Finite Group Databasebeta

← Group #238149

Character table — Group #238149

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222222244444444444444448888888888888888444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1111-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911111111-1-1-1-111111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-111-111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-11-1-111-11-1-11111-1-1-1-111
χ1111111111-1-1-1-111111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1111-1-1-111-1-11111-1-1
χ1211111111-1-1-1-111111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-111-1-111
χ1311111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-111-1-1-111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1111-1-1-11-1-111-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1111-111-1-11-1-1-11111-1-1-1-111
χ1611111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-11-1-11-1-1111111-1-111-1-111-1-1
χ1722222222222222-2-222-2-222-2-2-2-2-2-200000000000000000002-2200000-2000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-20000000000000000000-22-2000002000000000000
χ19222222222222-2-222-2-222-2-222-2-2-2-200000000000000002-220000000-20000000000000
χ20222222222222-2-222-2-222-2-222-2-2-2-20000000000000000-22-2000000020000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000002-22-200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000-22-2200000000
χ2322222222-2-2-2-222-2-222-2-2-2-222-222-200000000000000000002-2-2000002000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-222-222-20000000000000000000-22200000-2000000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-222-200000000000000002-2-2000000020000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-222-20000000000000000-2220000000-20000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2200000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-220000000000000000000000000000-222-200000000
χ29222-2-2-22-222-2-22222-2-2-2-22-22-222-2-200000000000000000000002-22-200000000000000
χ30222-2-2-22-222-2-22222-2-2-2-22-22-222-2-20000000000000000000000-22-2200000000000000
χ31222-2-2-22-222-2-222-2-2-2-2222-2-22-2-222000000000000000000000000000000002i−2i2i−2i0000
χ32222-2-2-22-222-2-222-2-2-2-2222-2-22-2-22200000000000000000000000000000000−2i2i−2i2i0000
χ33222-2-2-22-222-2-2-2-22222-2-2-222-2-2-2220000000000000000000000000000000000002i−2i2i−2i
χ34222-2-2-22-222-2-2-2-22222-2-2-222-2-2-222000000000000000000000000000000000000−2i2i−2i2i
χ35222-2-2-22-222-2-2-2-2-2-22222-22-2222-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ36222-2-2-22-222-2-2-2-2-2-22222-22-2222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ37222-2-2-22-2-2-2222222-2-2-2-2-22-222-22-200000000000000000000002-2-2200000000000000
χ38222-2-2-22-2-2-2222222-2-2-2-2-22-222-22-20000000000000000000000-222-200000000000000
χ39222-2-2-22-2-2-22222-2-2-2-222-222-2-22-22000000000000000000000000000000002i−2i−2i2i0000
χ40222-2-2-22-2-2-22222-2-2-2-222-222-2-22-2200000000000000000000000000000000−2i2i2i−2i0000
χ41222-2-2-22-2-2-222-2-22222-2-22-2-22-22-220000000000000000000000000000000000002i−2i−2i2i
χ42222-2-2-22-2-2-222-2-22222-2-22-2-22-22-22000000000000000000000000000000000000−2i2i2i−2i
χ43222-2-2-22-2-2-222-2-2-2-222222-22-22-22-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ44222-2-2-22-2-2-222-2-2-2-222222-22-22-22-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ4544-444-4-4-40000004-4004-400000000000000002222−22−222222−22−22000000000000000000000000
χ4644-444-4-4-40000004-4004-40000000000000000−22−222222−22−222222000000000000000000000000
χ4744-444-4-4-4000000-4400-44000000002222−22−222222−22−2200000000000000000000000000000000
χ4844-444-4-4-4000000-4400-4400000000−22−222222−22−22222200000000000000000000000000000000
χ4944-4-4-44-440000004-400-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000
χ5044-4-4-44-440000004-400-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000
χ5144-4-4-44-44000000-44004-400000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000
χ5244-4-4-44-44000000-44004-40000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000
χ534-444-44-4-400004-4004-400000000000000000022−2222−2222−2222−22000000000000000000000000
χ544-444-44-4-400004-4004-4000000000000000000−2222−2222−2222−2222000000000000000000000000
χ554-444-44-4-40000-4400-44000000000022−2222−2222−2222−2200000000000000000000000000000000
χ564-444-44-4-40000-4400-440000000000−2222−2222−2222−222200000000000000000000000000000000
χ574-44-44-4-4400004-400-4400000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ584-44-44-4-4400004-400-440000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ594-44-44-4-440000-44004-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000
χ604-44-44-4-440000-44004-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000
χ614-4-44-4-4444-44-400000000000000002-2-222-2-222-2-222-2-22000000000000000000000000
χ624-4-44-4-4444-44-40000000000000000-222-2-222-2-222-2-222-2000000000000000000000000
χ634-4-44-4-444-44-4400000000000000002-2-222-2-22-222-2-222-2000000000000000000000000
χ644-4-44-4-444-44-440000000000000000-222-2-222-22-2-222-2-22000000000000000000000000
χ654-4-4-4444-44-4-4400000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ664-4-4-4444-44-4-440000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ674-4-4-4444-4-444-400000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ684-4-4-4444-4-444-40000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000

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