Finite Group Databasebeta

← Group #349765

Character table — Group #349765

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444222244444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1-1-1-1-11-1-1111111-1-111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-11-1-1111111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111111111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111111111111-1-1-1-1-1-1-1-1-1-111111-1-11111-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-1-1-111111-1-11111-1-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-2-22-2-22222-2-222222222-2-2-2000000-2-2000000-20000000000000000000000
χ1822222222222-2-2-22-2-22222-2-2-2-2-2-2-2-2-2-2-22200000022000000-20000000000000000000000
χ1922222222222-2-2-22-2-2-2-2-2-2222222-2-2-2-2-2-2-20000002200000020000000000000000000000
χ2022222222222-2-2-22-2-2-2-2-2-222-2-2-2-22222-222000000-2-200000020000000000000000000000
χ2122222222-2-2-2222-22-222-2-2-2-200000000-20022-2-2-2-20022000020000000000000000000000
χ2222222222-2-2-2222-22-222-2-2-2-200000000-200-2-2222200-2-2000020000000000000000000000
χ2322222222-2-2-2222-22-2-2-2222200000000-20022-2-22200-2-20000-20000000000000000000000
χ2422222222-2-2-2222-22-2-2-2222200000000-200-2-222-2-200220000-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-22200000000200000000000022-2-2-222-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-222000000002000000000000-2-222-2-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-222-2-200000000200000000000022-2-22-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-222-2-2000000002000000000000-2-222222-2-2000000000000000000
χ29222-2-22-2-222-222-2-2-2200000022-2-20000-22-22-22-20000002-22-200000000000000000000000
χ30222-2-22-2-222-222-2-2-2200000022-2-20000-22-2-22-22000000-22-2200000000000000000000000
χ31222-2-22-2-222-222-2-2-22000000-2-2220000-2-222-22-2000000-22-2200000000000000000000000
χ32222-2-22-2-222-222-2-2-22000000-2-2220000-2-22-22-220000002-22-200000000000000000000000
χ33222-2-22-2-222-2-2-22-22-200000022-2-200002-2200002i−2i002i−2i000002i−2i2i−2i000000000000000000
χ34222-2-22-2-222-2-2-22-22-200000022-2-200002-220000−2i2i00−2i2i00000−2i2i−2i2i000000000000000000
χ35222-2-22-2-222-2-2-22-22-2000000-2-222000022-200002i−2i002i−2i00000−2i2i−2i2i000000000000000000
χ36222-2-22-2-222-2-2-22-22-2000000-2-222000022-20000−2i2i00−2i2i000002i−2i2i−2i000000000000000000
χ37222-2-22-2-2-2-2222-22-2-200000000002i2i−2i−2i2002-2-22002i−2i00000002i−2i−2i2i000000000000000000
χ38222-2-22-2-2-2-2222-22-2-200000000002i2i−2i−2i200-222-2002i−2i0000000−2i2i2i−2i000000000000000000
χ39222-2-22-2-2-2-2222-22-2-20000000000−2i−2i2i2i2002-2-2200−2i2i0000000−2i2i2i−2i000000000000000000
χ40222-2-22-2-2-2-2222-22-2-20000000000−2i−2i2i2i200-222-200−2i2i00000002i−2i−2i2i000000000000000000
χ41222-2-22-2-2-2-22-2-2222200000000002i2i−2i−2i-20000002i−2i−2i2i−2i2i-222-200000000000000000000000
χ42222-2-22-2-2-2-22-2-2222200000000002i2i−2i−2i-2000000−2i2i−2i2i2i−2i2-2-2200000000000000000000000
χ43222-2-22-2-2-2-22-2-222220000000000−2i−2i2i2i-20000002i−2i2i−2i−2i2i2-2-2200000000000000000000000
χ44222-2-22-2-2-2-22-2-222220000000000−2i−2i2i2i-2000000−2i2i2i−2i2i−2i-222-200000000000000000000000
χ452-2222-2-2-22-2-20002002-22-2002i−2i2i−2i2i−2i2i−2i000000000000000000000022−2−222−2−2i2−i2i2−i2000000
χ462-2222-2-2-22-2-20002002-22-2002i−2i2i−2i2i−2i2i−2i0000000000000000000000−2−222−2−222−i2i2−i2i2000000
χ472-2222-2-2-22-2-20002002-22-200−2i2i−2i2i−2i2i−2i2i000000000000000000000022−2−222−2−2−i2i2−i2i2000000
χ482-2222-2-2-22-2-20002002-22-200−2i2i−2i2i−2i2i−2i2i0000000000000000000000−2−222−2−222i2−i2i2−i2000000
χ492-2222-2-2-22-2-2000200-22-22002i−2i2i−2i−2i2i−2i2i000000000000000000000022−2−2−2−222i2−i2−i2i2000000
χ502-2222-2-2-22-2-2000200-22-22002i−2i2i−2i−2i2i−2i2i0000000000000000000000−2−22222−2−2−i2i2i2−i2000000
χ512-2222-2-2-22-2-2000200-22-2200−2i2i−2i2i2i−2i2i−2i000000000000000000000022−2−2−2−222−i2i2i2−i2000000
χ522-2222-2-2-22-2-2000200-22-2200−2i2i−2i2i2i−2i2i−2i0000000000000000000000−2−22222−2−2i2−i2−i2i2000000
χ5344-4-44-4-4400000000000004i−4i0000000000000000000000000000002-22-22i−2i2i−2i0000000000
χ5444-4-44-4-4400000000000004i−4i000000000000000000000000000000-22-22−2i2i−2i2i0000000000
χ5544-4-44-4-440000000000000−4i4i0000000000000000000000000000002-22-2−2i2i−2i2i0000000000
χ5644-4-44-4-440000000000000−4i4i000000000000000000000000000000-22-222i−2i2i−2i0000000000
χ574-4444-4-4-4-444000-4004-4-4400000000000000000000000000000000000000000000000000
χ584-4444-4-4-4-444000-400-444-400000000000000000000000000000000000000000000000000
χ594-44-4-4-4444-44000-4000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ604-44-4-4-4444-44000-400000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ614-44-4-4-444-44-400040000000000004-4-440000000000000000000000000000000000000000
χ624-44-4-4-444-44-40004000000000000-444-40000000000000000000000000000000000000000
χ634-4-44-44-440004-440-400000000000000000000000000000000000000000000000002i2−2i20000
χ644-4-44-44-440004-440-40000000000000000000000000000000000000000000000000−2i22i20000
χ654-4-44-44-44000-44-40400000000000000000000000000000000000000000000000000022−2200
χ664-4-44-44-44000-44-404000000000000000000000000000000000000000000000000000−222200
χ674-4-4-4444-40004-4-404000000000000000000000000000000000000022−22−222200000000000000
χ684-4-4-4444-40004-4-4040000000000000000000000000000000000000−222222−2200000000000000
χ694-4-4-4444-4000-4440-4000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ704-4-4-4444-4000-4440-400000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ7188-88-8-88-8000000000000000000000000000000000000000000000000000000000000000

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