Finite Group Databasebeta

← Group #397949

Character table — Group #397949

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222224444444488888888888888888888888888881616161616161616161616161616
order12442222222444444422224444444444444444444488888888888822244444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-111-11-1-1-1-1-1-111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111111-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-11111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1-1-11111
χ9111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-11111-1-1-1-1-1-1
χ10111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-1-11-1-1-111-1-111
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11-1-11-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ172222222-2-2-2-222-2-2-22-2000000002i2i−2i−2i00002i2i−2i−2i000022-2-20000000000000000000000
χ182222222-2-2-2-222-2-2-22-2000000002i2i−2i−2i0000−2i−2i2i2i0000-2-2220000000000000000000000
χ192222222-2-2-2-222-2-2-22-200000000−2i−2i2i2i00002i2i−2i−2i0000-2-2220000000000000000000000
χ202222222-2-2-2-222-2-2-22-200000000−2i−2i2i2i0000−2i−2i2i2i000022-2-20000000000000000000000
χ2122222-2-222-2-2-2-22-2-22222-2-222-2-200000000000000002-22-222-2-2000000000000000000
χ2222222-2-222-2-2-2-22-2-22222-2-222-2-20000000000000000-22-22-2-222000000000000000000
χ2322222-2-222-2-2-2-22-2-222-2-222-2-22200000000000000002-22-2-2-222000000000000000000
χ2422222-2-222-2-2-2-22-2-222-2-222-2-2220000000000000000-22-2222-2-2000000000000000000
χ2522222-2-2-2-222-2-2-2222-200000000000022-2-2000022-2-22-2-220000000000000000000000
χ2622222-2-2-2-222-2-2-2222-200000000000022-2-20000-2-222-222-20000000000000000000000
χ2722222-2-2-2-222-2-2-2222-2000000000000-2-222000022-2-2-222-20000000000000000000000
χ2822222-2-2-2-222-2-2-2222-2000000000000-2-2220000-2-2222-2-220000000000000000000000
χ292222-22-22-22-22-222-2-2-20000000000002-22-22i−2i2i−2i000000002i−2i2i−2i000000000000000000
χ302222-22-22-22-22-222-2-2-20000000000002-22-2−2i2i−2i2i00000000−2i2i−2i2i000000000000000000
χ312222-22-22-22-22-222-2-2-2000000000000-22-222i−2i2i−2i00000000−2i2i−2i2i000000000000000000
χ322222-22-22-22-22-222-2-2-2000000000000-22-22−2i2i−2i2i000000002i−2i2i−2i000000000000000000
χ332222-22-2-22-222-2-2-22-222-22-22-22-2000000002-2-222-22-200000000000000000000000000
χ342222-22-2-22-222-2-2-22-222-22-22-22-200000000-222-2-22-2200000000000000000000000000
χ352222-22-2-22-222-2-2-22-22-22-22-22-22000000002-2-22-22-2200000000000000000000000000
χ362222-22-2-22-222-2-2-22-22-22-22-22-2200000000-222-22-22-200000000000000000000000000
χ372222-2-222-2-22-222-22-2-2000000002i−2i2i−2i000000002-2-2200002i−2i−2i2i000000000000000000
χ382222-2-222-2-22-222-22-2-2000000002i−2i2i−2i00000000-222-20000−2i2i2i−2i000000000000000000
χ392222-2-222-2-22-222-22-2-200000000−2i2i−2i2i000000002-2-220000−2i2i2i−2i000000000000000000
χ402222-2-222-2-22-222-22-2-200000000−2i2i−2i2i00000000-222-200002i−2i−2i2i000000000000000000
χ412222-2-22-222-2-22-22-2-222-2-222-2-222-2-22-222-20000000000000000000000000000000000
χ422222-2-22-222-2-22-22-2-222-2-222-2-22-222-22-2-220000000000000000000000000000000000
χ432222-2-22-222-2-22-22-2-22-222-2-222-22-2-222-2-220000000000000000000000000000000000
χ442222-2-22-222-2-22-22-2-22-222-2-222-2-222-2-222-20000000000000000000000000000000000
χ4522-2-2222-2-2-2-2-2-2222-2222-2-2-2-22200000000000000000000000000000000002i−2i2i−2i0000
χ4622-2-2222-2-2-2-2-2-2222-2222-2-2-2-2220000000000000000000000000000000000−2i2i−2i2i0000
χ4722-2-2222-2-2-2-2-2-2222-22-2-22222-2-200000000000000000000000000000000002i−2i−2i2i0000
χ4822-2-2222-2-2-2-2-2-2222-22-2-22222-2-20000000000000000000000000000000000−2i2i2i−2i0000
χ4922-2-22-2-2-2-222222-2-2-222222-2-2-2-200000000000000000000000022-2-2200-20000000000
χ5022-2-22-2-2-2-222222-2-2-222222-2-2-2-2000000000000000000000000-2-222-20020000000000
χ5122-2-22-2-2-2-222222-2-2-22-2-2-2-2222200000000000000000000000022-2-2-20020000000000
χ5222-2-22-2-2-2-222222-2-2-22-2-2-2-22222000000000000000000000000-2-222200-20000000000
χ5322-2-2-22-22-22-2-22-2-22222-2-22-222-200000000000000000000000000000200-2000002-200
χ5422-2-2-22-22-22-2-22-2-22222-2-22-222-200000000000000000000000000000-200200000-2200
χ5522-2-2-22-22-22-2-22-2-2222-222-22-2-2200000000000000000000000000000200-200000-2200
χ5622-2-2-22-22-22-2-22-2-2222-222-22-2-2200000000000000000000000000000-2002000002-200
χ5722-2-2-2-222-2-222-2-22-2222-22-2-22-22000000000000000000000000000000200-20000002-2
χ5822-2-2-2-222-2-222-2-22-2222-22-2-22-22000000000000000000000000000000-2002000000-22
χ5922-2-2-2-222-2-222-2-22-222-22-222-22-2000000000000000000000000000000200-2000000-22
χ6022-2-2-2-222-2-222-2-22-222-22-222-22-2000000000000000000000000000000-20020000002-2
χ6144-4-44444444-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ6244-4-44-4-444-4-444-444-4-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-4-44-44-4444-44-400000000000000000000000000000000000000000000000000
χ6444-4-4-4-44-444-44-44-444-400000000000000000000000000000000000000000000000000
χ658-88i−8i000000000000000000000000000000000000000000000022−222i2−2i200000000000000
χ668-88i−8i0000000000000000000000000000000000000000000000−2222−2i22i200000000000000
χ678-8−8i8i000000000000000000000000000000000000000000000022−22−2i22i200000000000000
χ688-8−8i8i0000000000000000000000000000000000000000000000−22222i2−2i200000000000000

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