Finite Group Databasebeta

← Group #247176

Character table — Group #247176

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422244444444888888888888888844444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ4111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111111-1-111-1-111-1-111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111111
χ711111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111
χ811111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ911111111-1-1-1-1111111111111-1-1-1-111-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1111-111-1-1-1-111-1-1
χ1011111111-1-1-1-1111111111111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111111-1-1-1-1-111-1-111
χ1111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-111
χ1211111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-11-1-1111111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-11111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-111111-1-1-1-1-1-111
χ1722222222222222-2-222-2-20000-2-222-2-2-200220022000000000000000000-200-20000000000
χ1822222222222222-2-222-2-20000-2-222-2-2-200-2-200-2-200000000000000000020020000000000
χ19222222222222-2-222-2-222222222-2-2-2-2-22200-2-200-2-2000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-222-2-2-2-2-2-2-200220022000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-20000-2-2-2-22220000000000000000000000000002-20002-2000000
χ22222222222222-2-2-2-2-2-2-2-20000-2-2-2-2222000000000000000000000000000-22000-22000000
χ2322222222-2-2-2-222-2-222-2-2000022-2-2-2-22002200-2-2000000000000000000-20020000000000
χ2422222222-2-2-2-222-2-222-2-2000022-2-2-2-2200-2-20022000000000000000000200-20000000000
χ2522222222-2-2-2-2-2-222-2-2222222-2-222-2-22-2-2002200-2-2000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-222-2-2-2-2-2-222-2-222200-2-20022000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000222222-20000000000000000000000000002-2000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000222222-2000000000000000000000000000-220002-2000000
χ292-222-2-2-222i2i−2i−2i002-2002-22i2i−2i−2i2i−2i000002-2000000000000000022−2−2i2i2−i2−i20000000000i2−i22−2
χ302-222-2-2-222i2i−2i−2i002-2002-22i2i−2i−2i2i−2i000002-20000000000000000−2−222−i2−i2i2i20000000000−i2i2−22
χ312-222-2-2-222i2i−2i−2i002-2002-2−2i−2i2i2i2i−2i00000-22000000000000000022−2−2i2i2−i2−i20000000000−i2i2−22
χ322-222-2-2-222i2i−2i−2i002-2002-2−2i−2i2i2i2i−2i00000-220000000000000000−2−222−i2−i2i2i20000000000i2−i22−2
χ332-222-2-2-22−2i−2i2i2i002-2002-22i2i−2i−2i−2i2i00000-22000000000000000022−2−2−i2−i2i2i20000000000i2−i2−22
χ342-222-2-2-22−2i−2i2i2i002-2002-22i2i−2i−2i−2i2i00000-220000000000000000−2−222i2i2−i2−i20000000000−i2i22−2
χ352-222-2-2-22−2i−2i2i2i002-2002-2−2i−2i2i2i−2i2i000002-2000000000000000022−2−2−i2−i2i2i20000000000−i2i22−2
χ362-222-2-2-22−2i−2i2i2i002-2002-2−2i−2i2i2i−2i2i000002-20000000000000000−2−222i2i2−i2−i20000000000i2−i2−22
χ372-22-22-22-22i−2i2i−2i2-2002-2000000002i−2i000002i−2i002-200i2i2−i2−i222−2−22−22−2i2−i2i2−i200000000000000
χ382-22-22-22-22i−2i2i−2i2-2002-2000000002i−2i000002i−2i002-200−i2−i2i2i2−2−222−22−22−i2i2−i2i200000000000000
χ392-22-22-22-22i−2i2i−2i2-2002-2000000002i−2i00000−2i2i00-2200i2i2−i2−i222−2−2−22−22−i2i2−i2i200000000000000
χ402-22-22-22-22i−2i2i−2i2-2002-2000000002i−2i00000−2i2i00-2200−i2−i2i2i2−2−2222−22−2i2−i2i2−i200000000000000
χ412-22-22-22-2−2i2i−2i2i2-2002-200000000−2i2i000002i−2i00-2200i2i2−i2−i2−2−2222−22−2−i2i2−i2i200000000000000
χ422-22-22-22-2−2i2i−2i2i2-2002-200000000−2i2i000002i−2i00-2200−i2−i2i2i222−2−2−22−22i2−i2i2−i200000000000000
χ432-22-22-22-2−2i2i−2i2i2-2002-200000000−2i2i00000−2i2i002-200i2i2−i2−i2−2−222−22−22i2−i2i2−i200000000000000
χ442-22-22-22-2−2i2i−2i2i2-2002-200000000−2i2i00000−2i2i002-200−i2−i2i2i222−2−22−22−2−i2i2−i2i200000000000000
χ452-2-2-2-222200002-2-2-2-22222-22-200002-20000000002-200002-22-200000000000000002-20000
χ462-2-2-2-222200002-2-2-2-22222-22-200002-20000000002-20000-22-220000000000000000-220000
χ472-2-2-2-222200002-2-2-2-2222-22-2200002-2000000000-2200002-22-20000000000000000-220000
χ482-2-2-2-222200002-2-2-2-2222-22-2200002-2000000000-220000-22-2200000000000000002-20000
χ492-2-2-2-22220000-22-2-22-2222-22-20000-22000000000-222-22-200000000000000002-200000000
χ502-2-2-2-22220000-22-2-22-2222-22-20000-22000000000-22-22-220000000000000000-2200000000
χ512-2-2-2-22220000-22-2-22-222-22-220000-220000000002-22-22-20000000000000000-2200000000
χ522-2-2-2-22220000-22-2-22-222-22-220000-220000000002-2-22-2200000000000000002-200000000
χ53444-4-44-4-44-4-4400000000000000000000000000000000000002-2-222-2-2200000000000000
χ54444-4-44-4-44-4-440000000000000000000000000000000000000-222-2-222-200000000000000
χ55444-4-44-4-4-444-400000000000000000000000000000000000002-2-22-222-200000000000000
χ56444-4-44-4-4-444-40000000000000000000000000000000000000-222-22-2-2200000000000000
χ5744-44-4-44-400004400-4-400000000000000000000000000022−22−22220000000000000000000000
χ5844-44-4-44-400004400-4-4000000000000000000000000000−222222−220000000000000000000000
χ5944-44-4-44-40000-4-40044000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ6044-44-4-44-40000-4-4004400000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ6144-4-44-4-440000004-400-440000000000000004i−4i0000000000000000000000000000000000
χ6244-4-44-4-440000004-400-44000000000000000−4i4i0000000000000000000000000000000000
χ6344-4-44-4-44000000-44004-44i−4i−4i4i00000000000000000000000000000000000000000000000
χ6444-4-44-4-44000000-44004-4−4i4i4i−4i00000000000000000000000000000000000000000000000
χ654-444-4-4-444i4i−4i−4i00-4400-440000−4i4i000000000000000000000000000000000000000000000
χ664-444-4-4-44−4i−4i4i4i00-4400-4400004i−4i000000000000000000000000000000000000000000000
χ674-44-44-44-44i−4i4i−4i-4400-4400000000−4i4i0000000000000000000000000000000000000000000
χ684-44-44-44-4−4i4i−4i4i-4400-44000000004i−4i0000000000000000000000000000000000000000000
χ694-4-4-4-444400004-444-44-4-400000000-4400000000000000000000000000000000000000000
χ704-4-4-4-44440000-44444-4-4-4000000004-400000000000000000000000000000000000000000
χ718-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000

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