Finite Group Databasebeta

← Group #243228

Character table — Group #243228

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ1511111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ1611111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1722222222222222-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ19222222222222-2-222-2-2-2-2-2-222-2-222-2-2000000000000000022-2-222-2-200000000000000000000
χ20222222222222-2-222-2-2-2-2-2-222-2-222-2-20000000000000000-2-222-2-22200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-2-2-2222222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-2-2-22222-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2222222-2-222-2-2-2-222000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-222-2-2-2-2220000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ292-2222-2-2-222-2-22-22222-2-22-2-2-22-22-22-200000000000000000000000000000000000000002-22-2
χ302-2222-2-2-222-2-22-22222-2-22-2-2-22-22-22-20000000000000000000000000000000000000000-22-22
χ312-2222-2-2-222-2-22-2-2-222-2-22-222-22-22-22000000000000000000000000000000002i−2i00002i−2i0000
χ322-2222-2-2-222-2-22-2-2-222-2-22-222-22-22-2200000000000000000000000000000000−2i2i0000−2i2i0000
χ332-2222-2-2-222-2-2-2222-2-222-22-2-2-222-2-2200000000000000000000000022-2-222-2-2000000000000
χ342-2222-2-2-222-2-2-2222-2-222-22-2-2-222-2-22000000000000000000000000-2-222-2-222000000000000
χ352-2222-2-2-222-2-2-22-2-2-2-222-22222-2-222-200000000000000000000000000000000002i−2i2i−2i000000
χ362-2222-2-2-222-2-2-22-2-2-2-222-22222-2-222-20000000000000000000000000000000000−2i2i−2i2i000000
χ372-2222-2-2-2-2-2222-222-2-2222-2-2-22-2-22-2200000000000000000000000000000000000000002-2-22
χ382-2222-2-2-2-2-2222-222-2-2222-2-2-22-2-22-220000000000000000000000000000000000000000-222-2
χ392-2222-2-2-2-2-2222-2-2-2-2-2222-222-222-22-2000000000000000000000000000000002i−2i0000−2i2i0000
χ402-2222-2-2-2-2-2222-2-2-2-2-2222-222-222-22-200000000000000000000000000000000−2i2i00002i−2i0000
χ412-2222-2-2-2-2-222-222222-2-2-22-2-2-22-222-200000000000000000000000022-2-2-2-222000000000000
χ422-2222-2-2-2-2-222-222222-2-2-22-2-2-22-222-2000000000000000000000000-2-22222-2-2000000000000
χ432-2222-2-2-2-2-222-22-2-222-2-2-22222-22-2-2200000000000000000000000000000000002i−2i−2i2i000000
χ442-2222-2-2-2-2-222-22-2-222-2-2-22222-22-2-220000000000000000000000000000000000−2i2i2i−2i000000
χ452-22-2-22-222-22-222002-22-2-2-2000000002i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000000000
χ462-22-2-22-222-22-222002-22-2-2-2000000002i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000000000
χ472-22-2-22-222-22-222002-22-2-2-200000000−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000000000
χ482-22-2-22-222-22-222002-22-2-2-200000000−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000000000
χ492-22-2-22-222-22-2-2-200-22-22220000000000002-22-22−2−222−2−222−2−222−2−2200000000000000000000
χ502-22-2-22-222-22-2-2-200-22-22220000000000002-22-2−222−2−222−2−222−2−222−200000000000000000000
χ512-22-2-22-222-22-2-2-200-22-2222000000000000-22-222−2−222−2−22−222−2−222−200000000000000000000
χ522-22-2-22-222-22-2-2-200-22-2222000000000000-22-22−222−2−222−22−2−222−2−2200000000000000000000
χ532-22-2-22-22-22-222200-22-22-2-2000000002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000000000000000
χ542-22-2-22-22-22-222200-22-22-2-2000000002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000000000000000
χ552-22-2-22-22-22-222200-22-22-2-200000000−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000000000000000
χ562-22-2-22-22-22-222200-22-22-2-200000000−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000000000000000
χ572-22-2-22-22-22-22-2-2002-22-2220000000000002-2-222−2−22−222−22−2−22−222−200000000000000000000
χ582-22-2-22-22-22-22-2-2002-22-2220000000000002-2-22−222−22−2−22−222−22−2−2200000000000000000000
χ592-22-2-22-22-22-22-2-2002-22-222000000000000-222-22−2−22−222−2−222−22−2−2200000000000000000000
χ602-22-2-22-22-22-22-2-2002-22-222000000000000-222-2−222−22−2−222−2−22−222−200000000000000000000
χ61444-4-4-44-44-4-444-4004-4-44-440000000000000000000000000000000000000000000000000000
χ62444-4-4-44-44-4-44-4400-444-44-40000000000000000000000000000000000000000000000000000
χ63444-4-4-44-4-444-44-400-444-4-440000000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-444-4-44004-4-444-40000000000000000000000000000000000000000000000000000
χ6544-44-44-4-40000004-40000004-400000000000000000000000000000022−2222−220000000000000000
χ6644-44-44-4-40000004-40000004-4000000000000000000000000000000−2222−22220000000000000000
χ6744-44-44-4-4000000-44000000-44000000000000000000000000000000000022−2222−22000000000000
χ6844-44-44-4-4000000-44000000-440000000000000000000000000000000000−2222−2222000000000000
χ694-4-44-4-4440000004-4000000-4400000000000000000000000000000022−22−22220000000000000000
χ704-4-44-4-4440000004-4000000-44000000000000000000000000000000−222222−220000000000000000
χ714-4-44-4-444000000-440000004-4000000000000000000000000000000000022−22−2222000000000000
χ724-4-44-4-444000000-440000004-40000000000000000000000000000000000−222222−22000000000000
χ7388-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000

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