Finite Group Databasebeta

← Group #241521

Character table — Group #241521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444442244444444444444444444442244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-11-1-1-1111-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-11-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1111-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2220000-2-20000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-222-2-20000220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-20000220000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222220000-2-20000000000000000000000000000
χ2122222222-2-2-2-22222-2-2-2-222-2-222-2-200000000000000000000000002002-20-200000000
χ2222222222-2-2-2-22222-2-2-2-222-2-222-2-20000000000000000000000000-200-220200000000
χ2322222222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000202-200-2000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000-20-22002000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000020-2200-2000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2-2-222000000000000000000000000-202-2002000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-22222-2-20000000000000000000000000200-220-200000000
χ2822222222-2-2-2-2-2-2-2-22222-2-22222-2-20000000000000000000000000-2002-20200000000
χ29222-2-2-2-222-22-22i2i−2i−2i2i2i−2i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000002-22i−2i
χ30222-2-2-2-222-22-22i2i−2i−2i2i2i−2i−2i2i−2i2i−2i2-22-2000000000000000000000000000000000000-22−2i2i
χ31222-2-2-2-222-22-22i2i−2i−2i2i2i−2i−2i−2i2i−2i2i-22-22000000000000000000000000000000002i−2i2-20000
χ32222-2-2-2-222-22-22i2i−2i−2i2i2i−2i−2i−2i2i−2i2i-22-2200000000000000000000000000000000−2i2i-220000
χ33222-2-2-2-222-22-2−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i-22-22000000000000000000000000000000002i−2i-220000
χ34222-2-2-2-222-22-2−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i-22-2200000000000000000000000000000000−2i2i2-20000
χ35222-2-2-2-222-22-2−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i2-22-20000000000000000000000000000000000002-2−2i2i
χ36222-2-2-2-222-22-2−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i2-22-2000000000000000000000000000000000000-222i−2i
χ37222-2-2-2-22-22-222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i2-2-220000002i2i−2i−2i0022-2-2000000000000000000000000
χ38222-2-2-2-22-22-222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i2-2-22000000−2i−2i2i2i00-2-222000000000000000000000000
χ39222-2-2-2-22-22-222i2i−2i−2i−2i−2i2i2i−2i2i2i−2i-222-200000000000000002i2i−2i−2i22-2-20000000000000000
χ40222-2-2-2-22-22-222i2i−2i−2i−2i−2i2i2i−2i2i2i−2i-222-20000000000000000−2i−2i2i2i-2-2220000000000000000
χ41222-2-2-2-22-22-22−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i-222-200000000000000002i2i−2i−2i-2-2220000000000000000
χ42222-2-2-2-22-22-22−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i-222-20000000000000000−2i−2i2i2i22-2-20000000000000000
χ43222-2-2-2-22-22-22−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i2-2-220000002i2i−2i−2i00-2-222000000000000000000000000
χ44222-2-2-2-22-22-22−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i2-2-22000000−2i−2i2i2i0022-2-2000000000000000000000000
χ4544-44-44-4-4000000004-44-4000000000000002i−2i2i−2i002i−2i2i−2i000000000000000000000000
χ4644-44-44-4-4000000004-44-400000000000000−2i2i−2i2i00−2i2i−2i2i000000000000000000000000
χ4744-44-44-4-400000000-44-44000000000000002i−2i2i−2i00−2i2i−2i2i000000000000000000000000
χ4844-44-44-4-400000000-44-4400000000000000−2i2i−2i2i002i−2i2i−2i000000000000000000000000
χ4944-4-44-44-4000000004i−4i−4i4i000000000000002-2-22002i−2i−2i2i000000000000000000000000
χ5044-4-44-44-4000000004i−4i−4i4i00000000000000-222-200−2i2i2i−2i000000000000000000000000
χ5144-4-44-44-400000000−4i4i4i−4i000000000000002-2-2200−2i2i2i−2i000000000000000000000000
χ5244-4-44-44-400000000−4i4i4i−4i00000000000000-222-2002i−2i−2i2i000000000000000000000000
χ534-444-4-44-400004-44-400000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ544-444-4-44-400004-44-40000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ554-444-4-44-40000-44-4400000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ564-444-4-44-40000-44-440000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ574-44-444-4-400004i−4i−4i4i00000000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ584-44-444-4-400004i−4i−4i4i0000000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ594-44-444-4-40000−4i4i4i−4i00000000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ604-44-444-4-40000−4i4i4i−4i0000000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ614-4-444-4-4444-4-40000000000000000004i−4i000000000000000000000000000000000000
χ624-4-444-4-4444-4-4000000000000000000−4i4i000000000000000000000000000000000000
χ634-4-444-4-44-4-444000000000000000000004-40000000000000000000000000000000000
χ644-4-444-4-44-4-44400000000000000000000-440000000000000000000000000000000000
χ654-4-4-4-44444-4-4400000000000000004-400000000000000000000000000000000000000
χ664-4-4-4-44444-4-440000000000000000-4400000000000000000000000000000000000000
χ674-4-4-4-4444-444-4000000000000000000000000004-40000000000000000000000000000
χ684-4-4-4-4444-444-400000000000000000000000000-440000000000000000000000000000

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