Finite Group Databasebeta

← Group #239798

Character table — Group #239798

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444422444422444444888888888888888888888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111
χ911111111111-1-1-1-111-1-1-1-1111-1-11-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11-111-1-1
χ1011111111111-1-1-1-111-1-1-1-1111-1-11-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-11-1-111
χ1111111111111-1-1-1-111-1-1-1-1111-1-11-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-11-1-111
χ1211111111111-1-1-1-111-1-1-1-1111-1-11-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1111-111-1-1
χ1311111111111-1-1-1-111-1-1-1-1111-1-11-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1111-1-1
χ1411111111111-1-1-1-111-1-1-1-1111-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-111
χ1511111111111-1-1-1-111-1-1-1-1111-1-11-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-111-1-11-1-1-111
χ1611111111111-1-1-1-111-1-1-1-1111-1-11-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1111-1-1
χ17222222222222222-2-2-2-2-2-2-2-2222-2-2-2-200000000000000000000000000000000220000-2-20000
χ18222222222222222-2-2-2-2-2-2-2-2222-2-2-2-200000000000000000000000000000000-2-20000220000
χ1922222222222-2-2-2-2-2-22222-2-22-2-2-222-2000000000000000000000000000000002-20000-220000
χ2022222222222-2-2-2-2-2-22222-2-22-2-2-222-200000000000000000000000000000000-2200002-20000
χ2122222222-2-2-2222222222222-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ2222222222-2-2-2222222222222-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002-22-2
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000-22-22
χ2522222222-2-2-2-2-2-2-222-2-2-2-222-222-222-222-2-2-2-222000000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-222-2-2-2-222-222-222-2-2-22222-2-2000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-2222-2-2200000000000000000000000000000000000000002-2-22
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-2222-2-220000000000000000000000000000000000000000-222-2
χ2922-2-22-22-20002i2i−2i−2i2-22i2i−2i−2i2-20000000002i−2i002-200000000i2i2−i2−i222−2−222−2−2i2i2−i2−i2000000000000
χ3022-2-22-22-20002i2i−2i−2i2-22i2i−2i−2i2-20000000002i−2i002-200000000−i2−i2i2i2−2−222−2−222−i2−i2i2i2000000000000
χ3122-2-22-22-20002i2i−2i−2i2-22i2i−2i−2i2-2000000000−2i2i00-2200000000i2i2−i2−i222−2−2−2−222−i2−i2i2i2000000000000
χ3222-2-22-22-20002i2i−2i−2i2-22i2i−2i−2i2-2000000000−2i2i00-2200000000−i2−i2i2i2−2−22222−2−2i2i2−i2−i2000000000000
χ3322-2-22-22-2000−2i−2i2i2i2-2−2i−2i2i2i2-20000000002i−2i00-2200000000i2i2−i2−i2−2−22222−2−2−i2−i2i2i2000000000000
χ3422-2-22-22-2000−2i−2i2i2i2-2−2i−2i2i2i2-20000000002i−2i00-2200000000−i2−i2i2i222−2−2−2−222i2i2−i2−i2000000000000
χ3522-2-22-22-2000−2i−2i2i2i2-2−2i−2i2i2i2-2000000000−2i2i002-200000000i2i2−i2−i2−2−222−2−222i2i2−i2−i2000000000000
χ3622-2-22-22-2000−2i−2i2i2i2-2−2i−2i2i2i2-2000000000−2i2i002-200000000−i2−i2i2i222−2−222−2−2−i2−i2i2i2000000000000
