Finite Group Databasebeta

← Group #307469

Character table — Group #307469

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888224444888888888888882444444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-11-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-11-1-1-1-1-1111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-11111-1-11-1
χ911111111111111111-1-1-1-11111111-1-111111111-1-1-1-111111-11-1-1-1-1-1-1-11111-1-1
χ1011111111111111111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-111-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-111-1-1111-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11-1-111-1-1-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-111-1-11-1-111-1-1-11
χ172222222222-2-222-2-2-20000-22222220022-2-2000000000000-20-20000000000000
χ182222222222-2-222-2-2-20000-22222-2-200-2-2-2-20000000000002020000000000000
χ192222222222-2-222-2-2-20000-2-2-2-2-22200-2-22200000000000020-20000000000000
χ202222222222-2-222-2-2-20000-2-2-2-2-2-2-2002222000000000000-2020000000000000
χ2122222222-2-222-2-222-22222-2000000-2-2000022-2-2000000000200000-200000000
χ2222222222-2-222-2-222-22222-2000000-2-20000-2-222000000000-200000200000000
χ2322222222-2-222-2-222-2-2-2-2-2-200000022000022-2-2000000000-200000200000000
χ2422222222-2-222-2-222-2-2-2-2-2-2000000220000-2-222000000000200000-200000000
χ25222-2-2-22-22-2002-2000000002i2i−2i−2i2-2002i−2i00i2−i2i2−i2000022−2−20000000000i2−i22−200
χ26222-2-2-22-22-2002-2000000002i2i−2i−2i2-2002i−2i00−i2i2−i2i20000−2−2220000000000−i2i2−2200
χ27222-2-2-22-22-2002-2000000002i2i−2i−2i-2200−2i2i00i2−i2i2−i2000022−2−20000000000−i2i2−2200
χ28222-2-2-22-22-2002-2000000002i2i−2i−2i-2200−2i2i00−i2i2−i2i20000−2−2220000000000i2−i22−200
χ29222-2-2-22-22-2002-200000000−2i−2i2i2i2-200−2i2i00i2−i2i2−i20000−2−2220000000000i2−i2−2200
χ30222-2-2-22-22-2002-200000000−2i−2i2i2i2-200−2i2i00−i2i2−i2i2000022−2−20000000000−i2i22−200
χ31222-2-2-22-22-2002-200000000−2i−2i2i2i-22002i−2i00i2−i2i2−i20000−2−2220000000000−i2i22−200
χ32222-2-2-22-22-2002-200000000−2i−2i2i2i-22002i−2i00−i2i2−i2i2000022−2−20000000000i2−i2−2200
χ3322-2-222-2-22222-2-2-2-2-22i2i−2i−2i22-22-2002i−2i002-200002i2i−2i−2i00000000000000000000
χ3422-2-222-2-22222-2-2-2-2-22i2i−2i−2i2-22-22002i−2i00-220000−2i−2i2i2i00000000000000000000
χ3522-2-222-2-22222-2-2-2-2-2−2i−2i2i2i22-22-200−2i2i002-20000−2i−2i2i2i00000000000000000000
χ3622-2-222-2-22222-2-2-2-2-2−2i−2i2i2i2-22-2200−2i2i00-2200002i2i−2i−2i00000000000000000000
χ3722-2-222-2-222-2-2-2-22220000-22-22-2000000-220000000000000002i−2i2i−2i000000000
χ3822-2-222-2-222-2-2-2-22220000-22-22-2000000-22000000000000000−2i2i−2i2i000000000
χ3922-2-222-2-222-2-2-2-22220000-2-22-220000002-20000000000000002i−2i−2i2i000000000
χ4022-2-222-2-222-2-2-2-22220000-2-22-220000002-2000000000000000−2i2i2i−2i000000000
χ4122-2-222-2-2-2-22222-2-222i2i−2i−2i-2000000−2i2i0000000000002i−2i2i−2i000000002-2000000
χ4222-2-222-2-2-2-22222-2-222i2i−2i−2i-2000000−2i2i000000000000−2i2i−2i2i00000000-22000000
χ4322-2-222-2-2-2-22222-2-22−2i−2i2i2i-20000002i−2i0000000000002i−2i2i−2i00000000-22000000
χ4422-2-222-2-2-2-22222-2-22−2i−2i2i2i-20000002i−2i000000000000−2i2i−2i2i000000002-2000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ46444-4-4-44-4-4400-44000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ47444-4-4-44-4-4400-4400000000000000000000−2i22i22i2−2i2000000000000000000000000
χ4844-44-4-4-444-400-44000000004i−4i−4i4i000000000000000000000000000000000000
χ4944-44-4-4-444-400-4400000000−4i4i4i−4i000000000000000000000000000000000000
χ5044-44-4-4-44-44004-400000000000000000000000000002i2−2i2−2i22i20000000000000000
χ5144-44-4-4-44-44004-40000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5244-4-444-4-4-4-4-4-44444-4000040000000000000000000000000000000000000000
χ534-4444-4-4-4004-4004-400000000000000000000002i2−2i22i2−2i200000000000000000000
χ544-4444-4-4-4004-4004-40000000000000000000000−2i22i2−2i22i200000000000000000000
χ554-4444-4-4-400-4400-4404i−4i4i−4i00000000000000000000000000000000000000000
χ564-4444-4-4-400-4400-440−4i4i−4i4i00000000000000000000000000000000000000000
χ574-4-4-44-444004-400-44000000000000000000000022−22−222200000000000000000000
χ584-4-4-44-444004-400-440000000000000000000000−222222−2200000000000000000000
χ594-4-4-44-44400-44004-404-4-4400000000000000000000000000000000000000000
χ604-4-4-44-44400-44004-40-444-400000000000000000000000000000000000000000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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