χ574-4-4-444-44004-400-4400000000000000000000000022−22−2222000000000000000000
χ584-4-4-444-44004-400-44000000000000000000000000−222222−22000000000000000000
χ594-4-4-444-4400-44004-40000000000004-400000000000000000000000000000000
χ604-4-4-444-4400-44004-4000000000000-4400000000000000000000000000000000
χ618-8888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-88-8-888-8000000000000000000000000000000000000000000000000000000

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