Finite Group Databasebeta

← Group #287813

Character table — Group #287813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888822444444488888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-11
χ1011111111-1-1-1-111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111-1
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-11
χ1311111111-1-1-1-111111111-1-1-1-111-1-1-1-111111111111111-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111-1
χ1411111111-1-1-1-111111111-1-1-1-111-1-1-1-111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-11
χ1511111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-11
χ1611111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1111111-1-111-1-11-1
χ1722222222222222-22-2-2-2222-2-2-2-200000000000000002222-2-2-2-2-200000000000000000000000000
χ1822222222222222-22-2-2-2222-2-2-2-20000000000000000-2-2-2-2-2222200000000000000000000000000
χ19222222222222-2-22-2222-2-2-222-2-222222222000000000000-20000-2-200000000-2-200000000000000
χ20222222222222-2-22-2222-2-2-222-2-2-2-2-2-2-2-2-2-2000000000000-2000022000000002200000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i000020000002i2i−2i−2i00000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i00002000000−2i−2i2i2i00000000000000000000
χ2322222222-2-2-2-222-22-2-2-22-2-222-2-2000000000000000022-2-22-2-22200000000000000000000000000
χ2422222222-2-2-2-222-22-2-2-22-2-222-2-20000000000000000-2-222222-2-200000000000000000000000000
χ2522222222-2-2-2-2-2-22-2222-222-2-2-2-22222-2-2-2-2000000000000200002200000000-2-200000000000000
χ2622222222-2-2-2-2-2-22-2222-222-2-2-2-2-2-2-2-2222200000000000020000-2-2000000002200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i0000-2000000−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i0000-20000002i2i−2i−2i00000000000000000000
χ29222-22-2-2-222-2-2220-2000-22-2000022−2−222−2−222−2−222−2−22-22-2000002−22−22−200002−200000000000000
χ30222-22-2-2-222-2-2220-2000-22-2000022−2−222−2−2−2−222−2−222-22-22000002−2−22−2200002−200000000000000
χ31222-22-2-2-222-2-2220-2000-22-20000−2−222−2−22222−2−222−2−2-22-2200000−222−22−20000−2200000000000000
χ32222-22-2-2-222-2-2220-2000-22-20000−2−222−2−222−2−222−2−2222-22-200000−22−22−220000−2200000000000000
χ33222-22-2-2-222-2-2-2-2020002-22000022−2−222−2−2i2i2−i2−i2−i2−i2i2i2000002i−2i2i−2i−22i2−i2−i2i20000−2200000000000000
χ34222-22-2-2-222-2-2-2-2020002-22000022−2−222−2−2−i2−i2i2i2i2i2−i2−i200000−2i2i−2i2i−22−i2i2i2−i20000−2200000000000000
χ35222-22-2-2-222-2-2-2-2020002-220000−2−222−2−222i2i2−i2−i2−i2−i2i2i200000−2i2i−2i2i2−2i2−i2−i2i200002−200000000000000
χ36222-22-2-2-222-2-2-2-2020002-220000−2−222−2−222−i2−i2i2i2i2i2−i2−i2000002i−2i2i−2i2−2−i2i2i2−i200002−200000000000000
χ37222-22-2-2-2-2-222220-2000-2-22000022−2−2−2−22222−2−222−2−2-222-200000−22−22−2200002−200000000000000
χ38222-22-2-2-2-2-222220-2000-2-22000022−2−2−2−222−2−222−2−2222-2-2200000−222−22−200002−200000000000000
χ39222-22-2-2-2-2-222220-2000-2-220000−2−22222−2−222−2−222−2−22-2-22000002−2−22−220000−2200000000000000
χ40222-22-2-2-2-2-222220-2000-2-220000−2−22222−2−2−2−222−2−222-222-2000002−22−22−20000−2200000000000000
χ41222-22-2-2-2-2-222-2-20200022-2000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000−2i2i2i−2i2−2−i2i2i2−i20000−2200000000000000
χ42222-22-2-2-2-2-222-2-20200022-2000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000002i−2i−2i2i2−2i2−i2−i2i20000−2200000000000000
χ43222-22-2-2-2-2-222-2-20200022-20000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000002i−2i−2i2i−22−i2i2i2−i200002−200000000000000
