Finite Group Databasebeta

← Group #331128

Character table — Group #331128

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244444444444444444444444488888888888888883232323232323232
order12222222444444444444224444448888888888888888888888888888888824444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11-1-11-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-11
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1111-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-11-11-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-111-11-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-1-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1111-1-1-11
χ172222222222-2-2-2-222-2-2-2-22222-2-2-2-200000000000000000000000022-2-222-2-200000000
χ182222222222-2-2-2-222-2-2-2-22222-2-2-2-2000000000000000000000000-2-222-2-22200000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000022-2-2-2-22200000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000-2-22222-2-200000000
χ2122222222-2-222-2-2-2-222-2-222-2-222-2-2000000000000000022-2-222-2-20000000000000000
χ2222222222-2-222-2-2-2-222-2-222-2-222-2-20000000000000000-2-222-2-2220000000000000000
χ2322222222-2-222-2-2-2-222-2-2-2-222-2-222000000000000000022-2-2-2-2220000000000000000
χ2422222222-2-222-2-2-2-222-2-2-2-222-2-2220000000000000000-2-22222-2-20000000000000000
χ2522222222-2-2-2-222-2-2-2-22222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-222-2-2-2-22222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-22222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ29222-2-22-2-2002-200002-2002-2002-20022−2−222−2−222−2−222−2−2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i200000000
χ30222-2-22-2-2002-200002-2002-2002-20022−2−222−2−222−2−222−2−200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i200000000
χ31222-2-22-2-2002-200002-2002-2002-200−2−222−2−222−2−222−2−222002i−2i002i−2i−i2i2−i2i2−i2i2−i2i200000000
χ32222-2-22-2-2002-200002-2002-2002-200−2−222−2−222−2−222−2−22200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i200000000
χ33222-2-22-2-2002-200002-200-2200-220022−2−222−2−2−2−222−2−222002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i200000000
χ34222-2-22-2-2002-200002-200-2200-220022−2−222−2−2−2−222−2−22200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i200000000
χ35222-2-22-2-2002-200002-200-2200-2200−2−222−2−22222−2−222−2−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i200000000
χ36222-2-22-2-2002-200002-200-2200-2200−2−222−2−22222−2−222−2−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i200000000
χ37222-2-22-2-200-220000-22002-200-220022−2−2−2−22222−2−2−2−2222i−2i002i−2i00i2−i2−i2i2i2−i2−i2i200000000
χ38222-2-22-2-200-220000-22002-200-220022−2−2−2−22222−2−2−2−222−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i200000000
χ39222-2-22-2-200-220000-22002-200-2200−2−22222−2−2−2−22222−2−22i−2i002i−2i00−i2i2i2−i2−i2i2i2−i200000000
χ40222-2-22-2-200-220000-22002-200-2200−2−22222−2−2−2−22222−2−2−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i200000000
χ41222-2-22-2-200-220000-2200-22002-20022−2−2−2−222−2−22222−2−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i200000000
χ42222-2-22-2-200-220000-2200-22002-20022−2−2−2−222−2−22222−2−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i200000000
χ43222-2-22-2-200-220000-2200-22002-200−2−22222−2−222−2−2−2−2222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i200000000
χ44222-2-22-2-200-220000-2200-22002-200−2−22222−2−222−2−2−2−222−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i200000000
χ4544-44-4-44-400004-400004-4000000000000000000004i−4i4i−4i000000000000000000000000
χ4644-44-4-44-400004-400004-400000000000000000000−4i4i−4i4i000000000000000000000000
χ4744-44-4-44-40000-440000-4400000000000000004i−4i4i−4i0000000000000000000000000000
χ4844-44-4-44-40000-440000-440000000000000000−4i4i−4i4i0000000000000000000000000000
χ4944-4-44-4-444-400004-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000
χ5044-4-44-4-444-400004-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000
χ5144-4-44-4-44-440000-44000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000
χ5244-4-44-4-44-440000-4400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000
χ534-444-4-4-444-40000-440000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000
χ544-444-4-4-444-40000-44000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000
χ554-444-4-4-44-4400004-40000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ564-444-4-4-44-4400004-4000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ574-44-44-44-400004-40000-44000000004i−4i−4i4i000000000000000000000000000000000000
χ584-44-44-44-400004-40000-4400000000−4i4i4i−4i000000000000000000000000000000000000
χ594-44-44-44-40000-4400004-40000000000004i−4i−4i4i00000000000000000000000000000000
χ604-44-44-44-40000-4400004-4000000000000−4i4i4i−4i00000000000000000000000000000000
χ614-4-4444-4-4004-40000-4400004i−4i004i−4i0000000000000000000000000000000000000000
χ624-4-4444-4-4004-40000-440000−4i4i00−4i4i0000000000000000000000000000000000000000
χ634-4-4444-4-400-4400004-400004i−4i00−4i4i0000000000000000000000000000000000000000
χ644-4-4444-4-400-4400004-40000−4i4i004i−4i0000000000000000000000000000000000000000
χ654-4-4-4-4444444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ664-4-4-4-444444-4-4-4-4-4-44444000000000000000000000000000000000000000000000000
χ674-4-4-4-4444-4-444-4-444-4-444000000000000000000000000000000000000000000000000
χ684-4-4-4-4444-4-4-4-4444444-4-4000000000000000000000000000000000000000000000000

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