Finite Group Databasebeta

← Group #309021

Character table — Group #309021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882244444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-1111-1111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-11-1-1-11-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-111111-1
χ71111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-11-1
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-111-11
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-11111-1-11-1-1-11-11111-1-1-1-1
χ1011111111111111111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1111-11111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-11-1-111-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11-111-1-1-1-11111-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1111-1-1-1-11-1
χ17222222222-2-222-2-22-20000-22222002222-2-200000000000000-2000-2000000000
χ18222222222-2-222-2-22-20000-2222200-2-2-2-2-2-20000000000000020002000000000
χ19222222222-2-222-2-22-20000-2-2-2-2-20022-2-222000000000000002000-2000000000
χ20222222222-2-222-2-22-20000-2-2-2-2-200-2-2222200000000000000-20002000000000
χ2122222222-222-2-222-2-22222-20000-2-200000022-2-2000000000002000-200000000
χ2222222222-222-2-222-2-22222-20000-2-2000000-2-22200000000000-2000200000000
χ2322222222-222-2-222-2-2-2-2-2-2-200002200000022-2-200000000000-2000200000000
χ2422222222-222-2-222-2-2-2-2-2-2-2000022000000-2-222000000000002000-200000000
χ25222-2-2-22-22-2-2-2-222222i2i−2i−2i-200002i−2i000000000000002i2i−2i−2i0000000000002-200
χ26222-2-2-22-22-2-2-2-222222i2i−2i−2i-200002i−2i00000000000000−2i−2i2i2i000000000000-2200
χ27222-2-2-22-22-2-2-2-22222−2i−2i2i2i-20000−2i2i000000000000002i2i−2i−2i000000000000-2200
χ28222-2-2-22-22-2-2-2-22222−2i−2i2i2i-20000−2i2i00000000000000−2i−2i2i2i0000000000002-200
χ29222-2-2-22-2-22222-2-2-220000-222-2-20000002-20000000000002-2002-20000000000
χ30222-2-2-22-2-22222-2-2-220000-222-2-20000002-2000000000000-2200-220000000000
χ31222-2-2-22-2-22222-2-2-220000-2-2-222000000-220000000000002-200-220000000000
χ32222-2-2-22-2-22222-2-2-220000-2-2-222000000-22000000000000-22002-20000000000
χ33222-2-2-22-2-2-2-22222-2-22i2i−2i−2i222-2-2−2i2i0000-2200002i2i−2i−2i00000000000000000000
χ34222-2-2-22-2-2-2-22222-2-22i2i−2i−2i2-2-222−2i2i00002-20000−2i−2i2i2i00000000000000000000
χ35222-2-2-22-2-2-2-22222-2-2−2i−2i2i2i222-2-22i−2i0000-220000−2i−2i2i2i00000000000000000000
χ36222-2-2-22-2-2-2-22222-2-2−2i−2i2i2i2-2-2222i−2i00002-200002i2i−2i−2i00000000000000000000
χ3722-222-2-2-2-2002-20020000002i−2i2i−2i002-22i−2i002−22−20000i2−i2i2−i2000000002−2i2−i20000
χ3822-222-2-2-2-2002-20020000002i−2i2i−2i002-22i−2i00−22−220000−i2i2−i2i200000000−22−i2i20000
χ3922-222-2-2-2-2002-20020000002i−2i2i−2i00-22−2i2i002−22−20000i2−i2i2−i200000000−22−i2i20000
χ4022-222-2-2-2-2002-20020000002i−2i2i−2i00-22−2i2i00−22−220000−i2i2−i2i2000000002−2i2−i20000
χ4122-222-2-2-2-2002-2002000000−2i2i−2i2i002-2−2i2i002−22−20000−i2i2−i2i2000000002−2−i2i20000
χ4222-222-2-2-2-2002-2002000000−2i2i−2i2i002-2−2i2i00−22−220000i2−i2i2−i200000000−22i2−i20000
χ4322-222-2-2-2-2002-2002000000−2i2i−2i2i00-222i−2i002−22−20000−i2i2−i2i200000000−22i2−i20000
χ4422-222-2-2-2-2002-2002000000−2i2i−2i2i00-222i−2i00−22−220000i2−i2i2−i2000000002−2−i2i20000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ46444-4-4-44-4444-4-4-4-44-4000040000000000000000000000000000000000000000
χ4744-444-4-4-4400-4400-400000000000000000022−22−2222000000000000000000000000
χ4844-444-4-4-4400-4400-4000000000000000000−222222−22000000000000000000000000
χ4944-4-4-44-444004-400-40000004i−4i−4i4i000000000000000000000000000000000000
χ5044-4-4-44-444004-400-4000000−4i4i4i−4i000000000000000000000000000000000000
χ5144-4-4-44-44-400-440040000000000000000000000000022−22−22220000000000000000
χ5244-4-4-44-44-400-4400400000000000000000000000000−222222−220000000000000000
χ534-4-44-444-404-4004-4000000000000000000000002i2−2i22i2−2i200000000000000000000
χ544-4-44-444-404-4004-400000000000000000000000−2i22i2−2i22i200000000000000000000
χ554-4-44-444-40-4400-44004i−4i4i−4i00000000000000000000000000000000000000000
χ564-4-44-444-40-4400-4400−4i4i−4i4i00000000000000000000000000000000000000000
χ574-4-4-44-44404-400-44004-4-4400000000000000000000000000000000000000000
χ584-4-4-44-44404-400-4400-444-400000000000000000000000000000000000000000
χ594-4-4-44-4440-44004-40000000000000000000000022−22−222200000000000000000000
χ604-4-4-44-4440-44004-400000000000000000000000−222222−2200000000000000000000
χ618-888-8-8-88000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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