Finite Group Databasebeta

← Group #256656

Character table — Group #256656

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444224444448888888888888888444444444444244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111
χ91111111111-1-1-1-1111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1111111-1-11-1-1111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11-1-1-11111111-1-1-1-111
χ111111111111-1-1-1-1111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-11111-1-11111-1-1
χ121111111111-1-1-1-1111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-11111-1-1-1-1-1-1-111-1-111
χ131111111111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1111111-1-11-1-1-1-11-1-111-1-111-1-111
χ141111111111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-11-111111-1-1-1-11111-1-1
χ151111111111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11-1111-111-1-111-1-1-1-111
χ161111111111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1111111-111-1-1-1-1-11111-1-111-1-1
χ1722222222222222-2-222-2-2-2-2-2-2-222-20000000000000000000022000022-2-20000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-222-200000000000000000000-2-20000-2-2220000000000000000
χ192222222222-2-2-2-2-2-222-2-22222-2-2-2-200000000000000000000220000-2-2-220000000000000000
χ202222222222-2-2-2-2-2-222-2-22222-2-2-2-200000000000000000000-2-20000222-20000000000000000
χ2122222222-2-2222222-2-222-2-222-2-2-2-2000000000000000022220000000000-200-2000000000000
χ2222222222-2-2222222-2-222-2-222-2-2-2-20000000000000000-2-2-2-200000000002002000000000000
χ2322222222-2-22222-2-2-2-2-2-222-2-22-2-22000000000000000000000022-2-2000000002-20000000000
χ2422222222-2-22222-2-2-2-2-2-222-2-22-2-220000000000000000000000-2-22200000000-220000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-222-2000000000000000022-2-20000000000200-2000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-222-20000000000000000-2-2220000000000-2002000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000022-2-200000000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000-2-222000000002-20000000000
χ29222-2-2-2-222-22i2i−2i−2i002-200000002i−2i02222−2−2−2−2i2i2i2i2−i2−i2−i2−i200002i−2i00002-200000000000000i2−i22−2
χ30222-2-2-2-222-22i2i−2i−2i002-200000002i−2i02222−2−2−2−2i2i2i2i2−i2−i2−i2−i20000−2i2i0000-2200000000000000−i2i2−22
χ31222-2-2-2-222-22i2i−2i−2i002-200000002i−2i0−2−2−2−22222−i2−i2−i2−i2i2i2i2i200002i−2i00002-200000000000000−i2i2−22
χ32222-2-2-2-222-22i2i−2i−2i002-200000002i−2i0−2−2−2−22222−i2−i2−i2−i2i2i2i2i20000−2i2i0000-2200000000000000i2−i22−2
χ33222-2-2-2-222-2−2i−2i2i2i002-20000000−2i2i02222−2−2−2−2−i2−i2−i2−i2i2i2i2i200002i−2i0000-2200000000000000i2−i2−22
χ34222-2-2-2-222-2−2i−2i2i2i002-20000000−2i2i02222−2−2−2−2−i2−i2−i2−i2i2i2i2i20000−2i2i00002-200000000000000−i2i22−2
χ35222-2-2-2-222-2−2i−2i2i2i002-20000000−2i2i0−2−2−2−22222i2i2i2i2−i2−i2−i2−i200002i−2i0000-2200000000000000−i2i22−2
χ36222-2-2-2-222-2−2i−2i2i2i002-20000000−2i2i0−2−2−2−22222i2i2i2i2−i2−i2−i2−i20000−2i2i00002-200000000000000i2−i2−22
χ3722-2-222-2-22-200002-2-222-20000-200222-2-222-2-2000000000000002i−2i2i−2i000002i−2i0000000000000
χ3822-2-222-2-22-200002-2-222-20000-200222-2-222-2-200000000000000−2i2i−2i2i00000−2i2i0000000000000
χ3922-2-222-2-22-200002-2-222-20000-2002-2-222-2-222000000000000002i−2i2i−2i00000−2i2i0000000000000
χ4022-2-222-2-22-200002-2-222-20000-2002-2-222-2-22200000000000000−2i2i−2i2i000002i−2i0000000000000
