Finite Group Databasebeta

← Group #314756

Character table — Group #314756

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444224444448888888888888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111
χ9111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ10111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-11111
χ11111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ12111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111
χ13111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-11111
χ14111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ15111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ16111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1111111-1-1-1-111-1-1
χ17222222222222222-2-2-2-22-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-222222-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ20222222222-2-2-2-222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ2122222222-22222-2-22222-2-2-222-2-2-2-2000000000000000000002-200002-2000000000000
χ2222222222-22222-2-22222-2-2-222-2-2-2-200000000000000000000-220000-22000000000000
χ2322222222-22222-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000002i−2i000000002i−2i
χ2422222222-22222-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000−2i2i00000000−2i2i
χ2522222222-2-2-2-2-2-2-22222-222-2-2-2-222000000000000000000002-20000-22000000000000
χ2622222222-2-2-2-2-2-2-22222-222-2-2-2-22200000000000000000000-2200002-2000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000002i−2i00000000−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000−2i2i000000002i−2i
χ292222-2-2-2-2-200002-222-2-2200002-200000022-2-2000022-2-2002i−2i002i−2i0000000000000000
χ302222-2-2-2-2-200002-222-2-2200002-200000022-2-2000022-2-200−2i2i00−2i2i0000000000000000
χ312222-2-2-2-2-200002-222-2-2200002-2000000-2-2220000-2-222002i−2i00−2i2i0000000000000000
χ322222-2-2-2-2-200002-222-2-2200002-2000000-2-2220000-2-22200−2i2i002i−2i0000000000000000
χ332222-2-2-2-2-200002-2-2-22220000-2200000022-2-20000-2-2222i−2i0000002i−2i00000000000000
χ342222-2-2-2-2-200002-2-2-22220000-2200000022-2-20000-2-222−2i2i000000−2i2i00000000000000
χ352222-2-2-2-2-200002-2-2-22220000-22000000-2-222000022-2-22i−2i000000−2i2i00000000000000
χ362222-2-2-2-2-200002-2-2-22220000-22000000-2-222000022-2-2−2i2i0000002i−2i00000000000000
χ3722-2-2-2-22222i2i−2i−2i-2-2000020000002i−2i00002i−2i2i−2i22-2-20000000000000000002−2i2−i22−2i2−i200
χ3822-2-2-2-22222i2i−2i−2i-2-2000020000002i−2i00002i−2i2i−2i22-2-2000000000000000000−22−i2i2−22−i2i200
χ3922-2-2-2-22222i2i−2i−2i-2-2000020000002i−2i0000−2i2i−2i2i-2-2220000000000000000002−2i2−i2−22−i2i200
χ4022-2-2-2-22222i2i−2i−2i-2-2000020000002i−2i0000−2i2i−2i2i-2-222000000000000000000−22−i2i22−2i2−i200
χ4122-2-2-2-2222−2i−2i2i2i-2-200002000000−2i2i00002i−2i2i−2i-2-2220000000000000000002−2−i2i2−22i2−i200
χ4222-2-2-2-2222−2i−2i2i2i-2-200002000000−2i2i00002i−2i2i−2i-2-222000000000000000000−22i2−i22−2−i2i200
χ4322-2-2-2-2222−2i−2i2i2i-2-200002000000−2i2i0000−2i2i−2i2i22-2-20000000000000000002−2−i2i22−2−i2i200
χ4422-2-2-2-2222−2i−2i2i2i-2-200002000000−2i2i0000−2i2i−2i2i22-2-2000000000000000000−22i2−i2−22i2−i200
χ454444-4-4-4-440000-4444-4-4-40000-44000000000000000000000000000000000000000000
χ464444-4-4-4-440000-44-4-444-400004-4000000000000000000000000000000000000000000
χ4744-4-444-4-4400004-40000-40000000044-4-4000000000000000000000000000000000000
χ4844-4-444-4-4400004-40000-400000000-4-444000000000000000000000000000000000000
χ4944-4-444-4-4-40000-44000040000000000004i−4i−4i4i00000000000000000000000000000000
χ5044-4-444-4-4-40000-4400004000000000000−4i4i4i−4i00000000000000000000000000000000
χ5144-4-4-4-444-44i4i−4i−4i440000-4000000−4i4i0000000000000000000000000000000000000000
χ5244-4-4-4-444-4−4i−4i4i4i440000-40000004i−4i0000000000000000000000000000000000000000
χ534-44-44-44-40000000000004-4000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000
χ544-44-44-44-40000000000004-400000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000
χ554-44-44-44-4000000000000-44000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000
χ564-44-44-44-4000000000000-4400000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000
χ574-44-4-44-4404-44-40000000000000002i2−2i22i2−2i2000000002i2−2i2−2i22i2000000000000000000000000
χ584-44-4-44-4404-44-4000000000000000−2i22i2−2i22i200000000−2i22i22i2−2i2000000000000000000000000
χ594-44-4-44-440-44-440000000000000002i2−2i22i2−2i200000000−2i22i22i2−2i2000000000000000000000000
χ604-44-4-44-440-44-44000000000000000−2i22i2−2i22i2000000002i2−2i2−2i22i2000000000000000000000000
χ614-4-444-4-4404i−4i−4i4i004-44-40004i−4i00000000000000000000000000000000000000000000
χ624-4-444-4-4404i−4i−4i4i00-44-44000−4i4i00000000000000000000000000000000000000000000
χ634-4-444-4-440−4i4i4i−4i004-44-4000−4i4i00000000000000000000000000000000000000000000
χ644-4-444-4-440−4i4i4i−4i00-44-440004i−4i00000000000000000000000000000000000000000000
χ654-4-44-444-400000004-4-440000000002i2−2i2−2i22i200002i2−2i2−2i22i20000000000000000000000000000
χ664-4-44-444-400000004-4-44000000000−2i22i22i2−2i20000−2i22i22i2−2i20000000000000000000000000000
χ674-4-44-444-40000000-444-40000000002i2−2i2−2i22i20000−2i22i22i2−2i20000000000000000000000000000
χ684-4-44-444-40000000-444-4000000000−2i22i22i2−2i200002i2−2i2−2i22i20000000000000000000000000000

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