Finite Group Databasebeta

← Group #305921

Character table — Group #305921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444442222448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111-111-1-1-1-111-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-1111-1
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-1111-1
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1111111-1-1-11
χ91111111111111111-1-1-1-1111111-1-111111111-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-1-1-1111111-1-11-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111-1-1-11111-1-1-1-111-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1111-1-1-1-111-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-111111-1-1-1-111-1-11-1
χ172222222222-22-2-2-222222-2-20000-2-2000000220000-2-2000000002-20000000000
χ182222222222-22-2-2-222222-2-20000-2-2000000-2-200002200000000-220000000000
χ192222222222-22-2-2-22-2-2-2-2-2-2000022000000220000-2-200000000-220000000000
χ202222222222-22-2-2-22-2-2-2-2-2-2000022000000-2-2000022000000002-20000000000
χ2122222222-2-22-2222-20000-2-22222002222-2-2000000000000-200-2000000000000
χ2222222222-2-22-2222-20000-2-2222200-2-2-2-2-2-20000000000002002000000000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-20022-2-222000000000000-2002000000000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-200-2-22222000000000000200-2000000000000
χ25222-22-2-2-2222-2-22-2-222-2-2-2200002-20000000000000022-2-2000000002-2000000
χ26222-22-2-2-2222-2-22-2-222-2-2-2200002-200000000000000-2-22200000000-22000000
χ27222-22-2-2-2222-2-22-2-2-2-222-220000-220000000000000022-2-200000000-22000000
χ28222-22-2-2-2222-2-22-2-2-2-222-220000-2200000000000000-2-222000000002-2000000
χ29222-22-2-2-222-2-22-22-222-2-22-222-2-2-2200002-20022-2-20000000000000000000000
χ30222-22-2-2-222-2-22-22-222-2-22-2-2-222-220000-2200-2-2220000000000000000000000
χ31222-22-2-2-222-2-22-22-2-2-2222-222-2-22-200002-200-2-2220000000000000000000000
χ32222-22-2-2-222-2-22-22-2-2-2222-2-2-2222-20000-220022-2-20000000000000000000000
χ33222-22-2-2-2-2-2-222-2220000-2222-2-2000000-2200000000000002i−2i0002i−2i00000000
χ34222-22-2-2-2-2-2-222-2220000-2222-2-2000000-220000000000000−2i2i000−2i2i00000000
χ35222-22-2-2-2-2-2-222-2220000-22-2-2220000002-200000000000002i−2i000−2i2i00000000
χ36222-22-2-2-2-2-2-222-2220000-22-2-2220000002-20000000000000−2i2i0002i−2i00000000
χ372-2-222-2-2200-2022-200000002i−2i2i−2i002i−2i2-200i2−i20000i2−i22−22−200000000002−2i2−i200
χ382-2-222-2-2200-2022-200000002i−2i2i−2i002i−2i2-200−i2i20000−i2i2−22−220000000000−22−i2i200
χ392-2-222-2-2200-2022-200000002i−2i2i−2i00−2i2i-2200i2−i20000i2−i22−22−20000000000−22−i2i200
χ402-2-222-2-2200-2022-200000002i−2i2i−2i00−2i2i-2200−i2i20000−i2i2−22−2200000000002−2i2−i200
χ412-2-222-2-2200-2022-20000000−2i2i−2i2i002i−2i-2200i2−i20000i2−i2−22−2200000000002−2−i2i200
χ422-2-222-2-2200-2022-20000000−2i2i−2i2i002i−2i-2200−i2i20000−i2i22−22−20000000000−22i2−i200
χ432-2-222-2-2200-2022-20000000−2i2i−2i2i00−2i2i2-200i2−i20000i2−i2−22−220000000000−22i2−i200
χ442-2-222-2-2200-2022-20000000−2i2i−2i2i00−2i2i2-200−i2i20000−i2i22−22−200000000002−2−i2i200
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-44-4-4-4-4-444-44-4400004-40000000000000000000000000000000000000000
χ4744-44-44-4-44-404000-44-44-4000000000000000000000000000000000000000000
χ4844-44-44-4-44-404000-4-44-44000000000000000000000000000000000000000000
χ4944-44-44-4-4-440-40004000000000000000000002i2−2i22i2−2i20000000000000000000000
χ5044-44-44-4-4-440-4000400000000000000000000−2i22i2−2i22i20000000000000000000000
χ5144-4-4-4-4444-40-400044-4-44000000000000000000000000000000000000000000
χ5244-4-4-4-4444-40-40004-444-4000000000000000000000000000000000000000000
χ5344-4-4-4-444-4404000-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5444-4-4-4-444-4404000-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ554-4-444-4-440040-4-4400000000000000000002i2−2i20000−2i22i200000000000000000000
χ564-4-444-4-440040-4-440000000000000000000−2i22i200002i2−2i200000000000000000000
χ574-4-4-4444-400404-4-400000004i−4i−4i4i000000000000000000000000000000000000
χ584-4-4-4444-400404-4-40000000−4i4i4i−4i000000000000000000000000000000000000
χ594-4-4-4444-400-40-44400000000000000000000000000022−22−22220000000000000000
χ604-4-4-4444-400-40-444000000000000000000000000000−222222−220000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-8-88-88000000000000000000000000000000000000000000000000000000

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