Finite Group Databasebeta

← Group #270883

Character table — Group #270883

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222222244444444444422224444448888888888888888224444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ911111111-1-1-1-111111-1-1-1-11111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-11-1
χ1011111111-1-1-1-111111-1-1-1-11111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-11-1-111-1-111-11
χ1111111111-1-1-1-111111-1-1-1-11111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-111-11
χ1211111111-1-1-1-111111-1-1-1-11111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-11-1-11111-1-11-1
χ1311111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1-1-11111-1-1-11
χ1411111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1111-1-1-1-1111-1
χ1511111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-11-1-1-111-1-1111-1
χ1611111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-11
χ1722222222222222-2-2-2-2-2-2-222-2222222-2-2-2-200000000000000002200-2-2-2-20000000000000000000000
χ1822222222222222-2-2-2-2-2-2-222-2-2-2-2-222-2-2-2-20000000000000000-2-20022220000000000000000000000
χ19222222222222-2-22222222-2-220000-2-2-2-2-2-20000000000000000002200002200000000-2-20000000000
χ20222222222222-2-22222222-2-220000-2-2-2-2-2-2000000000000000000-2-20000-2-200000000220000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-222220000000000000000000000000000000000002-22-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-22222000000000000000000000000000000000000-22-22000000
χ2322222222-2-2-2-222-2-2-2222222-22222-2-2-222-20000000000000000-2-200-2-2220000000000000000000000
χ2422222222-2-2-2-222-2-2-2222222-2-2-2-2-2-2-2-222-20000000000000000220022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2222-2-2-2-2-2-22000022-222-2000000000000000000220000-2-200000000-220000000000
χ2622222222-2-2-2-2-2-2222-2-2-2-2-2-22000022-222-2000000000000000000-2-2000022000000002-20000000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-20000222-2-220000000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-20000222-2-22000000000000000000000000000000000000-222-2000000
χ292222-2-2-2-222-2-2220000000-2-2022-2-22-200002222−2−2−2−22222−2−2−2−22-20000000022−2−222−2−2000000000000
χ302222-2-2-2-222-2-2220000000-2-2022-2-22-20000−2−2−2−22222−2−2−2−222222-200000000−2−222−2−222000000000000
χ312222-2-2-2-222-2-2220000000-2-20-2-2222-200002222−2−2−2−22222−2−2−2−2-2200000000−2−222−2−222000000000000
χ322222-2-2-2-222-2-2220000000-2-20-2-2222-20000−2−2−2−22222−2−2−2−22222-220000000022−2−222−2−2000000000000
χ332222-2-2-2-2-2-222220000000-2-2022-2-2-2200002222−2−2−2−2−2−2−2−22222-220000000022−2−2−2−222000000000000
χ342222-2-2-2-2-2-222220000000-2-2022-2-2-220000−2−2−2−222222222−2−2−2−2-2200000000−2−22222−2−2000000000000
χ352222-2-2-2-2-2-222220000000-2-20-2-222-2200002222−2−2−2−2−2−2−2−222222-200000000−2−22222−2−2000000000000
χ362222-2-2-2-2-2-222220000000-2-20-2-222-220000−2−2−2−222222222−2−2−2−22-20000000022−2−2−2−222000000000000
χ3722-2-2-2-2222-22-2002-2-222-2-2002000000000022−2−222−2−222−2−222−2−2002-200002-2000000000000002−22−200
χ3822-2-2-2-2222-22-2002-2-222-2-2002000000000022−2−222−2−222−2−222−2−200-220000-2200000000000000−22−2200
χ3922-2-2-2-2222-22-2002-2-222-2-20020000000000−2−222−2−222−2−222−2−222002-200002-200000000000000−22−2200
χ4022-2-2-2-2222-22-2002-2-222-2-20020000000000−2−222−2−222−2−222−2−22200-220000-22000000000000002−22−200
χ4122-2-2-2-222-22-22002-2-2-2-222002000000000022−2−222−2−2−2−222−2−222002-20000-22000000000000002−2−2200
χ4222-2-2-2-222-22-22002-2-2-2-222002000000000022−2−222−2−2−2−222−2−22200-2200002-200000000000000−222−200
χ4322-2-2-2-222-22-22002-2-2-2-2220020000000000−2−222−2−22222−2−222−2−2002-20000-2200000000000000−222−200
χ4422-2-2-2-222-22-22002-2-2-2-2220020000000000−2−222−2−22222−2−222−2−200-2200002-2000000000000002−2−2200
