Finite Group Databasebeta

← Group #293521

Character table — Group #293521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444444444444448888888888888888222244444488888888444444888824
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
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ91111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-11-1
χ101111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1111-1-1-1-111-11
χ111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1-111-11
χ121111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1111-1-111-1-11-1
χ131111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-111-1-111-1-1-11
χ141111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-11-1-111-1-1111-1
χ151111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-11-111-1-1-1-1111-1
χ161111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-11
χ1722222222222222-2-2-2-2-2-222-2-2-2-2222222-2-20000000000000000-2-200-2-2220000000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-20000000000000000220022-2-20000000000000000000000
χ192222222222-2-2-2-2-2-2222222-2-222-2-22222-2-200000000000000002200-2-2-2-20000000000000000000000
χ202222222222-2-2-2-2-2-2222222-2-222-2-2-2-2-2-2-2-20000000000000000-2-20022220000000000000000000000
χ2122222222-2-22222222222-2-222-2-2-2-20000-2-20000000000000000002200002200000000-2-20000000000
χ2222222222-2-22222222222-2-222-2-2-2-20000-2-2000000000000000000-2-20000-2-200000000220000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-20000220000000000000000000000000000000000002-22-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-2000022000000000000000000000000000000000000-22-22000000
χ2522222222-2-2-2-2-2-222-2-2-2-2-2-22222220000-2-2000000000000000000220000-2-200000000-220000000000
χ2622222222-2-2-2-2-2-222-2-2-2-2-2-22222220000-2-2000000000000000000-2-2000022000000002-20000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2220000220000000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222000022000000000000000000000000000000000000-222-2000000
χ29222-2-2-22-22-22i2i−2i−2i0000002-200002i−2i22-2-2002222−2−2−2−2i2i2i2i2−i2−i2−i2−i20000002i−2i0022−2−2i2i2−i2−i2000000000000
χ30222-2-2-22-22-22i2i−2i−2i0000002-200002i−2i22-2-200−2−2−2−22222−i2−i2−i2−i2i2i2i2i20000002i−2i00−2−222−i2−i2i2i2000000000000
χ31222-2-2-22-22-22i2i−2i−2i0000002-200002i−2i-2-222002222−2−2−2−2i2i2i2i2−i2−i2−i2−i2000000−2i2i00−2−222−i2−i2i2i2000000000000
χ32222-2-2-22-22-22i2i−2i−2i0000002-200002i−2i-2-22200−2−2−2−22222−i2−i2−i2−i2i2i2i2i2000000−2i2i0022−2−2i2i2−i2−i2000000000000
χ33222-2-2-22-22-2−2i−2i2i2i0000002-20000−2i2i22-2-2002222−2−2−2−2−i2−i2−i2−i2i2i2i2i2000000−2i2i0022−2−2−i2−i2i2i2000000000000
χ34222-2-2-22-22-2−2i−2i2i2i0000002-20000−2i2i22-2-200−2−2−2−22222i2i2i2i2−i2−i2−i2−i2000000−2i2i00−2−222i2i2−i2−i2000000000000
χ35222-2-2-22-22-2−2i−2i2i2i0000002-20000−2i2i-2-222002222−2−2−2−2−i2−i2−i2−i2i2i2i2i20000002i−2i00−2−222i2i2−i2−i2000000000000
χ36222-2-2-22-22-2−2i−2i2i2i0000002-20000−2i2i-2-22200−2−2−2−22222i2i2i2i2−i2−i2−i2−i20000002i−2i0022−2−2−i2−i2i2i2000000000000
χ3722-2-222-2-2002i−2i2i−2i2-22i2i−2i−2i002-20000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2002-200002i−2i00000000000000i2−i22−200
χ3822-2-222-2-2002i−2i2i−2i2-22i2i−2i−2i002-20000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200-220000−2i2i00000000000000−i2i2−2200
χ3922-2-222-2-2002i−2i2i−2i2-22i2i−2i−2i002-20000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222002-200002i−2i00000000000000−i2i2−2200
χ4022-2-222-2-2002i−2i2i−2i2-22i2i−2i−2i002-20000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200-220000−2i2i00000000000000i2−i22−200
χ4122-2-222-2-200−2i2i−2i2i2-2−2i−2i2i2i002-20000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222002-20000−2i2i00000000000000i2−i2−2200
χ4222-2-222-2-200−2i2i−2i2i2-2−2i−2i2i2i002-20000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200-2200002i−2i00000000000000−i2i22−200
χ4322-2-222-2-200−2i2i−2i2i2-2−2i−2i2i2i002-20000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2002-20000−2i2i00000000000000−i2i22−200
