Finite Group Databasebeta

← Group #306085

Character table — Group #306085

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-1-11-111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111-111-1-1-1-1-1-111-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-11-1-111-1-111-1-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-11-1-1-1111111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1111-1-111-1-1111-1
χ17222222222-2-22-222-2-2-22222000000002222000000-2-2000000-2-2000000000000
χ18222222222-2-22-222-2-2-2222200000000-2-2-2-2000000-2-200000022000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-20000000022-2-200000022000000-22000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-200000000-2-222000000220000002-2000000000000
χ2122222222-222-22-2-22-2-2000022-2-222-2-2000022000000-2-2000000000000000000
χ2222222222-222-22-2-22-2-2000022-2-2-2-2220000-2-200000022000000000000000000
χ2322222222-222-22-2-22-2-20000-2-22222-2-20000-2-200000022000000000000000000
χ2422222222-222-22-2-22-2-20000-2-222-2-222000022000000-2-2000000000000000000
χ252222-2-2-2-2222-2-22-2-2-2200002-22-2000000000022-2-2000022-2-200000000000000
χ262222-2-2-2-2222-2-22-2-2-2200002-22-20000000000-2-2220000-2-22200000000000000
χ272222-2-2-2-2222-2-22-2-2-220000-22-22000000000022-2-20000-2-22200000000000000
χ282222-2-2-2-2222-2-22-2-2-220000-22-220000000000-2-222000022-2-200000000000000
χ292222-2-2-2-2-2222-2-22-22-222-2-22-2-22000000000000002-20000000000002-2000000
χ302222-2-2-2-2-2222-2-22-22-222-2-2-222-2000000000000002-2000000000000-22000000
χ312222-2-2-2-2-2222-2-22-22-2-2-2222-2-2200000000000000-22000000000000-22000000
χ322222-2-2-2-2-2222-2-22-22-2-2-222-222-200000000000000-220000000000002-2000000
χ332222-2-2-2-2-2-2-222-222-2222-2-2000000000000000000-22000000002i−2i2i−2i00000000
χ342222-2-2-2-2-2-2-222-222-2222-2-2000000000000000000-2200000000−2i2i−2i2i00000000
χ352222-2-2-2-2-2-2-222-222-22-2-2220000000000000000002-2000000002i−2i−2i2i00000000
χ362222-2-2-2-2-2-2-222-222-22-2-2220000000000000000002-200000000−2i2i2i−2i00000000
χ3722-2-2-2-22220020-2-20002-22-2000000002i−2i2i−2i2−20000002−22−22−200000000i2−i2i2−i200
χ3822-2-2-2-22220020-2-20002-22-2000000002i−2i2i−2i−22000000−22−22−2200000000−i2i2−i2i200
χ3922-2-2-2-22220020-2-20002-22-200000000−2i2i−2i2i2−20000002−22−22−200000000−i2i2−i2i200
χ4022-2-2-2-22220020-2-20002-22-200000000−2i2i−2i2i−22000000−22−22−2200000000i2−i2i2−i200
χ4122-2-2-2-22220020-2-2000-22-22000000002i−2i−2i2i2−20000002−2−22−2200000000i2−i2−i2i200
χ4222-2-2-2-22220020-2-2000-22-22000000002i−2i−2i2i−22000000−222−22−200000000−i2i2i2−i200
χ4322-2-2-2-22220020-2-2000-22-2200000000−2i2i2i−2i2−20000002−2−22−2200000000−i2i2i2−i200
χ4422-2-2-2-22220020-2-2000-22-2200000000−2i2i2i−2i−22000000−222−22−200000000i2−i2−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ464444-4-4-4-44-4-4-444-444-400000000000000000000000000000000000000000000
χ4744-4-444-4-4400-40-440000000000000000000000000000022−22−222200000000000000
χ4844-4-444-4-4400-40-4400000000000000000000000000000−222222−2200000000000000
χ4944-4-444-4-4-400404-40004-4-440000000000000000000000000000000000000000
χ5044-4-444-4-4-400404-4000-444-40000000000000000000000000000000000000000
χ5144-4-4-4-444-400-4044000000000000000000022−22000000−2222000000000000000000
χ5244-4-4-4-444-400-40440000000000000000000−222200000022−22000000000000000000
χ534-44-44-44-404-40400-400000000004-40000000000000000000000000000000000
χ544-44-44-44-404-40400-40000000000-440000000000000000000000000000000000
χ554-44-44-44-40-440-4004000000000000000000002i2−2i22i2−2i20000000000000000000000
χ564-44-44-44-40-440-400400000000000000000000−2i22i2−2i22i20000000000000000000000
χ574-44-4-44-4404-40-40040000000000004-400000000000000000000000000000000
χ584-44-4-44-4404-40-4004000000000000-4400000000000000000000000000000000
χ594-44-4-44-440-440400-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-44-4-44-440-440400-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ618-8-888-8-88000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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