Finite Group Databasebeta

← Group #270951

Character table — Group #270951

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
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1
χ911111111-1-1-1-111111-1-1-1-11111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-111-1-11-1
χ1011111111-1-1-1-111111-1-1-1-11111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1111-1-111-11
χ1111111111-1-1-1-111111-1-1-1-11111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-111-11
χ1211111111-1-1-1-111111-1-1-1-11111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1-111111-1-11-1
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
χ19222222222222-2-22222222-2-220000-2-2-2-2-2-20000000000000000002200002200000000-200-200000000
χ20222222222222-2-22222222-2-220000-2-2-2-2-2-2000000000000000000-2-20000-2-200000000200200000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-22222000000000000000000000000000000000002-202-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-2222200000000000000000000000000000000000-220-22000000
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
χ2522222222-2-2-2-2-2-2222-2-2-2-2-2-22000022-222-2000000000000000000220000-2-200000000-200200000000
χ2622222222-2-2-2-2-2-2222-2-2-2-2-2-22000022-222-2000000000000000000-2-200002200000000200-200000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-20000222-2-22000000000000000000000000000000000002-20-22000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-20000222-2-2200000000000000000000000000000000000-2202-2000000
χ29222-2-2-22-222-2-2002-2-222-2-200200000000002222−2−2−2−22222−2−2−2−2002i−2i00002i−2i00000000000000i2−i2i2−i200
χ30222-2-2-22-222-2-2002-2-222-2-200200000000002222−2−2−2−22222−2−2−2−200−2i2i0000−2i2i00000000000000−i2i2−i2i200
χ31222-2-2-22-222-2-2002-2-222-2-20020000000000−2−2−2−22222−2−2−2−22222002i−2i00002i−2i00000000000000−i2i2−i2i200
χ32222-2-2-22-222-2-2002-2-222-2-20020000000000−2−2−2−22222−2−2−2−2222200−2i2i0000−2i2i00000000000000i2−i2i2−i200
χ33222-2-2-22-2-2-222002-2-2-2-22200200000000002222−2−2−2−2−2−2−2−22222002i−2i0000−2i2i00000000000000i2−i2−i2i200
χ34222-2-2-22-2-2-222002-2-2-2-22200200000000002222−2−2−2−2−2−2−2−2222200−2i2i00002i−2i00000000000000−i2i2i2−i200
χ35222-2-2-22-2-2-222002-2-2-2-2220020000000000−2−2−2−222222222−2−2−2−2002i−2i0000−2i2i00000000000000−i2i2i2−i200
χ36222-2-2-22-2-2-222002-2-2-2-2220020000000000−2−2−2−222222222−2−2−2−200−2i2i00002i−2i00000000000000i2−i2−i2i200
χ3722-222-2-2-22-22-2-2-2000000022022-2-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ3822-222-2-2-22-22-2-2-2000000022022-2-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ3922-222-2-2-22-22-2-2-20000000220-2-2222-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-2200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ4022-222-2-2-22-22-2-2-20000000220-2-2222-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-2200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ4122-222-2-2-2-22-22-2-2000000022022-2-2-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-2200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ4222-222-2-2-2-22-22-2-2000000022022-2-2-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-2200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ4322-222-2-2-2-22-22-2-20000000220-2-222-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22-200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ4422-222-2-2-2-22-22-2-20000000220-2-222-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22-200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ452-22-222-2-200002-20002i−2i2i−2i2-202-22-20002i−2i0i2−i2i2−i2i2−i2i2−i22−22−22−22−20000002i−2i00i2−i2i2−i22−22−2000000000000