χ4422-2-222-2-200−2i2i−2i2i2-2−2i−2i2i2i002-20000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−200-2200002i−2i00000000000000i2−i2−2200
χ452-2222-2-2-22-20000002i−2i2i−2i-22002i−2i002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−22-2000000002−22−2i2−i2i2−i2000000000000
χ462-2222-2-2-22-20000002i−2i2i−2i-22002i−2i002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−222-200000000−22−22−i2i2−i2i2000000000000
χ472-2222-2-2-22-20000002i−2i2i−2i-22002i−2i00−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−2-2200000000−22−22−i2i2−i2i2000000000000
χ482-2222-2-2-22-20000002i−2i2i−2i-22002i−2i00−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−22-22000000002−22−2i2−i2i2−i2000000000000
χ492-2222-2-2-22-2000000−2i2i−2i2i-2200−2i2i002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−22-22000000002−22−2−i2i2−i2i2000000000000
χ502-2222-2-2-22-2000000−2i2i−2i2i-2200−2i2i002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2-2200000000−22−22i2−i2i2−i2000000000000
χ512-2222-2-2-22-2000000−2i2i−2i2i-2200−2i2i00−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−222-200000000−22−22i2−i2i2−i2000000000000
χ522-2222-2-2-22-2000000−2i2i−2i2i-2200−2i2i00−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−22-2000000002−22−2−i2i2−i2i2000000000000
χ532-22-2-22-222200002-20000-2-2-2200002i−2i−2i2i2-2000000002i−2i2i−2i−2i2i−2i2i00002i−2i00000000-222-2000000000000
χ542-22-2-22-222200002-20000-2-2-2200002i−2i−2i2i2-200000000−2i2i−2i2i2i−2i2i−2i00002i−2i000000002-2-22000000000000
χ552-22-2-22-222200002-20000-2-2-220000−2i2i2i−2i2-2000000002i−2i2i−2i−2i2i−2i2i0000−2i2i000000002-2-22000000000000
χ562-22-2-22-222200002-20000-2-2-220000−2i2i2i−2i2-200000000−2i2i−2i2i2i−2i2i−2i0000−2i2i00000000-222-2000000000000
χ572-22-2-22-22220000-220000-2-22-200002i−2i−2i2i-222i−2i2i−2i−2i2i−2i2i000000000000−2i2i00002-2-220000000000000000
χ582-22-2-22-22220000-220000-2-22-200002i−2i−2i2i-22−2i2i−2i2i2i−2i2i−2i000000000000−2i2i0000-222-20000000000000000
χ592-22-2-22-22220000-220000-2-22-20000−2i2i2i−2i-222i−2i2i−2i−2i2i−2i2i0000000000002i−2i0000-222-20000000000000000
χ602-22-2-22-22220000-220000-2-22-20000−2i2i2i−2i-22−2i2i−2i2i2i−2i2i−2i0000000000002i−2i00002-2-220000000000000000
χ61444-4-4-44-4-444i4i−4i−4i000000-440000−4i4i0000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-44−4i−4i4i4i000000-4400004i−4i0000000000000000000000000000000000000000000000000000
χ6344-44-4-4-44004-4-44000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6444-44-4-4-44004-4-4400000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6544-44-4-4-4400-444-4000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6644-44-4-4-4400-444-400000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6744-4-444-4-4004i−4i4i−4i-44−4i−4i4i4i00-4400000000000000000000000000000000000000000000000000000000
χ6844-4-444-4-400−4i4i−4i4i-444i4i−4i−4i00-4400000000000000000000000000000000000000000000000000000000
χ694-4444-4-4-4-440000004i−4i4i−4i4-400−4i4i000000000000000000000000000000000000000000000000000000
χ704-4444-4-4-4-44000000−4i4i−4i4i4-4004i−4i000000000000000000000000000000000000000000000000000000
χ714-44-4-44-44-4-400004-4000044-4400000000-440000000000000000000000000000000000000000000000
χ724-44-4-44-44-4-40000-440000444-4000000004-40000000000000000000000000000000000000000000000
χ734-4-44-444-400000044000000-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ744-4-44-444-400000044000000-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ754-4-44-444-4000000-4-400000044000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ764-4-44-444-4000000-4-4000000440000000000−222222−2222−22−222200000000000000000000000000000000000000
χ774-4-4-44-444000000004-4-44000000000000002-2-222-2-222-2-222-2-22000000000000000000000000000000
χ784-4-4-44-444000000004-4-4400000000000000-222-2-222-2-222-2-222-2000000000000000000000000000000
χ794-4-4-44-44400000000-444-4000000000000002-2-222-2-22-222-2-222-2000000000000000000000000000000
χ804-4-4-44-44400000000-444-400000000000000-222-2-222-22-2-222-2-22000000000000000000000000000000

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