Finite Group Databasebeta

← Group #322209

Character table — Group #322209

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888888888888888888882222444488888888444488882244
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-22-2-2-2222222222-2-2-2-2-2-2000000000000000000000000000000002-22-200000000
χ182222222222-22-2-2-2222222222-2-2-2-2-2-200000000000000000000000000000000-22-2200000000
χ192222222222-22-2-2-22-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-2-2200000000
χ202222222222-22-2-2-22-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-222-200000000
χ2122222222-2-22-2222-200000000-2-200002222-2-2-2-2000000002222-2-2-2-200000000000000000000
χ2222222222-2-22-2222-200000000-2-200002222-2-2-2-200000000-2-2-2-2222200000000000000000000
χ2322222222-2-22-2222-200000000-2-20000-2-2-2-222220000000022-2-2-2-22200000000000000000000
χ2422222222-2-22-2222-200000000-2-20000-2-2-2-2222200000000-2-22222-2-200000000000000000000
χ25222-2-2-2-2200202-2-202222−2−2−2−20022−2−222-2-200002222−2−2−2−200002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ26222-2-2-2-2200202-2-202222−2−2−2−20022−2−222-2-200002222−2−2−2−20000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ27222-2-2-2-2200202-2-202222−2−2−2−20022−2−2-2-2220000−2−2−2−2222200002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ28222-2-2-2-2200202-2-202222−2−2−2−20022−2−2-2-2220000−2−2−2−222220000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ29222-2-2-2-2200202-2-20−2−2−2−2222200−2−22222-2-20000−2−2−2−2222200002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ30222-2-2-2-2200202-2-20−2−2−2−2222200−2−22222-2-20000−2−2−2−222220000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ31222-2-2-2-2200202-2-20−2−2−2−2222200−2−222-2-22200002222−2−2−2−200002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ32222-2-2-2-2200202-2-20−2−2−2−2222200−2−222-2-22200002222−2−2−2−20000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ332-2-22-2-22222-2-222-2-2000000002-200002-22-222-2-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ342-2-22-2-22222-2-222-2-2000000002-200002-22-222-2-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ352-2-22-2-22222-2-222-2-2000000002-20000-22-22-2-22200000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ362-2-22-2-22222-2-222-2-2000000002-20000-22-22-2-2220000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ372-2-22-2-222-2-222-2-22222-2-222-2-22-22-22-20000000000000000000000000000000000002-22-20000
χ382-2-22-2-222-2-222-2-22222-2-222-2-22-22-22-2000000000000000000000000000000000000-22-220000
χ392-2-22-2-222-2-222-2-222-2-222-2-2222-2-22-220000000000000000000000000000000000002-2-220000
χ402-2-22-2-222-2-222-2-222-2-222-2-2222-2-22-22000000000000000000000000000000000000-222-20000
χ412-2-22-2-222-2-2-2222-2222-2-222-2-2-22-22-222-22-2-2-22222-2-222-2-20000000000000000000000000000
χ422-2-22-2-222-2-2-2222-2222-2-222-2-2-22-22-22-22-2222-2-2-2-222-2-2220000000000000000000000000000
χ432-2-22-2-222-2-2-2222-22-2-222-2-222-222-22-22-22-2-2-222-2-222-2-2220000000000000000000000000000
χ442-2-22-2-222-2-2-2222-22-2-222-2-222-222-22-2-22-2222-2-222-2-222-2-20000000000000000000000000000
χ452-2-2-222-2200-202-22022−2−2−2−22200−222−22-2-22000022−2−2−2−2222-22-200002−2−222−2−22000000000000
χ462-2-2-222-2200-202-22022−2−2−2−22200−222−22-2-22000022−2−2−2−222-22-220000−222−2−222−2000000000000
χ472-2-2-222-2200-202-22022−2−2−2−22200−222−2-222-20000−2−22222−2−22-2-2200002−2−22−222−2000000000000
χ482-2-2-222-2200-202-22022−2−2−2−22200−222−2-222-20000−2−22222−2−2-222-20000−222−22−2−22000000000000
χ492-2-2-222-2200-202-220−2−22222−2−2002−2−222-2-220000−2−22222−2−22-22-20000−222−2−222−2000000000000
χ502-2-2-222-2200-202-220−2−22222−2−2002−2−222-2-220000−2−22222−2−2-22-2200002−2−222−2−22000000000000
χ512-2-2-222-2200-202-220−2−22222−2−2002−2−22-222-2000022−2−2−2−2222-2-220000−222−22−2−22000000000000
χ522-2-2-222-2200-202-220−2−22222−2−2002−2−22-222-2000022−2−2−2−222-222-200002−2−22−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ54444-4-4-4-4400-40-444022222222−22−22−22−2200−22−22222200000000000000000000000000000000000000000000
χ55444-4-4-4-4400-40-4440−22−22−22−2222222222002222−22−2200000000000000000000000000000000000000000000
χ5644-444-4-4-40000000022−2222−2222−2222−2200000000002i2−2i22i2−2i22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ5744-444-4-4-40000000022−2222−2222−2222−220000000000−2i22i2−2i22i2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ5844-444-4-4-400000000−2222−2222−2222−222200000000002i2−2i22i2−2i2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ5944-444-4-4-400000000−2222−2222−2222−22220000000000−2i22i2−2i22i22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ6044-4-4-444-44-404000-400000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000
χ6144-4-4-444-44-404000-40000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000
χ6244-4-4-444-4-440-400044-44-4-44-4400000000000000000000000000000000000000000000000000
χ6344-4-4-444-4-440-40004-44-444-44-400000000000000000000000000000000000000000000000000
χ644-444-44-4-40000000022−22−222222−22−222200000000002i2−2i2−2i22i2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ654-444-44-4-40000000022−22−222222−22−22220000000000−2i22i22i2−2i22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ664-444-44-4-400000000−222222−22−222222−2200000000002i2−2i2−2i22i22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ674-444-44-4-400000000−222222−22−222222−220000000000−2i22i22i2−2i2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ684-44-44-44-44-40-400044-4-44-444-400000000000000000000000000000000000000000000000000
χ694-44-44-44-44-40-40004-444-44-4-4400000000000000000000000000000000000000000000000000
χ704-44-44-44-4-4404000-400000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ714-44-44-44-4-4404000-40000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ724-4-44-4-444444-4-4-44-400000000-44000000000000000000000000000000000000000000000000
χ734-4-4-444-440040-44-402222−22−22−22−2222220022−22−222200000000000000000000000000000000000000000000
χ744-4-4-444-440040-44-40−22−2222222222−22−2200−222222−2200000000000000000000000000000000000000000000

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