Finite Group Databasebeta

← Group #243400

Character table — Group #243400

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888222224444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111
χ911111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1
χ1211111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-1-111
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1-1-11111-1-1
χ1722222222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ1822222222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ19222222222222-2-22222-2-2-2-2-2-222-2-2000000000000000000002-22-20000000000000000
χ20222222222222-2-22222-2-2-2-2-2-222-2-200000000000000000000-22-220000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-2-222-2-2-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000002-2-220000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-222-2-22200000000000000000000-222-20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000−2i2i2i−2i
χ29222-22-2-2-22i2i−2i−2i2-222-2-22-22-22i−2i2i−2i2i−2i0000000000000000002-20000002i−2i000000000000
χ30222-22-2-2-22i2i−2i−2i2-222-2-22-22-22i−2i2i−2i2i−2i000000000000000000-22000000−2i2i000000000000
χ31222-22-2-2-22i2i−2i−2i2-2-2-2222-2-222i−2i−2i2i−2i2i00000000000000002-20000002i−2i00000000000000
χ32222-22-2-2-22i2i−2i−2i2-2-2-2222-2-222i−2i−2i2i−2i2i0000000000000000-22000000−2i2i00000000000000
χ33222-22-2-2-22i2i−2i−2i-2222-2-2-22-22−2i2i2i−2i−2i2i000000000000000000000000000000002-22i−2i0000
χ34222-22-2-2-22i2i−2i−2i-2222-2-2-22-22−2i2i2i−2i−2i2i00000000000000000000000000000000-22−2i2i0000
χ35222-22-2-2-22i2i−2i−2i-22-2-222-222-2−2i2i−2i2i2i−2i00000000000000000000000000002-22i−2i00000000
χ36222-22-2-2-22i2i−2i−2i-22-2-222-222-2−2i2i−2i2i2i−2i0000000000000000000000000000-22−2i2i00000000
χ37222-22-2-2-2−2i−2i2i2i2-222-2-22-22-2−2i2i−2i2i−2i2i0000000000000000002-2000000−2i2i000000000000
χ38222-22-2-2-2−2i−2i2i2i2-222-2-22-22-2−2i2i−2i2i−2i2i000000000000000000-220000002i−2i000000000000
χ39222-22-2-2-2−2i−2i2i2i2-2-2-2222-2-22−2i2i2i−2i2i−2i00000000000000002-2000000−2i2i00000000000000
χ40222-22-2-2-2−2i−2i2i2i2-2-2-2222-2-22−2i2i2i−2i2i−2i0000000000000000-220000002i−2i00000000000000
χ41222-22-2-2-2−2i−2i2i2i-2222-2-2-22-222i−2i−2i2i2i−2i000000000000000000000000000000002-2−2i2i0000
χ42222-22-2-2-2−2i−2i2i2i-2222-2-2-22-222i−2i−2i2i2i−2i00000000000000000000000000000000-222i−2i0000
χ43222-22-2-2-2−2i−2i2i2i-22-2-222-222-22i−2i2i−2i−2i2i00000000000000000000000000002-2−2i2i00000000
χ44222-22-2-2-2−2i−2i2i2i-22-2-222-222-22i−2i2i−2i−2i2i0000000000000000000000000000-222i−2i00000000
χ4544-44-44-4-40000004-44-4000000000000002i22i2−2i2−2i200002i22i2−2i2−2i2000000000000000000000000
χ4644-44-44-4-40000004-44-400000000000000−2i2−2i22i22i20000−2i2−2i22i22i2000000000000000000000000
χ4744-44-44-4-4000000-44-44000000000000002i22i2−2i2−2i20000−2i2−2i22i22i2000000000000000000000000
χ4844-44-44-4-4000000-44-4400000000000000−2i2−2i22i22i200002i22i2−2i2−2i2000000000000000000000000
χ4944-4-4-4-4440000004-4-4400000000002222−22−2200002222−22−220000000000000000000000000000
χ5044-4-4-4-4440000004-4-440000000000−22−2222220000−22−2222220000000000000000000000000000
χ5144-4-4-4-444000000-444-400000000002222−22−220000−22−2222220000000000000000000000000000
χ5244-4-4-4-444000000-444-40000000000−22−22222200002222−22−220000000000000000000000000000
χ534-444-4-44-44i−4i4i−4i000000000000000000002i2−2i22i2−2i222−2222−220000000000000000000000000000
χ544-444-4-44-44i−4i4i−4i00000000000000000000−2i22i2−2i22i2−2222−22220000000000000000000000000000
χ554-444-4-44-4−4i4i−4i4i000000000000000000002i2−2i22i2−2i2−2222−22220000000000000000000000000000
χ564-444-4-44-4−4i4i−4i4i00000000000000000000−2i22i2−2i22i222−2222−220000000000000000000000000000
χ574-44-4-44-444-4-44000000000000000022−2222−220000000022−2222−22000000000000000000000000
χ584-44-4-44-444-4-440000000000000000−2222−222200000000−2222−2222000000000000000000000000
χ594-44-4-44-44-444-4000000000000000022−2222−2200000000−2222−2222000000000000000000000000
χ604-44-4-44-44-444-40000000000000000−2222−22220000000022−2222−22000000000000000000000000
χ614-4-444-4-4400004-40000-44000000004-4-44000000000000000000000000000000000000
χ624-4-444-4-4400004-40000-4400000000-444-4000000000000000000000000000000000000
χ634-4-444-4-440000-4400004-40000000000004-4-4400000000000000000000000000000000
χ644-4-444-4-440000-4400004-4000000000000-444-400000000000000000000000000000000
χ654-4-4-4444-40000440000-4-4000000000000000000004i−4i−4i4i000000000000000000000000
χ664-4-4-4444-40000440000-4-400000000000000000000−4i4i4i−4i000000000000000000000000
χ674-4-4-4444-40000-4-400004400000000000000004-4-440000000000000000000000000000
χ684-4-4-4444-40000-4-40000440000000000000000-444-40000000000000000000000000000

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