Finite Group Databasebeta

← Group #284328

Character table — Group #284328

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111111-1-11-1-111-1-111-1-1
χ51111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111-11111-1-111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1111-1
χ10111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-11-1
χ11111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-11111111-1-1-111-1-1-1-1-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-111-1-11111-11
χ13111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-11
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1-1111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1111-1-11111-1-11-1
χ17222222222-2-2222-2-2-2-2000000222200-2-2-2-222000000-2-2000000000000000000
χ18222222222-2-2222-2-2-2-200000022-2-200-2-222-2-200000022000000000000000000
χ19222222222-2-2222-2-2-2-2000000-2-2220022-2-2-2-200000022000000000000000000
χ20222222222-2-2222-2-2-2-2000000-2-2-2-200222222000000-2-2000000000000000000
χ2122222222-222-2-2-222-2-22222220000-2-2000000-2-20000000000-20020000000000
χ2222222222-222-2-2-222-2-22222-2-2000022000000-2-20000000000200-20000000000
χ2322222222-222-2-2-222-2-2-2-2-2-222000022000000220000000000-200-20000000000
χ2422222222-222-2-2-222-2-2-2-2-2-2-2-20000-2-200000022000000000020020000000000
χ252-2-2-2-2222222-22-2-2-2-222i2i−2i−2i000000000000002i−2i000000000002i−2i02-200000000
χ262-2-2-2-2222222-22-2-2-2-222i2i−2i−2i000000000000002i−2i00000000000−2i2i0-2200000000
χ272-2-2-2-2222222-22-2-2-2-22−2i−2i2i2i00000000000000−2i2i000000000002i−2i0-2200000000
χ282-2-2-2-2222222-22-2-2-2-22−2i−2i2i2i00000000000000−2i2i00000000000−2i2i02-200000000
χ292-2-2-2-2222-2222-22-2-22-22i2i−2i−2i00002-200002-200−2i2i0000000000000000002i−2i0000
χ302-2-2-2-2222-2222-22-2-22-22i2i−2i−2i0000-220000-2200−2i2i000000000000000000−2i2i0000
χ312-2-2-2-2222-2222-22-2-22-2−2i−2i2i2i00002-200002-2002i−2i000000000000000000−2i2i0000
χ322-2-2-2-2222-2222-22-2-22-2−2i−2i2i2i0000-220000-22002i−2i0000000000000000002i−2i0000
χ332-2-2-2-2222-2-2-22-2222-22000000002-20000-22000022-2-20022-2-200000000000000
χ342-2-2-2-2222-2-2-22-2222-22000000002-20000-220000-2-22200-2-22200000000000000
χ352-2-2-2-2222-2-2-22-2222-2200000000-2200002-2000022-2-200-2-22200000000000000
χ362-2-2-2-2222-2-2-22-2222-2200000000-2200002-20000-2-2220022-2-200000000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ38444-4-44-4-44004-4-400000000004-4000000000000000000000000000000000000
χ39444-4-44-4-44004-4-40000000000-44000000000000000000000000000000000000
χ40444-4-44-4-4-400-4440000000000000000000000002i2−2i22i2−2i200000000000000000000
χ41444-4-44-4-4-400-444000000000000000000000000−2i22i2−2i22i200000000000000000000
χ4244-44-4-44-400000000002i2−2i22i2−2i200000000000022−22000000002i−2i2i−2i00000000000000
χ4344-44-4-44-400000000002i2−2i22i2−2i2000000000000−222200000000−2i2i−2i2i00000000000000
χ4444-44-4-44-40000000000−2i22i2−2i22i200000000000022−2200000000−2i2i−2i2i00000000000000
χ4544-44-4-44-40000000000−2i22i2−2i22i2000000000000−2222000000002i−2i2i−2i00000000000000
χ4644-4-44-4-4404-40004-40000000000004i−4i00000000000000000000000000000000
χ4744-4-44-4-4404-40004-4000000000000−4i4i00000000000000000000000000000000
χ4844-4-44-4-440-44000-44000000000000000000000000000000000000002i2−2i2000000
χ4944-4-44-4-440-44000-4400000000000000000000000000000000000000−2i22i2000000
χ504-444-4-4-4404-4000-440000004i−4i00000000000000000000000000000000000000
χ514-444-4-4-4404-4000-44000000−4i4i00000000000000000000000000000000000000
χ524-444-4-4-440-440004-40000000000000000000000000000000000000000002i2−2i200
χ534-444-4-4-440-440004-4000000000000000000000000000000000000000000−2i22i200
χ544-44-44-44-4000000000022−22−2222000000000000000000002i2−2i22i−2i−2i2i00000000000000
χ554-44-44-44-4000000000022−22−222200000000000000000000−2i22i2−2i2i2i−2i00000000000000
χ564-44-44-44-40000000000−222222−22000000000000000000002i2−2i2−2i2i2i−2i00000000000000
χ574-44-44-44-40000000000−222222−2200000000000000000000−2i22i22i−2i−2i2i00000000000000
χ584-4-4444-4-4400-4-440000000000000000000000002i2−2i2−2i22i200000000000000000000
χ594-4-4444-4-4400-4-44000000000000000000000000−2i22i22i2−2i200000000000000000000
χ604-4-4444-4-4-40044-400000000000000004i−4i000000000000000000000000000000
χ614-4-4444-4-4-40044-40000000000000000−4i4i000000000000000000000000000000
χ624-4-4-4-44444-4-4-44-4444-400000000000000000000000000000000000000000000

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