Finite Group Databasebeta

← Group #238129

Character table — Group #238129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ911111111-1-1-1-111111-1-1-1-11111-1-1-1-1111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111111-1-1-1-11111-1-1-1-1111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111
χ1111111111-1-1-1-111111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ1211111111-1-1-1-111111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ1311111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-111-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ1611111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-111-1-111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ1722222222222222-2-2-2-2-2-2-222-2-222-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ19222222222222-2-22222222-2-22-2-2-2-2-2-2000000002222-2-2-2-20000000000000000000000000000
χ20222222222222-2-22222222-2-22-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-22220000000000000000000000000000000000002-22-20000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-2222000000000000000000000000000000000000-22-220000
χ2322222222-2-2-2-222-2-2-2222222-2-2-2-222-222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2222222-2-2-2-222-2-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2222-2-2-2-2-2-22-22222-20000000022-2-2-2-2220000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2-2-2-2-22-22222-200000000-2-22222-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-2222-2-220000000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-2222-2-22000000000000000000000000000000000000-222-20000
χ2922-2-2-22-2222-2-20022-222-2-200-2000000000000002i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ3022-2-2-22-2222-2-20022-222-2-200-2000000000000002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ3122-2-2-22-2222-2-20022-222-2-200-200000000000000−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ3222-2-2-22-2222-2-20022-222-2-200-200000000000000−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ3322-2-2-22-22-2-2220022-2-2-22200-2000000000000002i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ3422-2-2-22-22-2-2220022-2-2-22200-2000000000000002i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ3522-2-2-22-22-2-2220022-2-2-22200-200000000000000−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ3622-2-2-22-22-2-2220022-2-2-22200-200000000000000−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ372-222-22-2-22-22-2222-222-22-2-2-2-222-22-2-2000000000000000000000000000000002-22-200000000
χ382-222-22-2-22-22-2222-222-22-2-2-2-222-22-2-200000000000000000000000000000000-22-2200000000
χ392-222-22-2-22-22-222-22-2-22-22-2-22-22-2-22200000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ402-222-22-2-22-22-222-22-2-22-22-2-22-22-2-2220000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ412-222-22-2-22-22-2-2-22-222-22-222-2-2-22-22200000000000000000000000000000000000000002i−2i2i−2i
χ422-222-22-2-22-22-2-2-22-222-22-222-2-2-22-2220000000000000000000000000000000000000000−2i2i−2i2i
χ432-222-22-2-22-22-2-2-2-22-2-22-222222-222-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ442-222-22-2-22-22-2-2-2-22-2-22-222222-222-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ452-222-22-2-2-22-22222-22-22-22-2-2-22-22-22-2000000000000000000000000000000002-2-2200000000
χ462-222-22-2-2-22-22222-22-22-22-2-2-22-22-22-200000000000000000000000000000000-222-200000000
χ472-222-22-2-2-22-2222-22-22-22-2-2-22-2-222-2200000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ482-222-22-2-2-22-2222-22-22-22-2-2-22-2-222-220000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ492-222-22-2-2-22-22-2-22-22-22-2222-2-22-22-2200000000000000000000000000000000000000002i−2i−2i2i
χ502-222-22-2-2-22-22-2-22-22-22-2222-2-22-22-220000000000000000000000000000000000000000−2i2i2i−2i
χ512-222-22-2-2-22-22-2-2-22-22-22-222222-2-22-20000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ522-222-22-2-2-22-22-2-2-22-22-22-222222-2-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ532-2-2-2222-22-2-2200-222-222-200-20000000000000000002i−2i2i−2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ542-2-2-2222-22-2-2200-222-222-200-20000000000000000002i−2i2i−2i−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ552-2-2-2222-22-2-2200-222-222-200-2000000000000000000−2i2i−2i2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ562-2-2-2222-22-2-2200-222-222-200-2000000000000000000−2i2i−2i2i−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ572-2-2-2222-2-222-200-2222-2-2200-20000000000000000002i−2i−2i2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ582-2-2-2222-2-222-200-2222-2-2200-20000000000000000002i−2i−2i2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ592-2-2-2222-2-222-200-2222-2-2200-2000000000000000000−2i2i2i−2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ602-2-2-2222-2-222-200-2222-2-2200-2000000000000000000−2i2i2i−2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ61444-44-4-4-400004-400000004-40000000004-40000000000000000000000000000000000000000
χ62444-44-4-4-400004-400000004-4000000000-440000000000000000000000000000000000000000
χ63444-44-4-4-40000-440000000-4400000004-4000000000000000000000000000000000000000000
χ64444-44-4-4-40000-440000000-440000000-44000000000000000000000000000000000000000000
χ6544-4-4-44-4444-4-400-4-44-4-44400400000000000000000000000000000000000000000000000000
χ6644-4-4-44-44-4-44400-4-4444-4-400400000000000000000000000000000000000000000000000000
χ674-44-4-4-44400004-40000000-44000000000004-400000000000000000000000000000000000000
χ684-44-4-4-44400004-40000000-4400000000000-4400000000000000000000000000000000000000
χ694-44-4-4-4440000-4400000004-400000000000004-4000000000000000000000000000000000000
χ704-44-4-4-4440000-4400000004-40000000000000-44000000000000000000000000000000000000
χ714-4-4-4444-44-4-44004-4-44-4-4400400000000000000000000000000000000000000000000000000
χ724-4-4-4444-4-444-4004-4-4-444-400400000000000000000000000000000000000000000000000000
χ7388-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000

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