χ462-22-222-2-200002-20002i−2i2i−2i2-202-22-20002i−2i0−i2i2−i2i2−i2i2−i2i2−22−22−22−220000002i−2i00−i2i2−i2i2−22−22000000000000
χ472-22-222-2-200002-20002i−2i2i−2i2-20-22-220002i−2i0i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000−2i2i00−i2i2−i2i2−22−22000000000000
χ482-22-222-2-200002-20002i−2i2i−2i2-20-22-220002i−2i0−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000−2i2i00i2−i2i2−i22−22−2000000000000
χ492-22-222-2-200002-2000−2i2i−2i2i2-202-22-2000−2i2i0i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000−2i2i00i2−i2i2−i2−22−22000000000000
χ502-22-222-2-200002-2000−2i2i−2i2i2-202-22-2000−2i2i0−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000−2i2i00−i2i2−i2i22−22−2000000000000
χ512-22-222-2-200002-2000−2i2i−2i2i2-20-22-22000−2i2i0i2−i2i2−i2i2−i2i2−i2−22−22−22−220000002i−2i00−i2i2−i2i22−22−2000000000000
χ522-22-222-2-200002-2000−2i2i−2i2i2-20-22-22000−2i2i0−i2i2−i2i2−i2i2−i2i22−22−22−22−20000002i−2i00i2−i2i2−i2−22−22000000000000
χ532-2-2-22-2220000-2222-200002-2-22-2-2200200-2000000002i−2i−2i2i2i−2i−2i2i00002-2000000002i−2i−2i2i000000000000
χ542-2-2-22-2220000-2222-200002-2-22-2-2200200-200000000−2i2i2i−2i−2i2i2i−2i00002-200000000−2i2i2i−2i000000000000
χ552-2-2-22-2220000-2222-200002-2-2-222-200200-2000000002i−2i−2i2i2i−2i−2i2i0000-2200000000−2i2i2i−2i000000000000
χ562-2-2-22-2220000-2222-200002-2-2-222-200200-200000000−2i2i2i−2i−2i2i2i−2i0000-22000000002i−2i−2i2i000000000000
χ572-2-2-22-2220000-22-2-2200002-222-2-2200-20022-2-222-2-22000000000000-2200002-2-220000000000000000
χ582-2-2-22-2220000-22-2-2200002-222-2-2200-2002-222-2-222-2000000000000-220000-222-20000000000000000
χ592-2-2-22-2220000-22-2-2200002-22-222-200-20022-2-222-2-220000000000002-20000-222-20000000000000000
χ602-2-2-22-2220000-22-2-2200002-22-222-200-2002-222-2-222-20000000000002-200002-2-220000000000000000
χ61444-4-4-44-444-4-400-444-4-44400-400000000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-4-44400-44444-4-400-400000000000000000000000000000000000000000000000000000000
χ6344-444-4-4-44-44-4440000000-4-400000-4400000000000000000000000000000000000000000000000000
χ6444-444-4-4-4-44-44440000000-4-4000004-400000000000000000000000000000000000000000000000000
χ6544-4-4-44-444-4-4400000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6644-4-4-44-444-4-440000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6744-4-4-44-44-444-400000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6844-4-4-44-44-444-40000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ694-444-4-4-440000000004i−4i−4i4i00000000000002i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000000000
χ704-444-4-4-440000000004i−4i−4i4i0000000000000−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000000000
χ714-444-4-4-44000000000−4i4i4i−4i00000000000002i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000000000
χ724-444-4-4-44000000000−4i4i4i−4i0000000000000−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000000000
χ734-44-444-4-40000-440004i−4i4i−4i-4400000000−4i4i00000000000000000000000000000000000000000000000
χ744-44-444-4-40000-44000−4i4i−4i4i-44000000004i−4i00000000000000000000000000000000000000000000000
χ754-4-44-444-40000004-44000000-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ764-4-44-444-40000004-44000000-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ774-4-44-444-4000000-44-40000004000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ784-4-44-444-4000000-44-400000040000000000−222222−2222−22−222200000000000000000000000000000000000000
χ794-4-4-44-44400004-444-40000-44-4000000-40040000000000000000000000000000000000000000000000
χ804-4-4-44-44400004-4-4-440000-444000000400-40000000000000000000000000000000000000000000000

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