Finite Group Databasebeta

← Group #173949

Character table — Group #173949

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222222244444444444444224444444444488888888888888888888888824444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-11-111
χ511111111111111111111111111-1-11-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111-1-11-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ811111111111111111111111111-1-11-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-11-11-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-111-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1-11-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-11-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-11
χ172222222222222222-2-2-2-22-2-2-22-200-20022002200000000000000000000000000-2-2000000
χ182222222222222222-2-2-2-22-2-2-22-200-200-2-200-2-20000000000000000000000000022000000
χ19222222222222-2-2-2-22222-22-2-2-2222-2220000000000000000000000000000000000-20-2000
χ20222222222222-2-2-2-22222-22-2-2-22-2-2-2-2-20000000000000000000000000000000000202000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-200200002200-2-200000000000000000000000000020-200
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-20020000-2-20022000000000000000000000000000-20200
χ2322222222-2-2-2-222222222-2-222-2-200-20000220022000000000000000000000000000-20-200
χ2422222222-2-2-2-222222222-2-222-2-200-20000-2-200-2-200000000000000000000000000020200
χ2522222222-2-2-2-22222-2-2-2-2-22-2-2-22222-2-20000000000000000000000000000000000-202000
χ2622222222-2-2-2-22222-2-2-2-2-22-2-2-22-2-2222000000000000000000000000000000000020-2000
χ2722222222-2-2-2-2-2-2-2-222222-2-2-22-2002002200-2-200000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-222222-2-2-22-200200-2-20022000000000000000000000000002-2000000
χ292-22-222-2-200002i2i−2i−2i2i2i−2i−2i002-20000000002-2002i−2i0000000022−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000
χ302-22-222-2-200002i2i−2i−2i2i2i−2i−2i002-20000000002-2002i−2i00000000−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000
χ312-22-222-2-200002i2i−2i−2i2i2i−2i−2i002-2000000000-2200−2i2i0000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000
χ322-22-222-2-200002i2i−2i−2i2i2i−2i−2i002-2000000000-2200−2i2i00000000−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000
χ332-22-222-2-20000−2i−2i2i2i−2i−2i2i2i002-20000000002-200−2i2i0000000022−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000
χ342-22-222-2-20000−2i−2i2i2i−2i−2i2i2i002-20000000002-200−2i2i00000000−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000
χ352-22-222-2-20000−2i−2i2i2i−2i−2i2i2i002-2000000000-22002i−2i0000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000
χ362-22-222-2-20000−2i−2i2i2i−2i−2i2i2i002-2000000000-22002i−2i00000000−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000
χ372-2-222-22-222-2-200002-22-202000-22-202-200000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-222-22-222-2-200002-22-202000-22-202-200000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-222-22-222-2-200002-22-202000-2-220-2200000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-222-22-222-2-200002-22-202000-2-220-2200000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-222-22-2-2-2220000-22-2202000-22-20-2200000000i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-2-222-22-2-2-2220000-22-2202000-22-20-2200000000−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-2-222-22-2-2-2220000-22-2202000-2-2202-200000000i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ442-2-222-22-2-2-2220000-22-2202000-2-2202-200000000−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ452-2-22-22-222-22-22-22-200002000-20000002i−2i002i−2i00i2−i2i2−i2i2−i2i2−i2000000002−22−22−22−200000000
χ462-2-22-22-222-22-22-22-200002000-20000002i−2i002i−2i00−i2i2−i2i2−i2i2−i2i200000000−22−22−22−2200000000
χ472-2-22-22-222-22-22-22-200002000-2000000−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i200000000−22−22−22−2200000000
χ482-2-22-22-222-22-22-22-200002000-2000000−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i2000000002−22−22−22−200000000
χ492-2-22-22-22-22-22-22-2200002000-20000002i−2i00−2i2i00i2−i2i2−i2−i2i2−i2i2000000002−22−2−22−2200000000
χ502-2-22-22-22-22-22-22-2200002000-20000002i−2i00−2i2i00−i2i2−i2i2i2−i2i2−i200000000−22−222−22−200000000
χ512-2-22-22-22-22-22-22-2200002000-2000000−2i2i002i−2i00i2−i2i2−i2−i2i2−i2i200000000−22−222−22−200000000
χ522-2-22-22-22-22-22-22-2200002000-2000000−2i2i002i−2i00−i2i2−i2i2i2−i2i2−i2000000002−22−2−22−2200000000
χ534444-4-4-4-44-4-440000000000000000000000000002-2-222-2-22000000000000000000000000
χ544444-4-4-4-44-4-44000000000000000000000000000-222-2-222-2000000000000000000000000
χ554444-4-4-4-4-444-40000000000000000000000000002-2-22-222-2000000000000000000000000
χ564444-4-4-4-4-444-4000000000000000000000000000-222-22-2-22000000000000000000000000
χ5744-4-44-4-44000000004i−4i−4i4i0000000000000000000000000002i−2i−2i2i-222-20000000000000000
χ5844-4-44-4-44000000004i−4i−4i4i000000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ5944-4-44-4-4400000000−4i4i4i−4i0000000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ6044-4-44-4-4400000000−4i4i4i−4i000000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ6144-4-4-444-400004i−4i−4i4i0000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ6244-4-4-444-400004i−4i−4i4i000000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ6344-4-4-444-40000−4i4i4i−4i0000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ6444-4-4-444-40000−4i4i4i−4i000000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ654-44-444-4-400004i4i−4i−4i−4i−4i4i4i00-4400000000000000000000000000000000000000000000000
χ664-44-444-4-40000−4i−4i4i4i4i4i−4i−4i00-4400000000000000000000000000000000000000000000000
χ674-4-444-44-444-4-40000-44-440-40004000000000000000000000000000000000000000000000
χ684-4-444-44-4-4-44400004-44-40-40004000000000000000000000000000000000000000000000
χ694-4-44-44-444-44-4-44-440000-400040000000000000000000000000000000000000000000000
χ704-4-44-44-44-44-444-44-40000-400040000000000000000000000000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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