Finite Group Databasebeta

← Group #255491

Character table — Group #255491

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444222244444422444444444888888888888888824444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-11-1-1-1-1111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111
χ711111111111111111111-1-1-1-1111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111
χ811111111111111111111-1-1-1-1111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-11111-1-1-1-1
χ911111111-1-1-1-1111111111111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1-1111-1-111-1-1
χ1011111111-1-1-1-1111111111111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-11-1-111-1-111
χ1111111111-1-1-1-1111111111111-1-1-1-111-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-111-111-1-1-1-111
χ1211111111-1-1-1-1111111111111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-111-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-111111-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111111-1-1-1-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-111111111-1-1-1-1111-1-1-111-1-1-1-111
χ1722222222222222-2-2-222-2000022-2-2-2-200-2000022220000000000000000-20000-200000000
χ1822222222222222-2-2-222-2000022-2-2-2-200-20000-2-2-2-2000000000000000020000200000000
χ19222222222222-2-2222-2-222222-2-222-2-222-2-2-2-2-20000000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-2-2-2-2-222-2-2-2-2-222220000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-20000-2-2-2-22200200000000000000000000000002-22-2000000000
χ22222222222222-2-2-2-2-2-2-2-20000-2-2-2-2220020000000000000000000000000-22-22000000000
χ2322222222-2-2-2-222-2-2-222-20000-2-222-2-2002000022-2-2000000000000000020000-200000000
χ2422222222-2-2-2-222-2-2-222-20000-2-222-2-20020000-2-2220000000000000000-20000200000000
χ2522222222-2-2-2-2-2-2222-2-22222222-2-2-2-2-2-22-2-2220000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-2-2-222-2-2-2-222222-2-20000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000022222200-200000000000000000000000002-2-22000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000022222200-20000000000000000000000000-222-2000000000
χ2922-2-22-2-2222-2-222000-2-2000002-2000000000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000
χ3022-2-22-2-2222-2-222000-2-2000002-2000000000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000
χ3122-2-22-2-2222-2-222000-2-2000002-200000000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000
χ3222-2-22-2-2222-2-222000-2-2000002-200000000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000
χ3322-2-22-2-22-2-22222000-2-200000-22000000000002i−2i−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000
χ3422-2-22-2-22-2-22222000-2-200000-22000000000002i−2i−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000
χ3522-2-22-2-22-2-22222000-2-200000-2200000000000−2i2i2i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000
χ3622-2-22-2-22-2-22222000-2-200000-2200000000000−2i2i2i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000
χ372-2-222-22-200002-222-22-2-222-2-200002-20002-200000000002i−2i2i−2i00000000000000002i−2i0000
χ382-2-222-22-200002-222-22-2-222-2-200002-20002-20000000000−2i2i−2i2i0000000000000000−2i2i0000
χ392-2-222-22-200002-222-22-2-2-2-22200002-2000-2200000000002i−2i2i−2i0000000000000000−2i2i0000
χ402-2-222-22-200002-222-22-2-2-2-22200002-2000-220000000000−2i2i−2i2i00000000000000002i−2i0000
χ412-2-222-22-20000-2222-2-22-222-2-20000-22000-220000002i−2i2i−2i0000000000000000002i−2i000000
χ422-2-222-22-20000-2222-2-22-222-2-20000-22000-22000000−2i2i−2i2i000000000000000000−2i2i000000
χ432-2-222-22-20000-2222-2-22-2-2-2220000-220002-20000002i−2i2i−2i000000000000000000−2i2i000000
χ442-2-222-22-20000-2222-2-22-2-2-2220000-220002-2000000−2i2i−2i2i0000000000000000002i−2i000000
χ452-2-2-2-22222-22-2002-2-20022-22-2002-2002-2000000000000000002−22−22−22−200000000002−22−2
χ462-2-2-2-22222-22-2002-2-20022-22-2002-2002-200000000000000000−22−22−22−220000000000−22−22
χ472-2-2-2-22222-22-2002-2-2002-22-22002-200-22000000000000000002−22−22−22−20000000000−22−22
χ482-2-2-2-22222-22-2002-2-2002-22-22002-200-2200000000000000000−22−22−22−2200000000002−22−2
χ492-2-2-2-2222-22-22002-2-20022-22-200-2200-22000000000000000002−22−2−22−2200000000002−2−22
χ502-2-2-2-2222-22-22002-2-20022-22-200-2200-2200000000000000000−22−222−22−20000000000−222−2
χ512-2-2-2-2222-22-22002-2-2002-22-2200-22002-2000000000000000002−22−2−22−220000000000−222−2
χ522-2-2-2-2222-22-22002-2-2002-22-2200-22002-200000000000000000−22−222−22−200000000002−2−22
χ53444-4-4-44-40000004-4400-44-4-4400000000000000000000000000000000000000000000000
χ54444-4-4-44-40000004-4400-4-444-400000000000000000000000000000000000000000000000
χ55444-4-4-44-4000000-44-40040000000000000004i−4i0000000000000000000000000000000000
χ56444-4-4-44-4000000-44-4004000000000000000−4i4i0000000000000000000000000000000000
χ5744-4-44-4-4444-4-4-4-40004400000-44000000000000000000000000000000000000000000000
χ5844-4-44-4-44-4-444-4-400044000004-4000000000000000000000000000000000000000000000
χ594-444-4-4-444-4-4400000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ604-444-4-4-444-4-440000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ614-444-4-4-44-444-400000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ624-444-4-4-44-444-40000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ634-44-444-4-400004-4000-44000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ644-44-444-4-400004-4000-4400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ654-44-444-4-40000-440004-400000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ664-44-444-4-40000-440004-40000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ674-4-444-44-400004-4-4-444-4400000000-4400000000000000000000000000000000000000000
χ684-4-444-44-40000-44-4-44-444000000004-400000000000000000000000000000000000000000
χ694-4-4-4-44444-44-400-44400-4000000-440000000000000000000000000000000000000000000
χ704-4-4-4-4444-44-4400-44400-40000004-40000000000000000000000000000000000000000000
χ7188-88-88-8-8000000000000000000000000000000000000000000000000000000000000000

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