Finite Group Databasebeta

← Group #242019

Character table — Group #242019

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888244444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11-1-1-1-1-11-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-11-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1111-1-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-11-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111
χ91111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-11-1-1111-111-1-111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-11111-1-1-1-111
χ111111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-111-1-11111-1-1
χ121111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-111-1-1-111-1111-1-1-1-111-1-111
χ131111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1-11-1-1-1-11-11111-1-111-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-1111111-1-1-1-1-1-11111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1-1-111-1-1-1-111
χ161111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-111-1-1-1-1-1-11111111-1-111-1-1
χ1722222222222222-2-222-2-2-2-222-2-2-2-200000000000000002200-200000-20000000000000
χ1822222222222222-2-222-2-2-2-222-2-2-2-20000000000000000-2-20020000020000000000000
χ192222222222-2-2-2-2-2-222-2-222-2-222-2-200000000000000002-200200000-20000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-222-2-20000000000000000-2200-20000020000000000000
χ2122222222-2-2222222-2-222-2-2-2-222-2-2000000000000000000220-200000-2000000000000
χ2222222222-2-2222222-2-222-2-2-2-222-2-2000000000000000000-2-202000002000000000000
χ2322222222-2-22222-2-2-2-2-2-222-2-2-2-22200000000000000000000002-200002-20000000000
χ2422222222-2-22222-2-2-2-2-2-222-2-2-2-2220000000000000000000000-220000-220000000000
χ2522222222-2-2-2-2-2-222-2-2222222-2-2-2-20000000000000000002-20-2000002000000000000
χ2622222222-2-2-2-2-2-222-2-2222222-2-2-2-2000000000000000000-220200000-2000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000002-20000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000-2200002-20000000000
χ29222-2-2-2-222-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i2-20000000000000000000000000000000000002i−2i2-2
χ30222-2-2-2-222-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i2-2000000000000000000000000000000000000−2i2i-22
χ31222-2-2-2-222-22i2i−2i−2i-222-2-22−2i2i2i−2i−2i2i-220000000000000000000000002i−2i00002-200000000
χ32222-2-2-2-222-22i2i−2i−2i-222-2-22−2i2i2i−2i−2i2i-22000000000000000000000000−2i2i0000-2200000000
χ33222-2-2-2-222-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i2-20000000000000000000000000000000000002i−2i-22
χ34222-2-2-2-222-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i2-2000000000000000000000000000000000000−2i2i2-2
χ35222-2-2-2-222-2−2i−2i2i2i-222-2-222i−2i−2i2i2i−2i-220000000000000000000000002i−2i0000-2200000000
χ36222-2-2-2-222-2−2i−2i2i2i-222-2-222i−2i−2i2i2i−2i-22000000000000000000000000−2i2i00002-200000000
χ37222-2-2-2-22-222i2i−2i−2i2-2-222-2−2i2i−2i2i2i−2i-222i2i2i2i−2i−2i−2i−2i2222-2-2-2-2000000000000000000000000
χ38222-2-2-2-22-222i2i−2i−2i2-2-222-2−2i2i−2i2i2i−2i-22−2i−2i−2i−2i2i2i2i2i-2-2-2-22222000000000000000000000000
χ39222-2-2-2-22-222i2i−2i−2i-22-22-222i−2i−2i2i−2i2i2-2000000000000000000000000000000002-22i−2i0000
χ40222-2-2-2-22-222i2i−2i−2i-22-22-222i−2i−2i2i−2i2i2-200000000000000000000000000000000-22−2i2i0000
χ41222-2-2-2-22-22−2i−2i2i2i2-2-222-22i−2i2i−2i−2i2i-222i2i2i2i−2i−2i−2i−2i-2-2-2-22222000000000000000000000000
χ42222-2-2-2-22-22−2i−2i2i2i2-2-222-22i−2i2i−2i−2i2i-22−2i−2i−2i−2i2i2i2i2i2222-2-2-2-2000000000000000000000000
χ43222-2-2-2-22-22−2i−2i2i2i-22-22-22−2i2i2i−2i2i−2i2-2000000000000000000000000000000002-2−2i2i0000
χ44222-2-2-2-22-22−2i−2i2i2i-22-22-22−2i2i2i−2i2i−2i2-200000000000000000000000000000000-222i−2i0000
χ4544-44-44-4-44-4000000-4400000000002222−22−222222−22−2200000000000000000000000000000000
χ4644-44-44-4-44-4000000-440000000000−22−222222−22−22222200000000000000000000000000000000
χ4744-44-44-4-4-440000004-40000000000000000002222−22−222222−22−22000000000000000000000000
χ4844-44-44-4-4-440000004-4000000000000000000−22−222222−22−222222000000000000000000000000
χ4944-4-44-44-444000000-4-40000000000000000002222−22−22−22−222222000000000000000000000000
χ5044-4-44-44-444000000-4-4000000000000000000−22−2222222222−22−22000000000000000000000000
χ5144-4-44-44-4-4-40000004400000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000
χ5244-4-44-44-4-4-4000000440000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000
χ534-4444-4-4-4004-44-4000000000000002-22-22-22-22-22-22-22-2000000000000000000000000
χ544-4444-4-4-4004-44-400000000000000-22-22-22-22-22-22-22-22000000000000000000000000
χ554-4444-4-4-400-44-44000000000000002-22-22-22-2-22-22-22-22000000000000000000000000
χ564-4444-4-4-400-44-4400000000000000-22-22-22-222-22-22-22-2000000000000000000000000
χ574-44-4-444-4004i−4i−4i4i000000000000002i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000
χ584-44-4-444-4004i−4i−4i4i00000000000000−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000
χ594-44-4-444-400−4i4i4i−4i000000000000002i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000
χ604-44-4-444-400−4i4i4i−4i00000000000000−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000
χ614-4-44-4-4440000004-400-440000000022−22−222222−22−222200000000000000000000000000000000
χ624-4-44-4-4440000004-400-4400000000−222222−22−222222−2200000000000000000000000000000000
χ634-4-44-4-444000000-44004-4000000000000000022−22−222222−22−2222000000000000000000000000
χ644-4-44-4-444000000-44004-40000000000000000−222222−22−222222−22000000000000000000000000
χ654-4-4-444-440000004400-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ664-4-4-444-440000004400-4-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000
χ674-4-4-444-44000000-4-40044000000000000000022−22−2222−222222−22000000000000000000000000
χ684-4-4-444-44000000-4-400440000000000000000−222222−2222−22−2222000000000000000000000000

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