Finite Group Databasebeta

← Group #499155

Character table — Group #499155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111122222222224444444444888888881616161616161616111122222222224444444444888888881616161616161616
order12222244448888881616161616161616448816161616222288882222224444888888161616161616161644881616161622228888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ92222222222-2-2-2-2-2-20000000022-2-20000000000002222222222-2-2-2-2-2-20000000022-2-2000000000000
χ102222222222-2-2-2-2-2-200000000-2-2220000000000002222222222-2-2-2-2-2-200000000-2-222000000000000
χ11222222-2-2-2-20000002222−2−2−2−2002i−2ii2i2−i2−i200000000222222-2-2-2-20000002222−2−2−2−2002i−2ii2i2−i2−i200000000
χ12222222-2-2-2-20000002222−2−2−2−200−2i2i−i2−i2i2i200000000222222-2-2-2-20000002222−2−2−2−200−2i2i−i2−i2i2i200000000
χ13222222-2-2-2-2000000−2−2−2−22222002i−2i−i2−i2i2i200000000222222-2-2-2-2000000−2−2−2−22222002i−2i−i2−i2i2i200000000
χ14222222-2-2-2-2000000−2−2−2−2222200−2i2ii2i2−i2−i200000000222222-2-2-2-2000000−2−2−2−2222200−2i2ii2i2−i2−i200000000
χ152222-2-222-2-22222-2-222-2-222-2-200000000000000002222-2-222-2-22222-2-222-2-222-2-20000000000000000
χ162222-2-222-2-22222-2-2-2-222-2-22200000000000000002222-2-222-2-22222-2-2-2-222-2-2220000000000000000
χ172222-2-222-2-2-2-2-2-2220000000000002i−2i2i−2i000000002222-2-222-2-2-2-2-2-2220000000000002i−2i2i−2i00000000
χ182222-2-222-2-2-2-2-2-222000000000000−2i2i−2i2i000000002222-2-222-2-2-2-2-2-222000000000000−2i2i−2i2i00000000
χ192222-2-2-2-22200000022−2−2−2−2222-2002−2−22000000002222-2-2-2-22200000022−2−2−2−2222-2002−2−2200000000
χ202222-2-2-2-22200000022−2−2−2−222-2200−222−2000000002222-2-2-2-22200000022−2−2−2−222-2200−222−200000000
χ212222-2-2-2-222000000−2−22222−2−22-200−222−2000000002222-2-2-2-222000000−2−22222−2−22-200−222−200000000
χ222222-2-2-2-222000000−2−22222−2−2-22002−2−22000000002222-2-2-2-222000000−2−22222−2−2-22002−2−2200000000
χ2322-2-22-22-22-222-2-22-200000000000000000000002i−2i22-2-22-22-22-222-2-22-200000000000000000000002i−2i
χ2422-2-22-22-22-222-2-22-20000000000000000000000−2i2i22-2-22-22-22-222-2-22-20000000000000000000000−2i2i
χ2522-2-22-22-22-2-2-222-220000000000000000002-2000022-2-22-22-22-2-2-222-220000000000000000002-20000
χ2622-2-22-22-22-2-2-222-22000000000000000000-22000022-2-22-22-22-2-2-222-22000000000000000000-220000
χ2722-2-2-222-2-2222-2-2-22000000000000000000002i−2i0022-2-2-222-2-2222-2-2-22000000000000000000002i−2i00
χ2822-2-2-222-2-2222-2-2-2200000000000000000000−2i2i0022-2-2-222-2-2222-2-2-2200000000000000000000−2i2i00
χ2922-2-2-222-2-22-2-2222-200000000000000002-200000022-2-2-222-2-22-2-2222-200000000000000002-2000000
χ3022-2-2-222-2-22-2-2222-20000000000000000-2200000022-2-2-222-2-22-2-2222-20000000000000000-22000000
χ3144-4-44-4-44-4400000000000000000000000000000044-4-44-4-44-44000000000000000000000000000000
χ3244-4-4-44-444-400000000000000000000000000000044-4-4-44-444-4000000000000000000000000000000
χ334-44-400000022−2222−2200002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ500000000000000004-44-400000022−2222−2200002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ50000000000000000
χ344-44-400000022−2222−220000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ500000000000000004-44-400000022−2222−220000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ50000000000000000
χ354-44-4000000−2222−222200002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ700000000000000004-44-4000000−2222−222200002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ70000000000000000
χ364-44-4000000−2222−22220000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ700000000000000004-44-4000000−2222−22220000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ70000000000000000
χ374-4-4400000022−22−2222002ζ3−2ζ5−2ζ3+2ζ5002ζ−2ζ7−2ζ+2ζ70000000000000000004-4-4400000022−22−2222002ζ3−2ζ5−2ζ3+2ζ5002ζ−2ζ7−2ζ+2ζ7000000000000000000
χ384-4-4400000022−22−222200−2ζ3+2ζ52ζ3−2ζ500−2ζ+2ζ72ζ−2ζ70000000000000000004-4-4400000022−22−222200−2ζ3+2ζ52ζ3−2ζ500−2ζ+2ζ72ζ−2ζ7000000000000000000
χ394-4-44000000−222222−22002ζ−2ζ7−2ζ+2ζ700−2ζ3+2ζ52ζ3−2ζ50000000000000000004-4-44000000−222222−22002ζ−2ζ7−2ζ+2ζ700−2ζ3+2ζ52ζ3−2ζ5000000000000000000
χ404-4-44000000−222222−2200−2ζ+2ζ72ζ−2ζ7002ζ3−2ζ5−2ζ3+2ζ50000000000000000004-4-44000000−222222−2200−2ζ+2ζ72ζ−2ζ7002ζ3−2ζ5−2ζ3+2ζ5000000000000000000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ43111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ44111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ451111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111
