Finite Group Databasebeta

← Group #398922

Character table — Group #398922

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111112222222222224444444444444444444488888888888888888816161616161616161616161616161616
order12222222222244444444444488888888888888882244444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-11-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-11-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i00200-20000002i2i−2i−2i000000000000000000
χ18222222222222-2-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i00200-2000000−2i−2i2i2i000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i00-2002000000−2i−2i2i2i000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i00-20020000002i2i−2i−2i000000000000000000
χ2122222222-2-2-2-222-22-2-2-2222-2-2000000000000000022-2-2-22-2-222000000000000000000000000
χ2222222222-2-2-2-222-22-2-2-2222-2-20000000000000000-2-2-222222-2-2000000000000000000000000
χ2322222222-2-2-2-222-22-2-2-22-2-2220000000000000000222-2-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-222-22-2-2-22-2-2220000000000000000-2-2222-2-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-22-2222-22222222222220000000000-200-20000-2-20000-2-20000000000000000
χ2622222222-2-2-2-2-2-22-2222-22222-2-2-2-2-2-2-2-20000000000-200-20000220000220000000000000000
χ2722222222-2-2-2-2-2-22-2222-2-2-2-2-22222-2-2-2-2000000000020020000-2-20000220000000000000000
χ2822222222-2-2-2-2-2-22-2222-2-2-2-2-2-2-2-2-22222000000000020020000220000-2-20000000000000000
χ29222-22-2-2-222-2-2222-2-2-22-20000000022-2-222-2-222-2-22-202-2000000000002-20000000000000000
χ30222-22-2-2-222-2-2222-2-2-22-20000000022-2-2-2-222-2-222-220-22000000000002-20000000000000000
χ31222-22-2-2-222-2-2222-2-2-22-200000000-2-22222-2-222-2-2-220-2200000000000-220000000000000000
χ32222-22-2-2-222-2-2222-2-2-22-200000000-2-222-2-222-2-2222-202-200000000000-220000000000000000
χ33222-22-2-2-222-2-2-2-2-2222-22000022-2-200002i2i−2i−2i−2i−2i2i2i0000002i−2i2i−2i2-20000000000000000000000
χ34222-22-2-2-222-2-2-2-2-2222-22000022-2-20000−2i−2i2i2i2i2i−2i−2i000000−2i2i−2i2i2-20000000000000000000000
χ35222-22-2-2-222-2-2-2-2-2222-220000-2-22200002i2i−2i−2i−2i−2i2i2i000000−2i2i−2i2i-220000000000000000000000
χ36222-22-2-2-222-2-2-2-2-2222-220000-2-2220000−2i−2i2i2i2i2i−2i−2i0000002i−2i2i−2i-220000000000000000000000
χ37222-22-2-2-2-2-22222-2-222-2-2000022-2-20000000000002-20-2200000-222-22-2000000000000000000
χ38222-22-2-2-2-2-22222-2-222-2-2000022-2-2000000000000-2202-200000-22-22-22000000000000000000
χ39222-22-2-2-2-2-22222-2-222-2-20000-2-2220000000000002-20-22000002-2-22-22000000000000000000
χ40222-22-2-2-2-2-22222-2-222-2-20000-2-222000000000000-2202-2000002-22-22-2000000000000000000
χ41222-22-2-2-2-2-222-2-222-2-2220000000022-2-2000000000000002i−2i−2i2i002i−2i−2i2i-220000000000000000
χ42222-22-2-2-2-2-222-2-222-2-2220000000022-2-200000000000000−2i2i2i−2i00−2i2i2i−2i-220000000000000000
χ43222-22-2-2-2-2-222-2-222-2-22200000000-2-222000000000000002i−2i−2i2i00−2i2i2i−2i2-20000000000000000
χ44222-22-2-2-2-2-222-2-222-2-22200000000-2-22200000000000000−2i2i2i−2i002i−2i−2i2i2-20000000000000000
χ452-2-2222-2-22-22-22-22-22-2-220000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i0000002-2
χ462-2-2222-2-22-22-22-22-22-2-220000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i000000-22
χ472-2-2222-2-22-22-22-22-22-2-22000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i000000-22
χ482-2-2222-2-22-22-22-22-22-2-22000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i0000002-2
χ492-2-2222-2-22-22-2-22-22-222-20000000000002-22-2-22-22000000000000000000002i−2i000000002i−2i00
χ502-2-2222-2-22-22-2-22-22-222-20000000000002-22-2-22-2200000000000000000000−2i2i00000000−2i2i00
χ512-2-2222-2-22-22-2-22-22-222-2000000000000-22-222-22-2000000000000000000002i−2i00000000−2i2i00
χ522-2-2222-2-22-22-2-22-22-222-2000000000000-22-222-22-200000000000000000000−2i2i000000002i−2i00
χ532-2-2-22-2222-2-222-222-22-2-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000002i−2i0000002-2000000
χ542-2-2-22-2222-2-222-222-22-2-20000000000002i−2i−2i2i2i−2i−2i2i000000000000000000−2i2i000000-22000000
χ552-2-2-22-2222-2-222-222-22-2-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000002i−2i000000-22000000
χ562-2-2-22-2222-2-222-222-22-2-2000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000−2i2i0000002-2000000
χ572-2-2-22-2222-2-22-22-2-22-2220000000000002-2-22-222-200000000000000000000002-200002-20000
χ582-2-2-22-2222-2-22-22-2-22-2220000000000002-2-22-222-20000000000000000000000-220000-220000
χ592-2-2-22-2222-2-22-22-2-22-222000000000000-222-22-2-2200000000000000000000002-20000-220000
χ602-2-2-22-2222-2-22-22-2-22-222000000000000-222-22-2-220000000000000000000000-2200002-20000
χ6144-44-4-4-44000000000000004i−4i22−2222−222i2−2i22i2−2i2000000000000000000000000000000000000000000
χ6244-44-4-4-44000000000000004i−4i−2222−2222−2i22i2−2i22i2000000000000000000000000000000000000000000
χ6344-44-4-4-4400000000000000−4i4i22−2222−22−2i22i2−2i22i2000000000000000000000000000000000000000000
χ6444-44-4-4-4400000000000000−4i4i−2222−22222i2−2i22i2−2i2000000000000000000000000000000000000000000
χ6544-4-4-444-40000000000004i−4i0022−22−22222i2−2i2−2i22i2000000000000000000000000000000000000000000
χ6644-4-4-444-40000000000004i−4i00−222222−22−2i22i22i2−2i2000000000000000000000000000000000000000000
χ6744-4-4-444-4000000000000−4i4i0022−22−2222−2i22i22i2−2i2000000000000000000000000000000000000000000
χ6844-4-4-444-4000000000000−4i4i00−222222−222i2−2i2−2i22i2000000000000000000000000000000000000000000
χ694-4-4444-4-4-44-444-4-4-4-4444000000000000000000000000000000000000000000000000000000
χ704-4-4444-4-4-44-44-44444-4-4-4000000000000000000000000000000000000000000000000000000
χ714-4-4-44-444-444-44-4-444-44-4000000000000000000000000000000000000000000000000000000
χ724-4-4-44-444-444-4-444-4-44-44000000000000000000000000000000000000000000000000000000
χ738-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000

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