χ44222-22-2-2-2-2-222-2-20200022-20000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000−2i2i2i−2i−22i2−i2−i2i200002−200000000000000
χ4522-2-2-222-22i−2i2i−2i0020-2-220002i−2i002i−2i2i−2i2-22-20000000000000000000000022−2−200i2i2−i2−i20000i2−i22−200
χ4622-2-2-222-22i−2i2i−2i0020-2-220002i−2i002i−2i2i−2i2-22-200000000000000000000000−2−22200−i2−i2i2i20000−i2i2−2200
χ4722-2-2-222-22i−2i2i−2i0020-2-220002i−2i00−2i2i−2i2i-22-220000000000000000000000022−2−200i2i2−i2−i20000−i2i2−2200
χ4822-2-2-222-22i−2i2i−2i0020-2-220002i−2i00−2i2i−2i2i-22-2200000000000000000000000−2−22200−i2−i2i2i20000i2−i22−200
χ4922-2-2-222-2−2i2i−2i2i0020-2-22000−2i2i002i−2i2i−2i-22-220000000000000000000000022−2−200−i2−i2i2i20000i2−i2−2200
χ5022-2-2-222-2−2i2i−2i2i0020-2-22000−2i2i002i−2i2i−2i-22-2200000000000000000000000−2−22200i2i2−i2−i20000−i2i22−200
χ5122-2-2-222-2−2i2i−2i2i0020-2-22000−2i2i00−2i2i−2i2i2-22-20000000000000000000000022−2−200−i2−i2i2i20000−i2i22−200
χ5222-2-2-222-2−2i2i−2i2i0020-2-22000−2i2i00−2i2i−2i2i2-22-200000000000000000000000−2−22200i2i2−i2−i20000i2−i2−2200
χ532-2-2-22-22200002-2222-2-2-200002-2000000002i−2i2i−2i2i−2i2i−2i0000000000000002-22-20000002i−2i00000000
χ542-2-2-22-22200002-2222-2-2-200002-2000000002i−2i2i−2i2i−2i2i−2i000000000000000-22-22000000−2i2i00000000
χ552-2-2-22-22200002-2222-2-2-200002-200000000−2i2i−2i2i−2i2i−2i2i0000000000000002-22-2000000−2i2i00000000
χ562-2-2-22-22200002-2222-2-2-200002-200000000−2i2i−2i2i−2i2i−2i2i000000000000000-22-220000002i−2i00000000
χ572-2-2-22-2220000-22-2-2-222200002-2000000002-22-2-22-220000000000000000000002-22-2002-2000000
χ582-2-2-22-2220000-22-2-2-222200002-2000000002-22-2-22-22000000000000000000000-22-2200-22000000
χ592-2-2-22-2220000-22-2-2-222200002-200000000-22-222-22-20000000000000000000002-22-200-22000000
χ602-2-2-22-2220000-22-2-2-222200002-200000000-22-222-22-2000000000000000000000-22-22002-2000000
χ6144-44-4-4-444i−4i−4i4i000000000000002i2−2i2−2i22i222−22−22220000000000000000000000000000000000000000000
χ6244-44-4-4-444i−4i−4i4i00000000000000−2i22i22i2−2i2−222222−220000000000000000000000000000000000000000000
χ6344-44-4-4-44−4i4i4i−4i000000000000002i2−2i2−2i22i2−222222−220000000000000000000000000000000000000000000
χ6444-44-4-4-44−4i4i4i−4i00000000000000−2i22i22i2−2i222−22−22220000000000000000000000000000000000000000000
χ6544-4-4-444-44i−4i4i−4i00-4044-4000−4i4i00000000000000000000000000000000000000000000000000000
χ6644-4-4-444-4−4i4i−4i4i00-4044-40004i−4i00000000000000000000000000000000000000000000000000000
χ674-444-4-44-400000040-44-40000000000000000000000000000000000000022−22−22220000000000000000
χ684-444-4-44-400000040-44-400000000000000000000000000000000000000−222222−220000000000000000
χ694-444-4-44-4000000-404-44000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ704-444-4-44-4000000-404-4400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ714-4-4444-4-400004-40-40004000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ724-4-4444-4-400004-40-4000400000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ734-4-4444-4-40000-4404000-40000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ744-4-4444-4-40000-4404000-400000000000000−222222−2222−22−222200000000000000000000000000000000000
χ754-4-4-44-44400004-4-44-444-40000-44000000000000000000000000000000000000000000000000000
χ764-4-4-44-4440000-444-44-4-440000-44000000000000000000000000000000000000000000000000000
χ778-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000

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