χ461111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ471111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ481111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ492222222222-2-2-2-2-2-20000000022-2-2000000000000-2-2-2-2-2-2-2-2-2-222222200000000-2-222000000000000
χ502222222222-2-2-2-2-2-200000000-2-222000000000000-2-2-2-2-2-2-2-2-2-22222220000000022-2-2000000000000
χ51222222-2-2-2-20000002222−2−2−2−2002i−2ii2i2−i2−i200000000-2-2-2-2-2-22222000000−2−2−2−2222200−2i2i−i2−i2i2i200000000
χ52222222-2-2-2-20000002222−2−2−2−200−2i2i−i2−i2i2i200000000-2-2-2-2-2-22222000000−2−2−2−22222002i−2ii2i2−i2−i200000000
χ53222222-2-2-2-2000000−2−2−2−22222002i−2i−i2−i2i2i200000000-2-2-2-2-2-222220000002222−2−2−2−200−2i2ii2i2−i2−i200000000
χ54222222-2-2-2-2000000−2−2−2−2222200−2i2ii2i2−i2−i200000000-2-2-2-2-2-222220000002222−2−2−2−2002i−2i−i2−i2i2i200000000
χ552222-2-222-2-22222-2-222-2-222-2-20000000000000000-2-2-2-222-2-222-2-2-2-222-2-222-2-2220000000000000000
χ562222-2-222-2-22222-2-2-2-222-2-2220000000000000000-2-2-2-222-2-222-2-2-2-22222-2-222-2-20000000000000000
χ572222-2-222-2-2-2-2-2-2220000000000002i−2i2i−2i00000000-2-2-2-222-2-2222222-2-2000000000000−2i2i−2i2i00000000
χ582222-2-222-2-2-2-2-2-222000000000000−2i2i−2i2i00000000-2-2-2-222-2-2222222-2-20000000000002i−2i2i−2i00000000
χ592222-2-2-2-22200000022−2−2−2−2222-2002−2−2200000000-2-2-2-22222-2-2000000−2−22222−2−2-2200−222−200000000
χ602222-2-2-2-22200000022−2−2−2−222-2200−222−200000000-2-2-2-22222-2-2000000−2−22222−2−22-2002−2−2200000000
χ612222-2-2-2-222000000−2−22222−2−22-200−222−200000000-2-2-2-22222-2-200000022−2−2−2−222-22002−2−2200000000
χ622222-2-2-2-222000000−2−22222−2−2-22002−2−2200000000-2-2-2-22222-2-200000022−2−2−2−2222-200−222−200000000
χ6322-2-22-22-22-222-2-22-200000000000000000000002i−2i-2-222-22-22-22-2-222-220000000000000000000000−2i2i
χ6422-2-22-22-22-222-2-22-20000000000000000000000−2i2i-2-222-22-22-22-2-222-2200000000000000000000002i−2i
χ6522-2-22-22-22-2-2-222-220000000000000000002-20000-2-222-22-22-2222-2-22-2000000000000000000-220000
χ6622-2-22-22-22-2-2-222-22000000000000000000-220000-2-222-22-22-2222-2-22-20000000000000000002-20000
χ6722-2-2-222-2-2222-2-2-22000000000000000000002i−2i00-2-2222-2-222-2-2-2222-200000000000000000000−2i2i00
χ6822-2-2-222-2-2222-2-2-2200000000000000000000−2i2i00-2-2222-2-222-2-2-2222-2000000000000000000002i−2i00
χ6922-2-2-222-2-22-2-2222-200000000000000002-2000000-2-2222-2-222-222-2-2-220000000000000000-22000000
χ7022-2-2-222-2-22-2-2222-20000000000000000-22000000-2-2222-2-222-222-2-2-2200000000000000002-2000000
χ7144-4-44-4-44-44000000000000000000000000000000-4-444-444-44-4000000000000000000000000000000
χ7244-4-4-44-444-4000000000000000000000000000000-4-4444-44-4-44000000000000000000000000000000
χ734-44-400000022−2222−2200002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ50000000000000000-44-44000000−2222−22220000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ50000000000000000
χ744-44-400000022−2222−220000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ50000000000000000-44-44000000−2222−222200002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ50000000000000000
χ754-44-4000000−2222−222200002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ70000000000000000-44-4400000022−2222−220000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ70000000000000000
χ764-44-4000000−2222−22220000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ70000000000000000-44-4400000022−2222−2200002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ70000000000000000
χ774-4-4400000022−22−2222002ζ3−2ζ5−2ζ3+2ζ5002ζ−2ζ7−2ζ+2ζ7000000000000000000-444-4000000−222222−2200−2ζ3+2ζ52ζ3−2ζ500−2ζ+2ζ72ζ−2ζ7000000000000000000
χ784-4-4400000022−22−222200−2ζ3+2ζ52ζ3−2ζ500−2ζ+2ζ72ζ−2ζ7000000000000000000-444-4000000−222222−22002ζ3−2ζ5−2ζ3+2ζ5002ζ−2ζ7−2ζ+2ζ7000000000000000000
χ794-4-44000000−222222−22002ζ−2ζ7−2ζ+2ζ700−2ζ3+2ζ52ζ3−2ζ5000000000000000000-444-400000022−22−222200−2ζ+2ζ72ζ−2ζ7002ζ3−2ζ5−2ζ3+2ζ5000000000000000000
χ804-4-44000000−222222−2200−2ζ+2ζ72ζ−2ζ7002ζ3−2ζ5−2ζ3+2ζ5000000000000000000-444-400000022−22−2222002ζ−2ζ7−2ζ+2ζ700−2ζ3+2ζ52ζ3−2ζ5000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.