Finite Group Databasebeta

← Group #288778

Character table — Group #288778

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888888888888888888884444444488888888244488884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1111-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-11-11-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111-1-1111-1-11-1-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-111-1-1-111-111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11-1-1111-1-1-111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-111-1-1-1111-1-11
χ172222222222-22-2-2-2222222222-2-200000000-2-2-2-200000000000000000000000022-2-200000000
χ182222222222-22-2-2-2222222222-2-200000000-2-2-2-2000000000000000000000000-2-22200000000
χ192222222222-22-2-2-22-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000002-22-200000000
χ202222222222-22-2-2-22-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000-22-2200000000
χ2122222222-2-22-2222-200000000-2-22222-2-2-2-20000000000002222-2-2-2-200000000000000000000
χ2222222222-2-22-2222-200000000-2-22222-2-2-2-2000000000000-2-2-2-2222200000000000000000000
χ2322222222-2-22-2222-200000000-2-2-2-2-2-2222200000000000022-2-2-2-22200000000000000000000
χ2422222222-2-22-2222-200000000-2-2-2-2-2-22222000000000000-2-22222-2-200000000000000000000
χ2522-22-2-2-2200-2022-20i2i2i2i2−i2−i2−i2−i20000002i2i−2i−2ii2i2−i2−i22222−2−2−2−2002i−2i2-200i2i2−i2−i222−2−2000000000000
χ2622-22-2-2-2200-2022-20i2i2i2i2−i2−i2−i2−i20000002i2i−2i−2ii2i2−i2−i22222−2−2−2−200−2i2i-2200−i2−i2i2i2−2−222000000000000
χ2722-22-2-2-2200-2022-20i2i2i2i2−i2−i2−i2−i2000000−2i−2i2i2ii2i2−i2−i2−2−2−2−22222002i−2i-2200−i2−i2i2i222−2−2000000000000
χ2822-22-2-2-2200-2022-20i2i2i2i2−i2−i2−i2−i2000000−2i−2i2i2ii2i2−i2−i2−2−2−2−2222200−2i2i2-200i2i2−i2−i2−2−222000000000000
χ2922-22-2-2-2200-2022-20−i2−i2−i2−i2i2i2i2i20000002i2i−2i−2i−i2−i2i2i2−2−2−2−22222002i−2i2-200−i2−i2i2i2−2−222000000000000
χ3022-22-2-2-2200-2022-20−i2−i2−i2−i2i2i2i2i20000002i2i−2i−2i−i2−i2i2i2−2−2−2−2222200−2i2i-2200i2i2−i2−i222−2−2000000000000
χ3122-22-2-2-2200-2022-20−i2−i2−i2−i2i2i2i2i2000000−2i−2i2i2i−i2−i2i2i22222−2−2−2−2002i−2i-2200i2i2−i2−i2−2−222000000000000
χ3222-22-2-2-2200-2022-20−i2−i2−i2−i2i2i2i2i2000000−2i−2i2i2i−i2−i2i2i22222−2−2−2−200−2i2i2-200−i2−i2i2i222−2−2000000000000
χ332-22-2-2-22200202-2-2022−2−222−2−20000002i−2i2i−2i2−22−2i2i2−i2−i2i2i2−i2−i22i−2i00002-2i2−i2i2−i22−22−2000000000000
χ342-22-2-2-22200202-2-2022−2−222−2−20000002i−2i2i−2i2−22−2i2i2−i2−i2i2i2−i2−i2−2i2i0000-22−i2i2−i2i2−22−22000000000000
χ352-22-2-2-22200202-2-2022−2−222−2−2000000−2i2i−2i2i2−22−2−i2−i2i2i2−i2−i2i2i22i−2i0000-22i2−i2i2−i2−22−22000000000000
χ362-22-2-2-22200202-2-2022−2−222−2−2000000−2i2i−2i2i2−22−2−i2−i2i2i2−i2−i2i2i2−2i2i00002-2−i2i2−i2i22−22−2000000000000
χ372-22-2-2-22200202-2-20−2−222−2−2220000002i−2i2i−2i−22−22−i2−i2i2i2−i2−i2i2i22i−2i00002-2−i2i2−i2i2−22−22000000000000
χ382-22-2-2-22200202-2-20−2−222−2−2220000002i−2i2i−2i−22−22−i2−i2i2i2−i2−i2i2i2−2i2i0000-22i2−i2i2−i22−22−2000000000000
χ392-22-2-2-22200202-2-20−2−222−2−222000000−2i2i−2i2i−22−22i2i2−i2−i2i2i2−i2−i22i−2i0000-22−i2i2−i2i22−22−2000000000000
χ402-22-2-2-22200202-2-20−2−222−2−222000000−2i2i−2i2i−22−22i2i2−i2−i2i2i2−i2−i2−2i2i00002-2i2−i2i2−i2−22−22000000000000
χ412-2-2-222-22222-2-22-2-22i2i−2i−2i−2i−2i2i2i-2200000000−2i2i2i−2i00000000000000000000000000002-22i−2i0000
