Finite Group Databasebeta

← Group #242109

Character table — Group #242109

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444444444444444888888888888888822444444888888882224444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11111-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-1-11-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-1111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1111-1-1-1-1111-1-1
χ101111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-11111-1-1-111
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1-1-11-1-1111-1-111
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-11111-111-1-1-111-1-1
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-111-111-1-1
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-11-1-111
χ1722222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-20000000000000000-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-22222-2-2222222-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ202222222222-2-2-2-22222-2-2222222-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ2122222222-2-22222222222-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000002-200-2000020000
χ2222222222-2-22222222222-2-2-2-2-2-222-2-2-2-20000000000000000000000000000000000-220020000-20000
χ2322222222-2-22222-2-2-2-2-2-22222-2-2-2-2-2-222000000000000000000000000000000002-2000002-20000000
χ2422222222-2-22222-2-2-2-2-2-22222-2-2-2-2-2-22200000000000000000000000000000000-2200000-220000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-200000-220000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-22000002-20000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-200000000000000000000000000000000002-20020000-20000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-20000000000000000000000000000000000-2200-2000020000
χ29222-2-2-22-22-22i2i−2i−2i2i2i−2i−2i2-22i2i−2i−2i2-22-22i−2i2-2000000000000000000000000000000000000000000002i−2i2-2
χ30222-2-2-22-22-22i2i−2i−2i2i2i−2i−2i2-22i2i−2i−2i2-22-22i−2i2-200000000000000000000000000000000000000000000−2i2i-22
χ31222-2-2-22-22-22i2i−2i−2i−2i−2i2i2i-22−2i−2i2i2i2-2-222i−2i-220000000000000000000000000000000000002i−2i0002-200000
χ32222-2-2-22-22-22i2i−2i−2i−2i−2i2i2i-22−2i−2i2i2i2-2-222i−2i-22000000000000000000000000000000000000−2i2i000-2200000
χ33222-2-2-22-22-2−2i−2i2i2i2i2i−2i−2i-222i2i−2i−2i2-2-22−2i2i-220000000000000000000000000000000000002i−2i000-2200000
χ34222-2-2-22-22-2−2i−2i2i2i2i2i−2i−2i-222i2i−2i−2i2-2-22−2i2i-22000000000000000000000000000000000000−2i2i0002-200000
χ35222-2-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-2−2i−2i2i2i2-22-2−2i2i2-2000000000000000000000000000000000000000000002i−2i-22
χ36222-2-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-2−2i−2i2i2i2-22-2−2i2i2-200000000000000000000000000000000000000000000−2i2i2-2
χ37222-2-2-22-2-222i2i−2i−2i2i2i−2i−2i2-2−2i−2i2i2i-222-2−2i2i-222i2i2i2i−2i−2i−2i−2i2222-2-2-2-200000000000000000000000000000000
χ38222-2-2-22-2-222i2i−2i−2i2i2i−2i−2i2-2−2i−2i2i2i-222-2−2i2i-22−2i−2i−2i−2i2i2i2i2i-2-2-2-2222200000000000000000000000000000000
χ39222-2-2-22-2-222i2i−2i−2i−2i−2i2i2i-222i2i−2i−2i-22-22−2i2i2-200000000000000000000000022-2-22i2i−2i−2i0000000000000000
χ40222-2-2-22-2-222i2i−2i−2i−2i−2i2i2i-222i2i−2i−2i-22-22−2i2i2-2000000000000000000000000-2-222−2i−2i2i2i0000000000000000
χ41222-2-2-22-2-22−2i−2i2i2i2i2i−2i−2i-22−2i−2i2i2i-22-222i−2i2-200000000000000000000000022-2-2−2i−2i2i2i0000000000000000
χ42222-2-2-22-2-22−2i−2i2i2i2i2i−2i−2i-22−2i−2i2i2i-22-222i−2i2-2000000000000000000000000-2-2222i2i−2i−2i0000000000000000
χ43222-2-2-22-2-22−2i−2i2i2i−2i−2i2i2i2-22i2i−2i−2i-222-22i−2i-222i2i2i2i−2i−2i−2i−2i-2-2-2-2222200000000000000000000000000000000
χ44222-2-2-22-2-22−2i−2i2i2i−2i−2i2i2i2-22i2i−2i−2i-222-22i−2i-22−2i−2i−2i−2i2i2i2i2i2222-2-2-2-200000000000000000000000000000000
χ452-2222-2-2-2-2200002i−2i2i−2i002i−2i2i−2i2-200000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2002-2002i−2ii2−i2i2−i22−22−20000000000000000
