Finite Group Databasebeta

← Group #316429

Character table — Group #316429

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888824444444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-111-1-111111111-11111-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111111111-1-111-1-111111111-11111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ121111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-2-2222-2-2-2-22222-2-2-2-220000-20000-2-200002200000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-2-2-2222220000-20000220000-2-200000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2222222-2-2-2-2-2000020000220000-2-200000000000000000000
χ2022222222222-2-2-2-22-2-2-2-222-2-2-2-22222-2000020000-2-200002200000000000000000000
χ2122222222-2-2-22222-222-2-22200000000-222-2-2-222-2-20000000000000000000000000000
χ2222222222-2-2-22222-222-2-22200000000-2-2-222-2-2-2220000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-200000000222-2-22-2-2220000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2000000002-2-222222-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000-2000020000002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000-200002000000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000000020000-20000002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000000020000-2000000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ2922-2-2-222-200022-2-202i−2i002i−2i22−2−222−2−20002-20002i−2ii2−i22−22−2i2−i2i2−i2i2−i20000000000000000
χ3022-2-2-222-200022-2-202i−2i002i−2i22−2−222−2−2000-22000−2i2ii2−i2−22−22i2−i2−i2i2−i2i20000000000000000
χ3122-2-2-222-200022-2-202i−2i002i−2i−2−222−2−2220002-20002i−2i−i2i2−22−22−i2i2−i2i2−i2i20000000000000000
χ3222-2-2-222-200022-2-202i−2i002i−2i−2−222−2−222000-22000−2i2i−i2i22−22−2−i2i2i2−i2i2−i20000000000000000
χ3322-2-2-222-200022-2-20−2i2i00−2i2i22−2−222−2−20002-2000−2i2i−i2i22−22−2−i2i2−i2i2−i2i20000000000000000
χ3422-2-2-222-200022-2-20−2i2i00−2i2i22−2−222−2−2000-220002i−2i−i2i2−22−22−i2i2i2−i2i2−i20000000000000000
χ3522-2-2-222-200022-2-20−2i2i00−2i2i−2−222−2−2220002-2000−2i2ii2−i2−22−22i2−i2i2−i2i2−i20000000000000000
χ3622-2-2-222-200022-2-20−2i2i00−2i2i−2−222−2−222000-220002i−2ii2−i22−22−2i2−i2−i2i2−i2i20000000000000000
χ3722-2-2-222-2000-2-22202i−2i00−2i2i22−2−2−2−22202i−2i0002-200−i2i2i2−i2−i2i2i2−i2−222−20000000000000000
χ3822-2-2-222-2000-2-22202i−2i00−2i2i22−2−2−2−2220−2i2i000-2200−i2i2−i2i2i2−i2i2−i22−2−220000000000000000
χ3922-2-2-222-2000-2-22202i−2i00−2i2i−2−22222−2−202i−2i0002-200i2−i2−i2i2i2−i2−i2i22−2−220000000000000000
χ4022-2-2-222-2000-2-22202i−2i00−2i2i−2−22222−2−20−2i2i000-2200i2−i2i2−i2−i2i2−i2i2−222−20000000000000000
χ4122-2-2-222-2000-2-2220−2i2i002i−2i22−2−2−2−22202i−2i000-2200i2−i2i2−i2−i2i2−i2i22−2−220000000000000000
χ4222-2-2-222-2000-2-2220−2i2i002i−2i22−2−2−2−2220−2i2i0002-200i2−i2−i2i2i2−i2−i2i2−222−20000000000000000
χ4322-2-2-222-2000-2-2220−2i2i002i−2i−2−22222−2−202i−2i000-2200−i2i2−i2i2i2−i2i2−i2−222−20000000000000000
χ4422-2-2-222-2000-2-2220−2i2i002i−2i−2−22222−2−20−2i2i0002-200−i2i2i2−i2−i2i2i2−i22−2−220000000000000000
χ452-22-2-2-22222-22-22-2-2002-2002i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i002-200000000
χ462-22-2-2-22222-22-22-2-2002-2002i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i00-2200000000
χ472-22-2-2-22222-22-22-2-2002-200−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i00-2200000000
χ482-22-2-2-22222-22-22-2-2002-200−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i002-200000000
χ492-22-2-2-22222-2-22-22-200-22002i−2i2i−2i−2i2i−2i2i00000000000000000000002i−2i002-20000000000
χ502-22-2-2-22222-2-22-22-200-22002i−2i2i−2i−2i2i−2i2i0000000000000000000000−2i2i00-220000000000
χ512-22-2-2-22222-2-22-22-200-2200−2i2i−2i2i2i−2i2i−2i00000000000000000000002i−2i00-220000000000
χ522-22-2-2-22222-2-22-22-200-2200−2i2i−2i2i2i−2i2i−2i0000000000000000000000−2i2i002-20000000000
χ53444-44-4-4-44-4-4000040000000000000000000000000000000000000000000000000022−22
χ54444-44-4-4-44-4-40000400000000000000000000000000000000000000000000000000−2222
χ55444-44-4-4-4-4440000-400000000000000000000000000000000000000000000000022−2200
χ56444-44-4-4-4-4440000-4000000000000000000000000000000000000000000000000−222200
χ574-444-44-4-44-440000-4000000000000000000000000000000000000000000000022−220000
χ584-444-44-4-44-440000-40000000000000000000000000000000000000000000000−22220000
χ594-444-44-4-4-44-400004000000000000000000000000000000000000000000002i2−2i2000000
χ604-444-44-4-4-44-40000400000000000000000000000000000000000000000000−2i22i2000000
χ614-44-4-4-444-4-444-44-4400-44000000000000000000000000000000000000000000000000
χ624-44-4-4-444-4-44-44-444004-4000000000000000000000000000000000000000000000000
χ634-4-444-44-40004-4-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ644-4-444-44-40004-4-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-4-444-44-4000-444-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ664-4-444-44-4000-444-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ6788-88-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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