Finite Group Databasebeta

← Group #242005

Character table — Group #242005

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422444444444444448888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ41111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111
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
χ911111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1211111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1411111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ17222222222222222222-2-222-2-2-2-2-2-2-2-20000220000-2-2-2-2220000000000000000000000000000
χ18222222222222222222-2-222-2-2-2-2-2-2-2-20000-2-200002222-2-20000000000000000000000000000
χ19222222222222-2-2-2-2-2-222-2-22222-2-2-2-2222200-2-2-2-20000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-2-20022220000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-2002-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2200-22000000
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-22222-2-20000220000-2-222-2-20000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-22222-2-20000-2-2000022-2-2220000000000000000000000000000
χ2522222222-2-2-2-2-2-2222222-2-222-2-222-2-222-2-200-2-2220000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-222-2-222-2-2-2-2220022-2-20000000000000000000000000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000-22002-2000000
χ2922-222-2-2-222-2-2-2-222-2-200220000000000002i−2i000000002i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ3022-222-2-2-222-2-2-2-222-2-200220000000000002i−2i000000002i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ3122-222-2-2-222-2-2-2-222-2-20022000000000000−2i2i00000000−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ3222-222-2-2-222-2-2-2-222-2-20022000000000000−2i2i00000000−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ3322-222-2-2-2-2-222-2-2-2-22200220000000000002i−2i00000000−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ3422-222-2-2-2-2-222-2-2-2-22200220000000000002i−2i00000000−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ3522-222-2-2-2-2-222-2-2-2-2220022000000000000−2i2i000000002i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ3622-222-2-2-2-2-222-2-2-2-2220022000000000000−2i2i000000002i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ372-222-2-2-222i−2i2i−2i2-22i−2i2i−2i2-22-22-22i−2i2i−2i2-200000000000000000000000000000000000000002i−2i2-2
χ382-222-2-2-222i−2i2i−2i2-22i−2i2i−2i2-22-22-22i−2i2i−2i2-20000000000000000000000000000000000000000−2i2i-22
χ392-222-2-2-222i−2i2i−2i2-22i−2i2i−2i-222-2-22−2i2i−2i2i-2200000000000000000000000000000000002i−2i002-20000
χ402-222-2-2-222i−2i2i−2i2-22i−2i2i−2i-222-2-22−2i2i−2i2i-220000000000000000000000000000000000−2i2i00-220000
χ412-222-2-2-222i−2i2i−2i-22−2i2i−2i2i2-2-222-22i−2i−2i2i-220000000000000000000000002-22-22i−2i2i−2i000000000000
χ422-222-2-2-222i−2i2i−2i-22−2i2i−2i2i2-2-222-22i−2i−2i2i-22000000000000000000000000-22-22−2i2i−2i2i000000000000
χ432-222-2-2-222i−2i2i−2i-22−2i2i−2i2i-22-22-22−2i2i2i−2i2-200000000000000002i−2i2i−2i2-22-200000000000000000000
χ442-222-2-2-222i−2i2i−2i-22−2i2i−2i2i-22-22-22−2i2i2i−2i2-20000000000000000−2i2i−2i2i-22-2200000000000000000000
χ452-222-2-2-22−2i2i−2i2i2-2−2i2i−2i2i2-22-22-2−2i2i−2i2i2-200000000000000000000000000000000000000002i−2i-22
χ462-222-2-2-22−2i2i−2i2i2-2−2i2i−2i2i2-22-22-2−2i2i−2i2i2-20000000000000000000000000000000000000000−2i2i2-2
χ472-222-2-2-22−2i2i−2i2i2-2−2i2i−2i2i-222-2-222i−2i2i−2i-2200000000000000000000000000000000002i−2i00-220000
χ482-222-2-2-22−2i2i−2i2i2-2−2i2i−2i2i-222-2-222i−2i2i−2i-220000000000000000000000000000000000−2i2i002-20000
χ492-222-2-2-22−2i2i−2i2i-222i−2i2i−2i2-2-222-2−2i2i2i−2i-220000000000000000000000002-22-2−2i2i−2i2i000000000000
χ502-222-2-2-22−2i2i−2i2i-222i−2i2i−2i2-2-222-2−2i2i2i−2i-22000000000000000000000000-22-222i−2i2i−2i000000000000
χ512-222-2-2-22−2i2i−2i2i-222i−2i2i−2i-22-22-222i−2i−2i2i2-200000000000000002i−2i2i−2i-22-2200000000000000000000
χ522-222-2-2-22−2i2i−2i2i-222i−2i2i−2i-22-22-222i−2i−2i2i2-20000000000000000−2i2i−2i2i2-22-200000000000000000000
χ532-2-22-222-22i−2i−2i2i2-2−2i2i2i−2i00-220000000000000000002-22i−2i002−2−22−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ542-2-22-222-22i−2i−2i2i2-2−2i2i2i−2i00-220000000000000000002-22i−2i00−222−2i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ552-2-22-222-22i−2i−2i2i2-2−2i2i2i−2i00-22000000000000000000-22−2i2i002−2−22−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ562-2-22-222-22i−2i−2i2i2-2−2i2i2i−2i00-22000000000000000000-22−2i2i00−222−2i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ572-2-22-222-2−2i2i2i−2i2-22i−2i−2i2i00-220000000000000000002-2−2i2i002−2−22i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ582-2-22-222-2−2i2i2i−2i2-22i−2i−2i2i00-220000000000000000002-2−2i2i00−222−2−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ592-2-22-222-2−2i2i2i−2i2-22i−2i−2i2i00-22000000000000000000-222i−2i002−2−22i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ602-2-22-222-2−2i2i2i−2i2-22i−2i−2i2i00-22000000000000000000-222i−2i00−222−2−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ6144-444-4-4-444-4-444-4-44400-4-40000000000000000000000000000000000000000000000000000
χ6244-444-4-4-4-4-4444444-4-400-4-40000000000000000000000000000000000000000000000000000
χ6344-4-4-44-4400000000004-400-44000000000000004i−4i0000000000000000000000000000000000
χ6444-4-4-44-4400000000004-400-4400000000000000−4i4i0000000000000000000000000000000000
χ6544-4-4-44-440000000000-44004-40000000000004i−4i000000000000000000000000000000000000
χ6644-4-4-44-440000000000-44004-4000000000000−4i4i000000000000000000000000000000000000
χ674-4-44-444-44i−4i−4i4i-444i−4i−4i4i004-40000000000000000000000000000000000000000000000000000
χ684-4-44-444-4−4i4i4i−4i-44−4i4i4i−4i004-40000000000000000000000000000000000000000000000000000
χ694-4-4-44-44400000000004400-4-4000000004i−4i0000000000000000000000000000000000000000
χ704-4-4-44-44400000000004400-4-400000000−4i4i0000000000000000000000000000000000000000
χ714-4-4-44-4440000000000-4-400440000004-4000000000000000000000000000000000000000000
χ724-4-4-44-4440000000000-4-40044000000-44000000000000000000000000000000000000000000
χ73888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000

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