χ372-22-2-222-20002i−2i2i−2i-222i−2i2i−2i2-200000002-2002i−2i0000000000i2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ382-22-2-222-20002i−2i2i−2i-222i−2i2i−2i2-200000002-2002i−2i0000000000−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ392-22-2-222-20002i−2i2i−2i-222i−2i2i−2i2-20000000-2200−2i2i0000000000i2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ402-22-2-222-20002i−2i2i−2i-222i−2i2i−2i2-20000000-2200−2i2i0000000000−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ412-22-2-222-2000−2i2i−2i2i-22−2i2i−2i2i2-200000002-200−2i2i0000000000i2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ422-22-2-222-2000−2i2i−2i2i-22−2i2i−2i2i2-200000002-200−2i2i0000000000−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ432-22-2-222-2000−2i2i−2i2i-22−2i2i−2i2i2-20000000-22002i−2i0000000000i2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ442-22-2-222-2000−2i2i−2i2i-22−2i2i−2i2i2-20000000-22002i−2i0000000000−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ452-2-22-2-22222-22-2-2222-222-2-2-2-22-2-22-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ462-2-22-2-22222-22-2-2222-222-2-2-2-22-2-22-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ472-2-22-2-22222-22-2-22-2-22-2-2222-22-22-22-20000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ482-2-22-2-22222-22-2-22-2-22-2-2222-22-22-22-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ492-2-22-2-22222-2-222-2222-2-22-2-2-2-22-2-222000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ502-2-22-2-22222-2-222-2222-2-22-2-2-2-22-2-22200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ512-2-22-2-22222-2-222-2-2-2-222-222-2-2222-2-20000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ522-2-22-2-22222-2-222-2-2-2-222-222-2-2222-2-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ532-2-22-2-222-2-222-2-2222-222-2-2-22-222-22-200000000000000000000000000000000002i−2i2i−2i000000
χ542-2-22-2-222-2-222-2-2222-222-2-2-22-222-22-20000000000000000000000000000000000−2i2i−2i2i000000
χ552-2-22-2-222-2-222-2-22-2-22-2-22222-22-22-2200000000000000002-2-222-2-2200000000000000000000
χ562-2-22-2-222-2-222-2-22-2-22-2-22222-22-22-220000000000000000-222-2-222-200000000000000000000
χ572-2-22-2-222-2-22-222-2222-2-22-2-222-222-2-200000000000000000000000000000000002i−2i−2i2i000000
χ582-2-22-2-222-2-22-222-2222-2-22-2-222-222-2-20000000000000000000000000000000000−2i2i2i−2i000000
χ592-2-22-2-222-2-22-222-2-2-2-222-22222-2-2-22200000000000000002-2-22-222-200000000000000000000
χ602-2-22-2-222-2-22-222-2-2-2-222-22222-2-2-2220000000000000000-222-22-2-2200000000000000000000
χ6144-44-44-4-44-44000000000000-40000000000000022−2222−2200000000000000000000000000000000
χ6244-44-44-4-44-44000000000000-400000000000000−2222−222200000000000000000000000000000000
χ6344-44-44-4-4-44-400000000000040000000000000000002i2−2i22i2−2i20000000000000000000000000000
χ6444-44-44-4-4-44-40000000000004000000000000000000−2i22i2−2i22i20000000000000000000000000000
χ6544-4-44-44-40004i4i−4i−4i-44−4i−4i4i4i-44000000000000000000000000000000000000000000000000000
χ6644-4-44-44-4000−4i−4i4i4i-444i4i−4i−4i-44000000000000000000000000000000000000000000000000000
χ674-4444-4-4-44-4-40000000000004000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ684-4444-4-4-44-4-4000000000000400000000000000−2i22i22i2−2i200000000000000000000000000000000
χ694-4444-4-4-4-444000000000000-400000000000000000022−22−22220000000000000000000000000000
χ704-4444-4-4-4-444000000000000-4000000000000000000−222222−220000000000000000000000000000
χ714-44-4-444-40004i−4i4i−4i4-4−4i4i−4i4i-44000000000000000000000000000000000000000000000000000
χ724-44-4-444-4000−4i4i−4i4i4-44i−4i4i−4i-44000000000000000000000000000000000000000000000000000
χ73888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000

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