χ462-2222-2-2-2-2200002i−2i2i−2i002i−2i2i−2i2-200000022−2−222−2−2i2i2−i2−i2i2i2−i2−i200-2200−2i2i−i2i2−i2i2−22−220000000000000000
χ472-2222-2-2-2-2200002i−2i2i−2i002i−2i2i−2i2-2000000−2−222−2−222−i2−i2i2i2−i2−i2i2i2002-2002i−2i−i2i2−i2i2−22−220000000000000000
χ482-2222-2-2-2-2200002i−2i2i−2i002i−2i2i−2i2-2000000−2−222−2−222−i2−i2i2i2−i2−i2i2i200-2200−2i2ii2−i2i2−i22−22−20000000000000000
χ492-2222-2-2-2-220000−2i2i−2i2i00−2i2i−2i2i2-200000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2002-200−2i2i−i2i2−i2i22−22−20000000000000000
χ502-2222-2-2-2-220000−2i2i−2i2i00−2i2i−2i2i2-200000022−2−222−2−2−i2−i2i2i2−i2−i2i2i200-22002i−2ii2−i2i2−i2−22−220000000000000000
χ512-2222-2-2-2-220000−2i2i−2i2i00−2i2i−2i2i2-2000000−2−222−2−222i2i2−i2−i2i2i2−i2−i2002-200−2i2ii2−i2i2−i2−22−220000000000000000
χ522-2222-2-2-2-220000−2i2i−2i2i00−2i2i−2i2i2-2000000−2−222−2−222i2i2−i2−i2i2i2−i2−i200-22002i−2i−i2i2−i2i22−22−20000000000000000
χ532-22-2-22-222200002-2-2200-222-2-2-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-2002-200i2−i2−i2i2i2−i2−i2i20000000000000000
χ542-22-2-22-222200002-2-2200-222-2-2-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-2200-2200−i2i2i2−i2−i2i2i2−i20000000000000000
χ552-22-2-22-222200002-2-2200-222-2-2-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-2002-200−i2i2i2−i2−i2i2i2−i20000000000000000
χ562-22-2-22-222200002-2-2200-222-2-2-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-2200-2200i2−i2−i2i2i2−i2−i2i20000000000000000
χ572-22-2-22-22220000-222-2002-2-22-2-2000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-200-2200i2−i2−i2i2−i2i2i2−i20000000000000000
χ582-22-2-22-22220000-222-2002-2-22-2-2000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-22002-200−i2i2i2−i2i2−i2−i2i20000000000000000
χ592-22-2-22-22220000-222-2002-2-22-2-2000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-200-2200−i2i2i2−i2i2−i2−i2i20000000000000000
χ602-22-2-22-22220000-222-2002-2-22-2-2000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-22002-200i2−i2−i2i2−i2i2i2−i20000000000000000
χ6144-44-4-4-44004-44-40000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6244-44-4-4-44004-44-4000000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6344-44-4-4-4400-44-440000000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6444-44-4-4-4400-44-44000000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6544-4-444-4-4004i−4i−4i4i0000000000000000002-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6644-4-444-4-4004i−4i−4i4i000000000000000000-22-222-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6744-4-444-4-400−4i4i4i−4i0000000000000000002-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6844-4-444-4-400−4i4i4i−4i000000000000000000-22-222-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ694-4444-4-4-44-400004i−4i4i−4i00−4i4i−4i4i-44000000000000000000000000000000000000000000000000000000
χ704-4444-4-4-44-40000−4i4i−4i4i004i−4i4i−4i-44000000000000000000000000000000000000000000000000000000
χ714-44-4-44-44-4-400004-4-44004-4-4444000000000000000000000000000000000000000000000000000000
χ724-44-4-44-44-4-40000-444-400-444-444000000000000000000000000000000000000000000000000000000
χ734-4-44-444-4000000000044000000-4-400002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ744-4-44-444-4000000000044000000-4-40000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ754-4-44-444-40000000000-4-40000004400000000000022−22−222222−22−222200000000000000000000000000000000
χ764-4-44-444-40000000000-4-400000044000000000000−222222−22−222222−2200000000000000000000000000000000
χ774-4-4-44-44400000000004-4000000-44000022−22−2222−222222−220000000000000000000000000000000000000000
χ784-4-4-44-44400000000004-4000000-440000−222222−2222−22−22220000000000000000000000000000000000000000
χ794-4-4-44-4440000000000-440000004-400000000000022−22−2222−222222−2200000000000000000000000000000000
χ804-4-4-44-4440000000000-440000004-4000000000000−222222−2222−22−222200000000000000000000000000000000

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