Finite Group Databasebeta

← Group #288865

Character table — Group #288865

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888888888888888888882244444488888888224488882444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-111-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-1-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-111-1
χ91111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11-11-1-1-111-11-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-11-1111-1-11-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111-11-1-1-1111-11-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-11-1111-1-1-11-11
χ17222222222-2-22-222-222222222-2-2-2-2-2-2000000000000000000000000000000002-2-2200000000
χ18222222222-2-22-222-222222222-2-2-2-2-2-200000000000000000000000000000000-222-200000000
χ19222222222-2-22-222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000022-2-200000000
χ20222222222-2-22-222-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2-22200000000
χ2122222222-222-22-2-2200000000-2-200002222-2-2-2-2000000002222-2-2-2-200000000000000000000
χ2222222222-222-22-2-2200000000-2-200002222-2-2-2-200000000-2-2-2-2222200000000000000000000
χ2322222222-222-22-2-2200000000-2-20000-2-2-2-222220000000022-2-2-2-22200000000000000000000
χ2422222222-222-22-2-2200000000-2-20000-2-2-2-2222200000000-2-22222-2-200000000000000000000
χ2522-22-2-2-2202-20200-22222−2−2−2−20022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i2002-22i−2i0022−2−2i2i2−i2−i2000000000000
χ2622-22-2-2-2202-20200-22222−2−2−2−20022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i200-22−2i2i00−2−222−i2−i2i2i2000000000000
χ2722-22-2-2-2202-20200-22222−2−2−2−20022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i2002-2−2i2i0022−2−2−i2−i2i2i2000000000000
χ2822-22-2-2-2202-20200-22222−2−2−2−20022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i200-222i−2i00−2−222i2i2−i2−i2000000000000
χ2922-22-2-2-2202-20200-2−2−2−2−2222200−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i2002-22i−2i00−2−222−i2−i2i2i2000000000000
χ3022-22-2-2-2202-20200-2−2−2−2−2222200−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i200-22−2i2i0022−2−2i2i2−i2−i2000000000000
χ3122-22-2-2-2202-20200-2−2−2−2−2222200−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i2002-2−2i2i00−2−222i2i2−i2−i2000000000000
χ3222-22-2-2-2202-20200-2−2−2−2−2222200−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i200-222i−2i0022−2−2−i2−i2i2i2000000000000
χ332-22-22-2-22222-2-22-2-200000000-2200002i2i−2i−2i2i−2i2i−2i00000000000000002-22-22i−2i2i−2i000000000000
χ342-22-22-2-22222-2-22-2-200000000-2200002i2i−2i−2i2i−2i2i−2i0000000000000000-22-22−2i2i−2i2i000000000000
χ352-22-22-2-22222-2-22-2-200000000-220000−2i−2i2i2i−2i2i−2i2i00000000000000002-22-2−2i2i−2i2i000000000000
χ362-22-22-2-22222-2-22-2-200000000-220000−2i−2i2i2i−2i2i−2i2i0000000000000000-22-222i−2i2i−2i000000000000
χ372-22-22-2-22-2222-2-22-222-2-222-2-22-22-22-22i2i−2i−2i−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ382-22-22-2-22-2222-2-22-222-2-222-2-22-22-22-2−2i−2i2i2i2i−2i2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ392-22-22-2-22-2222-2-22-2-2-222-2-2222-2-22-222i2i−2i−2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ402-22-22-2-22-2222-2-22-2-2-222-2-2222-2-22-22−2i−2i2i2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ412-22-22-2-22-2-2-222-22222-2-222-2-2-22-22-220000000000000000000000000000000000002-22-20000
χ422-22-22-2-22-2-2-222-22222-2-222-2-2-22-22-22000000000000000000000000000000000000-22-220000
χ432-22-22-2-22-2-2-222-222-2-222-2-222-222-22-20000000000000000000000000000000000002-2-220000
χ442-22-22-2-22-2-2-222-222-2-222-2-222-222-22-2000000000000000000000000000000000000-222-20000
χ452-2-2-2-222202-20-200222−2−2−2−222002−2−2200002-2-22−2−22222−2−22-200002-22−2−222−2−22000000000000
χ462-2-2-2-222202-20-200222−2−2−2−222002−2−2200002-2-22−2−22222−2−2-220000-22−222−2−222−2000000000000
χ472-2-2-2-222202-20-200222−2−2−2−222002−2−220000-222-222−2−2−2−2222-20000-22−222−22−2−22000000000000
χ482-2-2-2-222202-20-200222−2−2−2−222002−2−220000-222-222−2−2−2−222-2200002-22−2−22−222−2000000000000
χ492-2-2-2-222202-20-2002−2−22222−2−200−222−200002-2-2222−2−2−2−2222-200002-2−222−2−222−2000000000000
χ502-2-2-2-222202-20-2002−2−22222−2−200−222−200002-2-2222−2−2−2−222-220000-222−2−222−2−22000000000000
χ512-2-2-2-222202-20-2002−2−22222−2−200−222−20000-222-2−2−22222−2−22-20000-222−2−22−222−2000000000000
χ522-2-2-2-222202-20-2002−2−22222−2−200−222−20000-222-2−2−22222−2−2-2200002-2−222−22−2−22000000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ54444-4-4-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i20000002i2−2i22i2−2i200002-22-22-22-20000000000000000000000000000
χ55444-4-4-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i2000000−2i22i2−2i22i20000-22-22-22-220000000000000000000000000000
χ56444-4-4-44-400000000−2i22i2−2i22i2−2i22i2−2i22i20000002i2−2i22i2−2i20000-22-22-22-220000000000000000000000000000
χ57444-4-4-44-400000000−2i22i2−2i22i2−2i22i2−2i22i2000000−2i22i2−2i22i200002-22-22-22-20000000000000000000000000000
χ5844-44-4-4-440-440-400422222222−22−22−22−2200−22−22222200000000000000000000000000000000000000000000
χ5944-44-4-4-440-440-4004−22−22−22−2222222222002222−22−2200000000000000000000000000000000000000000000
χ6044-4-444-4-4400-40-44000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000
χ6144-4-444-4-4400-40-4400000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000
χ6244-4-444-4-4-400404-404i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6344-4-444-4-4-400404-40−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ644-444-44-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000022−22−22220000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ654-444-44-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000−222222−2200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ664-444-44-4-400000000−2i22i22i2−2i2−2i22i22i2−2i200000022−22−222200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ674-444-44-4-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000−222222−220000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ684-44-44-4-444-4-4-444-44000000004-4000000000000000000000000000000000000000000000000
χ694-4-444-44-440040-4-404i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ704-4-444-44-440040-4-40−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ714-4-444-44-4-400-40440000000000000000000000022−22−2222−222222−220000000000000000000000000000
χ724-4-444-44-4-400-404400000000000000000000000−222222−2222−22−22220000000000000000000000000000
χ734-4-4-4-44440-440400-42222−22−22−22−22222200−222222−2200000000000000000000000000000000000000000000
χ744-4-4-4-44440-440400-4−22−2222222222−22−220022−22−222200000000000000000000000000000000000000000000

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