Finite Group Databasebeta

← Group #238128

Character table — Group #238128

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
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
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
χ1111111111-1-1-1-111111-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-111111-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ1311111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ1411111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
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
χ1722222222222222-2-2-2-2-2-2-222-2-222-2-2-2000022220000-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-222-2-222-2-2-20000-2-2-2-2000022220000000000000000000000000000
χ19222222222222-2-22222222-2-22-2-2-2-2-2-222220000-2-2-2-200000000000000000000000000000000
χ20222222222222-2-22222222-2-22-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
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
χ2322222222-2-2-2-222-2-2-2222222-2-2-2-222-2000022-2-20000-2-2220000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2222222-2-2-2-222-20000-2-222000022-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2222-2-2-2-2-2-22-22222-222-2-20000-2-22200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2-2-2-2-22-22222-2-2-222000022-2-200000000000000000000000000000000
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
χ29222-2-22-2-222-2-22222-222-2-2-2-2-222-22-2-2000000000000000000000000000000002-22-200000000
χ30222-2-22-2-222-2-22222-222-2-2-2-2-222-22-2-200000000000000000000000000000000-22-2200000000
χ31222-2-22-2-222-2-222-2-22-2-222-2-22-22-2-22200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ32222-2-22-2-222-2-222-2-22-2-222-2-22-22-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ33222-2-22-2-222-2-2-2-222-222-2-222-2-2-22-22200000000000000000000000000000000000000002i−2i2i−2i
χ34222-2-22-2-222-2-2-2-222-222-2-222-2-2-22-2220000000000000000000000000000000000000000−2i2i−2i2i
χ35222-2-22-2-222-2-2-2-2-2-22-2-2222222-222-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ36222-2-22-2-222-2-2-2-2-2-22-2-2222222-222-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ37222-2-22-2-2-2-2222222-2-2-222-2-2-22-22-22-2000000000000000000000000000000002-2-2200000000
χ38222-2-22-2-2-2-2222222-2-2-222-2-2-22-22-22-200000000000000000000000000000000-222-200000000
χ39222-2-22-2-2-2-22222-2-2222-2-2-2-22-2-222-2200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ40222-2-22-2-2-2-22222-2-2222-2-2-2-22-2-222-220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ41222-2-22-2-2-2-222-2-222-2-2-22222-2-22-22-2200000000000000000000000000000000000000002i−2i−2i2i
χ42222-2-22-2-2-2-222-2-222-2-2-22222-2-22-22-220000000000000000000000000000000000000000−2i2i2i−2i
χ43222-2-22-2-2-2-222-2-2-2-2222-2-222222-2-22-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ44222-2-22-2-2-2-222-2-2-2-2222-2-222222-2-22-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ452-2-22-222-22-22-2002-222-22-200-2000000000000002i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ462-2-22-222-22-22-2002-222-22-200-2000000000000002i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ472-2-22-222-22-22-2002-222-22-200-200000000000000−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ482-2-22-222-22-22-2002-222-22-200-200000000000000−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ492-2-22-222-2-22-22002-22-22-2200-2000000000000002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ502-2-22-222-2-22-22002-22-22-2200-2000000000000002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ512-2-22-222-2-22-22002-22-22-2200-200000000000000−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ522-2-22-222-2-22-22002-22-22-2200-200000000000000−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ532-2-2-222-222-2-2200-222-222-200-20000002i−2i2i−2i0000000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ542-2-2-222-222-2-2200-222-222-200-20000002i−2i2i−2i000000000000−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ552-2-2-222-222-2-2200-222-222-200-2000000−2i2i−2i2i0000000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ562-2-2-222-222-2-2200-222-222-200-2000000−2i2i−2i2i000000000000−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ572-2-2-222-22-222-200-2222-2-2200-20000002i−2i−2i2i0000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ582-2-2-222-22-222-200-2222-2-2200-20000002i−2i−2i2i000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ592-2-2-222-22-222-200-2222-2-2200-2000000−2i2i2i−2i0000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ602-2-2-222-22-222-200-2222-2-2200-2000000−2i2i2i−2i000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ6144-44-4-4-4400004-400000004-400000000000004i−4i000000000000000000000000000000000000
χ6244-44-4-4-4400004-400000004-40000000000000−4i4i000000000000000000000000000000000000
χ6344-44-4-4-440000-440000000-44000000000004i−4i00000000000000000000000000000000000000
χ6444-44-4-4-440000-440000000-4400000000000−4i4i00000000000000000000000000000000000000
χ6544-4-44-44-400004-40000000-4400000000000000000004i−4i000000000000000000000000000000
χ6644-4-44-44-400004-40000000-440000000000000000000−4i4i000000000000000000000000000000
χ6744-4-44-44-40000-4400000004-40000000000000000000004i−4i0000000000000000000000000000
χ6844-4-44-44-40000-4400000004-4000000000000000000000−4i4i0000000000000000000000000000
χ694-4-44-444-44-44-400-44-4-44-4400400000000000000000000000000000000000000000000000000
χ704-4-44-444-4-44-4400-44-44-44-400400000000000000000000000000000000000000000000000000
χ714-4-4-444-444-4-44004-4-44-4-4400400000000000000000000000000000000000000000000000000
χ724-4-4-444-44-444-4004-4-4-444-400400000000000000000000000000000000000000000000000000
χ738-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000

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