χ452-2-222-22-200002-20002i−2i2i−2i2-202-22-20002i−2i02−22−22−22−2i2−i2i2−i2i2−i2i2−i20000002i−2i002−22−2i2−i2i2−i2000000000000
χ462-2-222-22-200002-20002i−2i2i−2i2-202-22-20002i−2i0−22−22−22−22−i2i2−i2i2−i2i2−i2i20000002i−2i00−22−22−i2i2−i2i2000000000000
χ472-2-222-22-200002-20002i−2i2i−2i2-20-22-220002i−2i02−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000−2i2i00−22−22−i2i2−i2i2000000000000
χ482-2-222-22-200002-20002i−2i2i−2i2-20-22-220002i−2i0−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000−2i2i002−22−2i2−i2i2−i2000000000000
χ492-2-222-22-200002-2000−2i2i−2i2i2-202-22-2000−2i2i02−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000−2i2i002−22−2−i2i2−i2i2000000000000
χ502-2-222-22-200002-2000−2i2i−2i2i2-202-22-2000−2i2i0−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000−2i2i00−22−22i2−i2i2−i2000000000000
χ512-2-222-22-200002-2000−2i2i−2i2i2-20-22-22000−2i2i02−22−22−22−2−i2i2−i2i2−i2i2−i2i20000002i−2i00−22−22i2−i2i2−i2000000000000
χ522-2-222-22-200002-2000−2i2i−2i2i2-20-22-22000−2i2i0−22−22−22−22i2−i2i2−i2i2−i2i2−i20000002i−2i002−22−2−i2i2−i2i2000000000000
χ532-2-22-22-2200002-222-20000-22-22-2-2200200-2000000002i−2i2i−2i−2i2i−2i2i00002-2000000002i−2i−2i2i000000000000
χ542-2-22-22-2200002-222-20000-22-22-2-2200200-200000000−2i2i−2i2i2i−2i2i−2i00002-200000000−2i2i2i−2i000000000000
χ552-2-22-22-2200002-222-20000-22-2-222-200200-2000000002i−2i2i−2i−2i2i−2i2i0000-2200000000−2i2i2i−2i000000000000
χ562-2-22-22-2200002-222-20000-22-2-222-200200-200000000−2i2i−2i2i2i−2i2i−2i0000-22000000002i−2i−2i2i000000000000
χ572-2-22-22-2200002-2-2-220000-2222-2-2200-20022-22-2-22-22000000000000-2200002-2-220000000000000000
χ582-2-22-22-2200002-2-2-220000-2222-2-2200-2002-22-222-22-2000000000000-220000-222-20000000000000000
χ592-2-22-22-2200002-2-2-220000-222-222-200-20022-22-2-22-220000000000002-20000-222-20000000000000000
χ602-2-22-22-2200002-2-2-220000-222-222-200-2002-22-222-22-20000000000002-200002-2-220000000000000000
χ614444-4-4-4-444-4-4-4-400000004400000-4400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-444-4-4000000044000004-400000000000000000000000000000000000000000000000000
χ6344-4-444-4-44-4-44000000000000000000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000
χ6444-4-444-4-44-4-440000000000000000000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000
χ6544-4-444-4-4-444-4000000000000000000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000
χ6644-4-444-4-4-444-40000000000000000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000
χ6744-4-4-4-4444-44-400-444-4-44400-400000000000000000000000000000000000000000000000000000000
χ6844-4-4-4-444-44-4400-44444-4-400-400000000000000000000000000000000000000000000000000000000
χ694-44-44-4-440000004-44000000-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ704-44-44-4-440000004-44000000-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ714-44-44-4-44000000-44-40000004000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ724-44-44-4-44000000-44-400000040000000000−222222−2222−22−222200000000000000000000000000000000000000
χ734-44-4-444-40000000004i−4i−4i4i00000000000002-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ744-44-4-444-40000000004i−4i−4i4i0000000000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ754-44-4-444-4000000000−4i4i4i−4i00000000000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ764-44-4-444-4000000000−4i4i4i−4i0000000000000-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ774-4-444-44-40000-440004i−4i4i−4i-4400000000−4i4i00000000000000000000000000000000000000000000000
χ784-4-444-44-40000-44000−4i4i−4i4i-44000000004i−4i00000000000000000000000000000000000000000000000
χ794-4-44-44-440000-4444-400004-4-4000000-40040000000000000000000000000000000000000000000000
χ804-4-44-44-440000-44-4-4400004-44000000400-40000000000000000000000000000000000000000000000

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