Finite Group Databasebeta

← Group #288871

Character table — Group #288871

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888888888888888888884444444488888888444488882444
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
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-11-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-11-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11-1111-1-111-1-1
χ17222222222-2-22-222-222222222-2-20000-2-2-2-200000000000000000000000000002-2-2200000000
χ18222222222-2-22-222-222222222-2-20000-2-2-2-20000000000000000000000000000-222-200000000
χ19222222222-2-22-222-2-2-2-2-2-2-2-2-2-2-200002222000000000000000000000000000022-2-200000000
χ20222222222-2-22-222-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000000000-2-22200000000
χ2122222222-222-22-2-2200000000-2-222220000-2-2-2-20000000022-2-222-2-200000000000000000000
χ2222222222-222-22-2-2200000000-2-222220000-2-2-2-200000000-2-222-2-22200000000000000000000
χ2322222222-222-22-2-2200000000-2-2-2-2-2-2000022220000000022-2-2-2-22200000000000000000000
χ2422222222-222-22-2-2200000000-2-2-2-2-2-20000222200000000-2-22222-2-200000000000000000000
χ25222-2-2-22-202-20-20022222−2−2−2−2002i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i2002i−2i002-2i2i2−i2−i222−2−2000000000000
χ26222-2-2-22-202-20-20022222−2−2−2−2002i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i200−2i2i00-22−i2−i2i2i2−2−222000000000000
χ27222-2-2-22-202-20-20022222−2−2−2−200−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i2002i−2i00-22i2i2−i2−i2−2−222000000000000
χ28222-2-2-22-202-20-20022222−2−2−2−200−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i200−2i2i002-2−i2−i2i2i222−2−2000000000000
χ29222-2-2-22-202-20-2002−2−2−2−22222002i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i2002i−2i002-2−i2−i2i2i2−2−222000000000000
χ30222-2-2-22-202-20-2002−2−2−2−22222002i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i200−2i2i00-22i2i2−i2−i222−2−2000000000000
χ31222-2-2-22-202-20-2002−2−2−2−2222200−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i2002i−2i00-22−i2−i2i2i222−2−2000000000000
χ32222-2-2-22-202-20-2002−2−2−2−2222200−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i200−2i2i002-2i2i2−i2−i2−2−222000000000000
χ332-2-22-222-202-20200-222−2−222−2−2002-22-22−22−2000022−2−222−2−22i−2i002i−2i00i2−i2i2−i2i2−i2i2−i2000000000000
χ342-2-22-222-202-20200-222−2−222−2−2002-22-22−22−2000022−2−222−2−2−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i2000000000000
χ352-2-22-222-202-20200-222−2−222−2−200-22-222−22−20000−2−222−2−2222i−2i00−2i2i00i2−i2i2−i2−i2i2−i2i2000000000000
χ362-2-22-222-202-20200-222−2−222−2−200-22-222−22−20000−2−222−2−222−2i2i002i−2i00−i2i2−i2i2i2−i2i2−i2000000000000
χ372-2-22-222-202-20200-2−2−222−2−222002-22-2−22−220000−2−222−2−2222i−2i002i−2i00−i2i2−i2i2−i2i2−i2i2000000000000
χ382-2-22-222-202-20200-2−2−222−2−222002-22-2−22−220000−2−222−2−222−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i2000000000000
χ392-2-22-222-202-20200-2−2−222−2−22200-22-22−22−22000022−2−222−2−22i−2i00−2i2i00−i2i2−i2i2i2−i2i2−i2000000000000
χ402-2-22-222-202-20200-2−2−222−2−22200-22-22−22−22000022−2−222−2−2−2i2i002i−2i00i2−i2i2−i2−i2i2−i2i2000000000000
χ412-2-2-22-222222-2-22-2-200000000-222i−2i−2i2i00002i2i−2i−2i00000000000000002-2-22−2i2i2i−2i000000000000
χ422-2-2-22-222222-2-22-2-200000000-222i−2i−2i2i00002i2i−2i−2i0000000000000000-222-22i−2i−2i2i000000000000
χ432-2-2-22-222222-2-22-2-200000000-22−2i2i2i−2i0000−2i−2i2i2i00000000000000002-2-222i−2i−2i2i000000000000
χ442-2-2-22-222222-2-22-2-200000000-22−2i2i2i−2i0000−2i−2i2i2i0000000000000000-222-2−2i2i2i−2i000000000000
χ452-2-2-22-222-2222-2-22-222-2-2-2-2222-22i−2i−2i2i2-2-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ462-2-2-22-222-2222-2-22-222-2-2-2-2222-2−2i2i2i−2i2-2-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ472-2-2-22-222-2222-2-22-2-2-22222-2-22-22i−2i−2i2i-222-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ482-2-2-22-222-2222-2-22-2-2-22222-2-22-2−2i2i2i−2i-222-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ492-2-2-22-222-2-2-222-22222-2-2-2-222-220000-222-2000000000000000000000000000000002-22-20000
χ502-2-2-22-222-2-2-222-22222-2-2-2-222-220000-222-200000000000000000000000000000000-22-220000
χ512-2-2-22-222-2-2-222-222-2-22222-2-2-2200002-2-22000000000000000000000000000000002-2-220000
χ522-2-2-22-222-2-2-222-222-2-22222-2-2-2200002-2-2200000000000000000000000000000000-222-20000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ54444-4-4-44-40-440400-422222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000
χ55444-4-4-44-40-440400-4−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000
χ5644-444-4-4-440040-4-40000000000000000000000022−2222−2222−2222−220000000000000000000000000000
χ5744-444-4-4-440040-4-400000000000000000000000−2222−2222−2222−22220000000000000000000000000000
χ5844-444-4-4-4-400-404404i−4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ5944-444-4-4-4-400-40440−4i4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6044-4-4-44-44000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000022−2222−222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ6144-4-4-44-44000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000−2222−2222−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ6244-4-4-44-4400000000−2i22i2−2i22i22i2−2i22i2−2i2000000000022−2222−22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ6344-4-4-44-4400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000−2222−22222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ644-444-4-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i200000000002i2−2i2−2i22i22-2-222-2-220000000000000000000000000000
χ654-444-4-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000−2i22i22i2−2i2-222-2-222-20000000000000000000000000000
χ664-444-4-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i200000000002i2−2i2−2i22i2-222-2-222-20000000000000000000000000000
χ674-444-4-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000−2i22i22i2−2i22-2-222-2-220000000000000000000000000000
χ684-44-444-4-4400-40-4404i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ694-44-444-4-4400-40-440−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ704-44-444-4-4-400404-4000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ714-44-444-4-4-400404-400000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ724-4-44-444-40-440-40042222−22−222222−22−22000000−2222−22220000000000000000000000000000000000000000
χ734-4-44-444-40-440-4004−22−222222−22−22222200000022−2222−220000000000000000000000000000000000000000
χ744-4-4-44-4444-4-4-444-44000000004-4000000000000000000000000000000000000000000000000

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