χ422-2-2-222-22222-2-22-2-22i2i−2i−2i−2i−2i2i2i-2200000000−2i2i2i−2i0000000000000000000000000000-22−2i2i0000
χ432-2-2-222-22222-2-22-2-2−2i−2i2i2i2i2i−2i−2i-22000000002i−2i−2i2i00000000000000000000000000002-2−2i2i0000
χ442-2-2-222-22222-2-22-2-2−2i−2i2i2i2i2i−2i−2i-22000000002i−2i−2i2i0000000000000000000000000000-222i−2i0000
χ452-2-2-222-2222-2-22-22-22i2i−2i−2i−2i−2i2i2i2-222-2-22-2-222i−2i−2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ462-2-2-222-2222-2-22-22-22i2i−2i−2i−2i−2i2i2i2-2-2-222-222-22i−2i−2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ472-2-2-222-2222-2-22-22-2−2i−2i2i2i2i2i−2i−2i2-222-2-22-2-22−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ482-2-2-222-2222-2-22-22-2−2i−2i2i2i2i2i−2i−2i2-2-2-222-222-2−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ492-2-2-222-22-2-2-222-22200000000-2222-2-2-222-2000000000000000000002-2-22-222-2000000000000
χ502-2-2-222-22-2-2-222-22200000000-2222-2-2-222-200000000000000000000-222-22-2-22000000000000
χ512-2-2-222-22-2-2-222-22200000000-22-2-2222-2-22000000000000000000002-2-222-2-22000000000000
χ522-2-2-222-22-2-2-222-22200000000-22-2-2222-2-2200000000000000000000-222-2-222-2000000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ54444-44-4-4-40000000022−2222−2222−2222−220022−2222−22000000002-22-22-22-20000000000000000000000000000
χ55444-44-4-4-40000000022−2222−2222−2222−2200−2222−222200000000-22-22-22-220000000000000000000000000000
χ56444-44-4-4-400000000−2222−2222−2222−22220022−2222−2200000000-22-22-22-220000000000000000000000000000
χ57444-44-4-4-400000000−2222−2222−2222−222200−2222−2222000000002-22-22-22-20000000000000000000000000000
χ5844-44-4-4-440040-4-4402i22i22i22i2−2i2−2i2−2i2−2i20000000000−2i2−2i22i22i2000000000000000000000000000000000000
χ5944-44-4-4-440040-4-440−2i2−2i2−2i2−2i22i22i22i22i200000000002i22i2−2i2−2i2000000000000000000000000000000000000
χ6044-4-4-444-44-404000-4000000000000000000000022−2222−22−2222−22220000000000000000000000000000
χ6144-4-4-444-44-404000-40000000000000000000000−2222−222222−2222−220000000000000000000000000000
χ6244-4-4-444-4-440-400044i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6344-4-4-444-4-440-40004−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ644-444-44-4-44-40-4000400000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ654-444-44-4-44-40-400040000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ664-444-44-4-4-4404000-44-4-444-4-4400000000000000000000000000000000000000000000000000
χ674-444-44-4-4-4404000-4-444-4-444-400000000000000000000000000000000000000000000000000
χ684-44-4-4-44400-40-44402222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000
χ694-44-4-4-44400-40-4440−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000
χ704-4-444-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i20022−22−222200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ714-4-444-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i200−222222−22000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ724-4-444-44-400000000−2i22i22i2−2i22i2−2i2−2i22i20022−22−2222000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ734-4-444-44-400000000−2i22i22i2−2i22i2−2i2−2i22i200−222222−2200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ744-4-4-444-44-4-444-44-44000000004-4000000000000000000000000000000000000000000000000

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