Finite Group Databasebeta

← Group #309014

Character table — Group #309014

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882244444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-111-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111-1-111-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111111-1-11-1
χ911111111111111111-1-1-1-111111-1-111111111-1-1-1-1111111-1-11-1-1-1-11-1-11111-1-1
χ1011111111111111111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-111111-1-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1111-1-111-1-1-11
χ172222222222-22-2-2-22-22222-20000-2-2000000220000-2-20000000002-2000000000
χ182222222222-22-2-2-22-22222-20000-2-2000000-2-2000022000000000-22000000000
χ192222222222-22-2-2-22-2-2-2-2-2-2000022000000220000-2-2000000000-22000000000
χ202222222222-22-2-2-22-2-2-2-2-2-2000022000000-2-20000220000000002-2000000000
χ2122222222-2-22-2222-2-20000-22222002222-2-200000000000000-20000-200000000
χ2222222222-2-22-2222-2-20000-2222200-2-2-2-2-2-20000000000000020000200000000
χ2322222222-2-22-2222-2-20000-2-2-2-2-20022-2-22200000000000000-20000200000000
χ2422222222-2-22-2222-2-20000-2-2-2-2-200-2-222220000000000000020000-200000000
χ25222-22-2-2-222-2-222-2-220000-222-2-20000002-20000000000002-202-200000000000
χ26222-22-2-2-222-2-222-2-220000-222-2-20000002-2000000000000-220-2200000000000
χ27222-22-2-2-222-2-222-2-220000-2-2-222000000-220000000000002-20-2200000000000
χ28222-22-2-2-222-2-222-2-220000-2-2-222000000-22000000000000-2202-200000000000
χ29222-22-2-2-2-2-222-2-22222i2i−2i−2i-200002i−2i000000000000002i2i−2i−2i000000002-2000000
χ30222-22-2-2-2-2-222-2-22222i2i−2i−2i-200002i−2i00000000000000−2i−2i2i2i00000000-22000000
χ31222-22-2-2-2-2-222-2-2222−2i−2i2i2i-20000−2i2i000000000000002i2i−2i−2i00000000-22000000
χ32222-22-2-2-2-2-222-2-2222−2i−2i2i2i-20000−2i2i00000000000000−2i−2i2i2i000000002-2000000
χ33222-22-2-2-2-2-2-2222-22-22i2i−2i−2i222-2-2−2i2i0000-22002i2i−2i−2i0000000000000000000000
χ34222-22-2-2-2-2-2-2222-22-22i2i−2i−2i2-2-222−2i2i00002-200−2i−2i2i2i0000000000000000000000
χ35222-22-2-2-2-2-2-2222-22-2−2i−2i2i2i222-2-22i−2i0000-2200−2i−2i2i2i0000000000000000000000
χ36222-22-2-2-2-2-2-2222-22-2−2i−2i2i2i2-2-2222i−2i00002-2002i2i−2i−2i0000000000000000000000
χ372-2-222-2-2200202-2-200000002-22-2002i−2i2i−2i002−200002−22−22−20000000000i2−i2i2−i200
χ382-2-222-2-2200202-2-200000002-22-2002i−2i2i−2i00−220000−22−22−220000000000−i2i2−i2i200
χ392-2-222-2-2200202-2-200000002-22-200−2i2i−2i2i002−200002−22−22−20000000000−i2i2−i2i200
χ402-2-222-2-2200202-2-200000002-22-200−2i2i−2i2i00−220000−22−22−220000000000i2−i2i2−i200
χ412-2-222-2-2200202-2-20000000-22-22002i−2i−2i2i002−200002−2−22−220000000000i2−i2−i2i200
χ422-2-222-2-2200202-2-20000000-22-22002i−2i−2i2i00−220000−222−22−20000000000−i2i2i2−i200
χ432-2-222-2-2200202-2-20000000-22-2200−2i2i2i−2i002−200002−2−22−220000000000−i2i2i2−i200
χ442-2-222-2-2200202-2-20000000-22-2200−2i2i2i−2i00−220000−222−22−20000000000i2−i2−i2i200
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ46444-44-4-4-4444-4-4-44-4-4000040000000000000000000000000000000000000000
χ4744-44-44-4-44-404000-404-44-400000000000000000000000000000000000000000
χ4844-44-44-4-44-404000-40-44-4400000000000000000000000000000000000000000
χ4944-44-44-4-4-440-40004000000000000000000002i2−2i22i2−2i20000000000000000000000
χ5044-44-44-4-4-440-4000400000000000000000000−2i22i2−2i22i20000000000000000000000
χ5144-4-4-4-4444-40-400040000000000000000000022−22−22220000000000000000000000
χ5244-4-4-4-4444-40-4000400000000000000000000−222222−220000000000000000000000
χ5344-4-4-4-444-4404000-404i−4i−4i4i00000000000000000000000000000000000000000
χ5444-4-4-4-444-4404000-40−4i4i4i−4i00000000000000000000000000000000000000000
χ554-4-444-4-4400-40-444000000000000000000022−220000−222200000000000000000000
χ564-4-444-4-4400-40-4440000000000000000000−2222000022−2200000000000000000000
χ574-4-4-4444-40040-44-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ584-4-4-4444-40040-44-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ594-4-4-4444-400-404-4400000004-4-44000000000000000000000000000000000000
χ604-4-4-4444-400-404-440000000-444-4000000000000000000000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-8-88-88000000000000000000000000000000000000000000000000000000

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