Finite Group Databasebeta

← Group #340710

Character table — Group #340710

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888244444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111111111-1-1-1-1-1111-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-111
χ4111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1
χ51111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-11-1-1-11111-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1111-11-1-111-1-1-1-11
χ10111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11-1-1-111-1-1-1-11111-1
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-1111-11
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-11111-1-1-11-1
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1111-11-1-1-1-111-11-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-111-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-11-1-1-1-11111-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1111-111-1-111-1-11
χ17222222222-2-22-222-2-2-2222200000022-2-2000000000000-2-20020000000000
χ18222222222-2-22-222-2-2-22222000000-2-2-2-20000000000002200-20000000000
χ19222222222-2-22-222-2-2-2-2-2-2-200000022220000000000002-200-20000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000000-2-222000000000000-220020000000000
χ2122222222-222-22-2-22-2-200002222-2-20000220000-2-2000000000-2000000000
χ2222222222-222-22-2-22-2-2000022-2-2-2-20000-2-20000220000000002000000000
χ2322222222-222-22-2-22-2-20000-2-222220000-2-2000022000000000-2000000000
χ2422222222-222-22-2-22-2-20000-2-2-2-2220000220000-2-20000000002000000000
χ252-2-22-2-22202-20200-20022−2−2002i−2i2-2002−20022−2−22i−2ii2i2−i2−i2000000i2−i20000000
χ262-2-22-2-22202-20200-20022−2−2002i−2i-22002−200−2−222−2i2i−i2−i2i2i2000000i2−i20000000
χ272-2-22-2-22202-20200-20022−2−200−2i2i2-2002−20022−2−2−2i2i−i2−i2i2i2000000−i2i20000000
χ282-2-22-2-22202-20200-20022−2−200−2i2i-22002−200−2−2222i−2ii2i2−i2−i2000000−i2i20000000
χ292-2-22-2-22202-20200-200−2−222002i−2i2-200−2200−2−2222i−2i−i2−i2i2i2000000−i2i20000000
χ302-2-22-2-22202-20200-200−2−222002i−2i-2200−220022−2−2−2i2ii2i2−i2−i2000000−i2i20000000
χ312-2-22-2-22202-20200-200−2−22200−2i2i2-200−2200−2−222−2i2ii2i2−i2−i2000000i2−i20000000
χ322-2-22-2-22202-20200-200−2−22200−2i2i-2200−220022−2−22i−2i−i2−i2i2i2000000i2−i20000000
χ332-2-2-2222-2-2222-2-22-2-2200000000000000002i−2i2i−2i000000002-20000002i−2i000
χ342-2-2-2222-2-2222-2-22-2-2200000000000000002i−2i2i−2i00000000-22000000−2i2i000
χ352-2-2-2222-2-2222-2-22-2-220000000000000000−2i2i−2i2i000000002-2000000−2i2i000
χ362-2-2-2222-2-2222-2-22-2-220000000000000000−2i2i−2i2i00000000-220000002i−2i000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-4-44-404-40-40040000000000000000002i2−2i2−2i22i2000000000000000000000
χ39444-4-4-44-404-40-4004000000000000000000−2i22i22i2−2i2000000000000000000000
χ40444-4-4-44-40-440400-40000004-400000000000000000000000000000000000
χ41444-4-4-44-40-440400-4000000-4400000000000000000000000000000000000
χ4244-444-4-4-440040-4-4000000000000000000000000000000000000022−2200000
χ4344-444-4-4-440040-4-40000000000000000000000000000000000000−222200000
χ4444-444-4-4-4-400-404400000000000004i−4i00000000000000000000000000000
χ4544-444-4-4-4-400-40440000000000000−4i4i00000000000000000000000000000
χ4644-4-4-44-4400000000002i2−2i22i2−2i200000000002i2−2i20000002-22-2000000000000000
χ4744-4-4-44-4400000000002i2−2i22i2−2i20000000000−2i22i2000000-22-22000000000000000
χ4844-4-4-44-440000000000−2i22i2−2i22i200000000002i2−2i2000000-22-22000000000000000
χ4944-4-4-44-440000000000−2i22i2−2i22i20000000000−2i22i20000002-22-2000000000000000
χ504-44-44-4-44400-40-4400000000000000000000000002i2−2i2−2i22i2000000000000000
χ514-44-44-4-44400-40-440000000000000000000000000−2i22i22i2−2i2000000000000000
χ524-44-44-4-44-400404-40004i−4i−4i4i0000000000000000000000000000000000000
χ534-44-44-4-44-400404-4000−4i4i4i−4i0000000000000000000000000000000000000
χ544-4-44-4-4440-440-4004002222−22−2200000000−2222000000000000000000000000000
χ554-4-44-4-4440-440-400400−22−2222220000000022−22000000000000000000000000000
χ564-4-4-4444-4444-4-44-4-44-400000000000000000000000000000000000000000
χ574-4-4-4444-44-4-4-444-44-4400000000000000000000000000000000000000000
χ584-4-4-4444-4-4-4-444-4444-400000000000000000000000000000000000000000
χ598-888-88-8-8000000000000000000000000000000000000000000000000000

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