χ4122-2-222-2-2-220000-222-2-220000-20020000000022-2-222-2-20000002i−2i−2i2i00000000002i−2i00000000
χ4222-2-222-2-2-220000-222-2-220000-20020000000022-2-222-2-2000000−2i2i2i−2i0000000000−2i2i00000000
χ4322-2-222-2-2-220000-222-2-220000-200200000000-2-222-2-2220000002i−2i−2i2i0000000000−2i2i00000000
χ4422-2-222-2-2-220000-222-2-220000-200200000000-2-222-2-222000000−2i2i2i−2i00000000002i−2i00000000
χ452-22-2-222-2002i−2i2i−2i-22002-2002i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i22-22i−2i0000000000000000002−2i2−i20000
χ462-22-2-222-2002i−2i2i−2i-22002-2002i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i2-22−2i2i000000000000000000−22−i2i20000
χ472-22-2-222-2002i−2i2i−2i-22002-2002i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i22-22i−2i000000000000000000−22−i2i20000
χ482-22-2-222-2002i−2i2i−2i-22002-2002i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i2-22−2i2i0000000000000000002−2i2−i20000
χ492-22-2-222-200−2i2i−2i2i-22002-200−2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i22-2−2i2i0000000000000000002−2−i2i20000
χ502-22-2-222-200−2i2i−2i2i-22002-200−2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i2-222i−2i000000000000000000−22i2−i20000
χ512-22-2-222-200−2i2i−2i2i-22002-200−2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i22-2−2i2i000000000000000000−22i2−i20000
χ522-22-2-222-200−2i2i−2i2i-22002-200−2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i2-222i−2i0000000000000000002−2−i2i20000
χ53444-4-4-4-44-444i4i−4i−4i00-440000000−4i4i00000000000000000000000000000000000000000000000
χ54444-4-4-4-44-44−4i−4i4i4i00-4400000004i−4i00000000000000000000000000000000000000000000000
χ5544-44-4-44-444000000-4-400000000002222−22−22−22−22222200000000000000000000000000000000000000
χ5644-44-4-44-444000000-4-40000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5744-44-4-44-4-4-4000000440000000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000
χ5844-44-4-44-4-4-400000044000000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000
χ5944-4-444-4-44-40000-44-44-440000400-40000000000000000000000000000000000000000000000
χ6044-4-444-4-4-4400004-44-44-40000400-40000000000000000000000000000000000000000000000
χ614-4444-4-4-4004-4-44000000000000002-22-2-22-222-22-2-22-22000000000000000000000000000000
χ624-4444-4-4-4004-4-4400000000000000-22-222-22-2-22-222-22-2000000000000000000000000000000
χ634-4444-4-4-400-444-4000000000000002-22-2-22-22-22-222-22-2000000000000000000000000000000
χ644-4444-4-4-400-444-400000000000000-22-222-22-22-22-2-22-22000000000000000000000000000000
χ654-44-4-444-4004i−4i4i−4i4-400-4400−4i4i00000000000000000000000000000000000000000000000000
χ664-44-4-444-400−4i4i−4i4i4-400-44004i−4i00000000000000000000000000000000000000000000000000
χ674-4-44-44-440000004400-4-400000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ684-4-44-44-440000004400-4-40000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ694-4-44-44-44000000-4-400440000000022−22−222222−22−222200000000000000000000000000000000000000
χ704-4-44-44-44000000-4-4004400000000−222222−22−222222−2200000000000000000000000000000000000000
χ714-4-4-44-4440000000000004-40000002-2-22-222-22-2-22-222-2000000000000000000000000000000
χ724-4-4-44-4440000000000004-4000000-222-22-2-22-222-22-2-22000000000000000000000000000000
χ734-4-4-44-444000000000000-440000002-2-22-222-2-222-22-2-22000000000000000000000000000000
χ744-4-4-44-444000000000000-44000000-222-22-2-222-2-22-222-2000000000000000000000000000000

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