Finite Group Databasebeta

← Group #316390

Character table — Group #316390

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888822244444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ12111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-2222-2-222-2-22222-2-2-2-2-2002000000220000-2-200000000000000000000
χ18222222222-2-2-2-2222-2-222-2-2-2-2-2-22222-2002000000-2-200002200000000000000000000
χ19222222222-2-2-2-2222-2-2-2-2222222-2-2-2-2200-2000000-2-200002200000000000000000000
χ20222222222-2-2-2-2222-2-2-2-222-2-2-2-22222200-2000000220000-2-200000000000000000000
χ2122222222-22222-2-2-2-2-2222200000000-222-222-2-2-2-20000000000000000000000000000
χ2222222222-22222-2-2-2-2-2222200000000-2-2-2-2-2-222220000000000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-2000000002222-2-222-2-20000000000000000000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-2000000002-2-2222-2-2220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000200-2000000002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000200-200000000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000-2002000000002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000-200200000000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ2922-2-222-2-2022-2-2000002i−2i2i−2i22−2−222−2−20000002-22i−2ii2−i22−22−2i2−i2i2−i2i2−i20000000000000000
χ3022-2-222-2-2022-2-2000002i−2i2i−2i22−2−222−2−2000000-22−2i2ii2−i2−22−22i2−i2−i2i2−i2i20000000000000000
χ3122-2-222-2-2022-2-2000002i−2i2i−2i−2−222−2−2220000002-22i−2i−i2i2−22−22−i2i2−i2i2−i2i20000000000000000
χ3222-2-222-2-2022-2-2000002i−2i2i−2i−2−222−2−222000000-22−2i2i−i2i22−22−2−i2i2i2−i2i2−i20000000000000000
χ3322-2-222-2-2022-2-200000−2i2i−2i2i22−2−222−2−20000002-2−2i2i−i2i22−22−2−i2i2−i2i2−i2i20000000000000000
χ3422-2-222-2-2022-2-200000−2i2i−2i2i22−2−222−2−2000000-222i−2i−i2i2−22−22−i2i2i2−i2i2−i20000000000000000
χ3522-2-222-2-2022-2-200000−2i2i−2i2i−2−222−2−2220000002-2−2i2ii2−i2−22−22i2−i2i2−i2i2−i20000000000000000
χ3622-2-222-2-2022-2-200000−2i2i−2i2i−2−222−2−222000000-222i−2ii2−i22−22−2i2−i2−i2i2−i2i20000000000000000
χ3722-2-222-2-20-2-222000002i−2i−2i2i22−2−2−2−22202-202i−2i0000i2−i2i2−i2−i2i2−i2i2−222−20000000000000000
χ3822-2-222-2-20-2-222000002i−2i−2i2i22−2−2−2−2220-220−2i2i0000i2−i2−i2i2i2−i2−i2i22−2−220000000000000000
χ3922-2-222-2-20-2-222000002i−2i−2i2i−2−22222−2−202-202i−2i0000−i2i2−i2i2i2−i2i2−i22−2−220000000000000000
χ4022-2-222-2-20-2-222000002i−2i−2i2i−2−22222−2−20-220−2i2i0000−i2i2i2−i2−i2i2i2−i2−222−20000000000000000
χ4122-2-222-2-20-2-22200000−2i2i2i−2i22−2−2−2−22202-20−2i2i0000−i2i2−i2i2i2−i2i2−i2−222−20000000000000000
χ4222-2-222-2-20-2-22200000−2i2i2i−2i22−2−2−2−2220-2202i−2i0000−i2i2i2−i2−i2i2i2−i22−2−220000000000000000
χ4322-2-222-2-20-2-22200000−2i2i2i−2i−2−22222−2−202-20−2i2i0000i2−i2i2−i2−i2i2−i2i22−2−220000000000000000
χ4422-2-222-2-20-2-22200000−2i2i2i−2i−2−22222−2−20-2202i−2i0000i2−i2−i2i2i2−i2−i2i2−222−20000000000000000
χ452-2-222-2-2222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i002-200000000
χ462-2-222-2-2222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i00-2200000000
χ472-2-222-2-2222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i00-2200000000
χ482-2-222-2-2222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i002-200000000
χ492-2-222-2-222-22-222-2-2-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000002i−2i002-20000000000
χ502-2-222-2-222-22-222-2-2-2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000−2i2i00-220000000000
χ512-2-222-2-222-22-222-2-2-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000002i−2i00-220000000000
χ522-2-222-2-222-22-222-2-2-220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000−2i2i002-20000000000
χ53444-4-4-4-4440000-44-40000000000000000000000000000000000000000000000000022−22
χ54444-4-4-4-4440000-44-400000000000000000000000000000000000000000000000000−2222
χ55444-4-4-4-44-400004-440000000000000000000000000000000000000000000000002i2−2i200
χ56444-4-4-4-44-400004-44000000000000000000000000000000000000000000000000−2i22i200
χ574-44-44-44-404-4-440000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ584-44-44-44-404-4-44000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-44-44-44-40-444-40000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ604-44-44-44-40-444-4000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ614-4-444-4-44-44-44-4-444-4400000000000000000000000000000000000000000000000000
χ624-4-444-4-44-4-44-44-4444-400000000000000000000000000000000000000000000000000
χ634-4-4-4-444440000-4-44000000000000000000000000000000000000000000000022−220000
χ644-4-4-4-444440000-4-440000000000000000000000000000000000000000000000−22220000
χ654-4-4-4-4444-4000044-40000000000000000000000000000000000000000000022−22000000
χ664-4-4-4-4444-4000044-400000000000000000000000000000000000000000000−2222000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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