Finite Group Databasebeta

← Group #311337

Character table — Group #311337

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888244444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-11-1-11111-1-11-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111-1-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-11111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11111-1111-1-111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-1111-1
χ172222222222-2-22-2-22-22222-2000000000022-2-200-2-22200000000-2-20000000000000000
χ182222222222-2-22-2-22-22222-20000000000-2-2-2-20022-2-200000000220000000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-20000000000222200-2-2-2-200000000220000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-20000000000-2-22200222200000000-2-20000000000000000
χ2122222222-2-222-222-2-20000-22222-2-2-2-222000022000000000000000000-2-20000000000
χ2222222222-2-222-222-2-20000-22222-2-2-2-2-2-20000-2-2000000000000000000220000000000
χ2322222222-2-222-222-2-20000-2-2-2-2-22222220000-2-2000000000000000000-220000000000
χ2422222222-2-222-222-2-20000-2-2-2-2-22222-2-20000220000000000000000002-20000000000
χ2522-22-2-22-22-2-2-2222-2-2000022i2i−2i−2i2i2i−2i−2i00000000000000000000000000002i−2i2-2000000
χ2622-22-2-22-22-2-2-2222-2-2000022i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i-22000000
χ2722-22-2-22-22-2-2-2222-2-200002−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i-22000000
χ2822-22-2-22-22-2-2-2222-2-200002−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i2-2000000
χ2922-22-2-22-2-2222-2-2-22-22i2i−2i−2i20000000000002i−2i00000000002i2i−2i−2i0022-2-2000000000000
χ3022-22-2-22-2-2222-2-2-22-22i2i−2i−2i20000000000002i−2i0000000000−2i−2i2i2i00-2-222000000000000
χ3122-22-2-22-2-2222-2-2-22-2−2i−2i2i2i2000000000000−2i2i00000000002i2i−2i−2i00-2-222000000000000
χ3222-22-2-22-2-2222-2-2-22-2−2i−2i2i2i2000000000000−2i2i0000000000−2i−2i2i2i0022-2-2000000000000
χ3322-22-2-22-2-22-2-2-222222i2i−2i−2i-22i2i−2i−2i−2i−2i2i2i0000−2i2i00000022-2-20000000000000000000000
χ3422-22-2-22-2-22-2-2-222222i2i−2i−2i-2−2i−2i2i2i2i2i−2i−2i0000−2i2i000000-2-2220000000000000000000000
χ3522-22-2-22-2-22-2-2-22222−2i−2i2i2i-22i2i−2i−2i−2i−2i2i2i00002i−2i000000-2-2220000000000000000000000
χ3622-22-2-22-2-22-2-2-22222−2i−2i2i2i-2−2i−2i2i2i2i2i−2i−2i00002i−2i00000022-2-20000000000000000000000
χ372-222-2-2-222200-200-202i−2i2i−2i02−22−22−22−2000000002-200i2−i2i2−i22−22−22i−2ii2−i2i2−i2000000000000
χ382-222-2-2-222200-200-202i−2i2i−2i02−22−22−22−200000000-2200i2−i2i2−i2−22−22−2i2i−i2i2−i2i2000000000000
χ392-222-2-2-222200-200-202i−2i2i−2i0−22−22−22−22000000002-200−i2i2−i2i2−22−222i−2i−i2i2−i2i2000000000000
χ402-222-2-2-222200-200-202i−2i2i−2i0−22−22−22−2200000000-2200−i2i2−i2i22−22−2−2i2ii2−i2i2−i2000000000000
χ412-222-2-2-222200-200-20−2i2i−2i2i02−22−22−22−2000000002-200−i2i2−i2i22−22−2−2i2i−i2i2−i2i2000000000000
χ422-222-2-2-222200-200-20−2i2i−2i2i02−22−22−22−200000000-2200−i2i2−i2i2−22−222i−2ii2−i2i2−i2000000000000
χ432-222-2-2-222200-200-20−2i2i−2i2i0−22−22−22−22000000002-200i2−i2i2−i2−22−22−2i2ii2−i2i2−i2000000000000
χ442-222-2-2-222200-200-20−2i2i−2i2i0−22−22−22−2200000000-2200i2−i2i2−i22−22−22i−2i−i2i2−i2i2000000000000
χ452-2-2222-2-2-2200200-202-2-220i2−i2−i2i2−i2i2i2−i2002-20000002-2−i2i2i2−i2i2−i2−i2i200−i2i2i2−i2000000000000
χ462-2-2222-2-2-2200200-202-2-220i2−i2−i2i2−i2i2i2−i200-22000000-22−i2i2i2−i2−i2i2i2−i200i2−i2−i2i2000000000000
χ472-2-2222-2-2-2200200-202-2-220−i2i2i2−i2i2−i2−i2i2002-20000002-2i2−i2−i2i2−i2i2i2−i200i2−i2−i2i2000000000000
χ482-2-2222-2-2-2200200-202-2-220−i2i2i2−i2i2−i2−i2i200-22000000-22i2−i2−i2i2i2−i2−i2i200−i2i2i2−i2000000000000
χ492-2-2222-2-2-2200200-20-222-20i2−i2−i2i2−i2i2i2−i2002-2000000-22i2−i2−i2i2i2−i2−i2i200i2−i2−i2i2000000000000
χ502-2-2222-2-2-2200200-20-222-20i2−i2−i2i2−i2i2i2−i200-220000002-2i2−i2−i2i2−i2i2i2−i200−i2i2i2−i2000000000000
χ512-2-2222-2-2-2200200-20-222-20−i2i2i2−i2i2−i2−i2i2002-2000000-22−i2i2i2−i2−i2i2i2−i200−i2i2i2−i2000000000000
χ522-2-2222-2-2-2200200-20-222-20−i2i2i2−i2i2−i2−i2i200-220000002-2−i2i2i2−i2i2−i2−i2i200i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ5444-44-4-44-44-4444-4-4-440000-40000000000000000000000000000000000000000000000
χ554-444-4-4-44-4-400400400000022−2222−22−2222−222200000000000000000000000000000000000000
χ564-444-4-4-44-4-4004004000000−2222−222222−2222−2200000000000000000000000000000000000000
χ574-44-44-44-4004-404-40000000000000004i−4i000000000000000000000000000000000000
χ584-44-44-44-4004-404-4000000000000000−4i4i000000000000000000000000000000000000
χ594-44-44-44-400-440-44000000000000000000000000000000000000000000000002i2−2i20000
χ604-44-44-44-400-440-4400000000000000000000000000000000000000000000000−2i22i20000
χ614-4-4444-4-44-400-40040000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ624-4-4444-4-44-400-4004000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ634-4-4-4-4444004-40-44000000000000000000000000000000000000000000000000022−2200
χ644-4-4-4-4444004-40-440000000000000000000000000000000000000000000000000−222200
χ654-4-4-4-444400-4404-40000000000000000000004-4000000000000000000000000000000
χ664-4-4-4-444400-4404-4000000000000000000000-44000000000000000000000000000000
χ67888-8-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6888-8-88-8-88000000000000000000000000000000000000000000000000000000000000

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