Finite Group Databasebeta

← Group #255436

Character table — Group #255436

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422244444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111-1-1-1-1-1-111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111
χ7111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-1111111-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1111111-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1111-1-111
χ11111111111111-1-1-1-11111-1-1-1-1111111-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-111
χ12111111111111-1-1-1-11111-1-1-1-1111111-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-11111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-111111-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111111-1-1-1-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-111
χ172222222222-2-2222222-2-2-2-2222222-2-2-2-2-222-2-20000000000000000000000000000000000
χ182222222222-2-2222222-2-2-2-222-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-222-2-22222-2-22-2-2-2-2220000000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-222222-2-20000000000000000000000000000000000
χ2122222222-2-2222222-2-22222-2-20000-2-2-20000002222000000000000000000-20000-2000000
χ2222222222-2-2222222-2-22222-2-20000-2-2-2000000-2-2-2-2000000000000000000200002000000
χ2322222222-2-222-2-2-2-2-2-222-2-2220000-2-2200000022-2-200000000000000000020000-2000000
χ2422222222-2-222-2-2-2-2-2-222-2-2220000-2-22000000-2-222000000000000000000-200002000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-20000222000000000000000000000000002-202-2000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-2000022200000000000000000000000000-220-22000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-2000000000000000000000000002-20-22000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-200000000000000000000000000-2202-2000000000
χ29222-2-22-2-2002-22i2i−2i−2i002-22i−2i0000000000000002-22i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000000000
χ30222-2-22-2-2002-22i2i−2i−2i002-22i−2i0000000000000002-22i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000000000
χ31222-2-22-2-2002-22i2i−2i−2i002-22i−2i000000000000000-22−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000000000
χ32222-2-22-2-2002-22i2i−2i−2i002-22i−2i000000000000000-22−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000000000
χ33222-2-22-2-2002-2−2i−2i2i2i002-2−2i2i0000000000000002-2−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000000000
χ34222-2-22-2-2002-2−2i−2i2i2i002-2−2i2i0000000000000002-2−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000000000
χ35222-2-22-2-2002-2−2i−2i2i2i002-2−2i2i000000000000000-222i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000000000
χ36222-2-22-2-2002-2−2i−2i2i2i002-2−2i2i000000000000000-222i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000000000
χ3722-22-2-22-22-2002i−2i2i−2i2-200002i−2i2i2i−2i−2i000002-200000000000000i2−i2i2−i22−22−200000000002−2i2−i2
χ3822-22-2-22-22-2002i−2i2i−2i2-200002i−2i2i2i−2i−2i000002-200000000000000−i2i2−i2i2−22−220000000000−22−i2i2
χ3922-22-2-22-22-2002i−2i2i−2i2-200002i−2i−2i−2i2i2i00000-2200000000000000i2−i2i2−i22−22−20000000000−22−i2i2
χ4022-22-2-22-22-2002i−2i2i−2i2-200002i−2i−2i−2i2i2i00000-2200000000000000−i2i2−i2i2−22−2200000000002−2i2−i2
χ4122-22-2-22-22-200−2i2i−2i2i2-20000−2i2i2i2i−2i−2i00000-2200000000000000i2−i2i2−i2−22−2200000000002−2−i2i2
χ4222-22-2-22-22-200−2i2i−2i2i2-20000−2i2i2i2i−2i−2i00000-2200000000000000−i2i2−i2i22−22−20000000000−22i2−i2
χ4322-22-2-22-22-200−2i2i−2i2i2-20000−2i2i−2i−2i2i2i000002-200000000000000i2−i2i2−i2−22−220000000000−22i2−i2
χ4422-22-2-22-22-200−2i2i−2i2i2-20000−2i2i−2i−2i2i2i000002-200000000000000−i2i2−i2i22−22−200000000002−2−i2i2
χ452-2-22-22-22222-20000-2-2-2200002-22-22-202-2000000002i−2i2i−2i000000000000000002i−2i0000000
χ462-2-22-22-22222-20000-2-2-2200002-22-22-202-200000000−2i2i−2i2i00000000000000000−2i2i0000000
χ472-2-22-22-22222-20000-2-2-220000-22-222-20-22000000002i−2i2i−2i00000000000000000−2i2i0000000
χ482-2-22-22-22222-20000-2-2-220000-22-222-20-2200000000−2i2i−2i2i000000000000000002i−2i0000000
χ492-2-22-22-2222-220000-2-22-200002-22-2-220-220000000000002i−2i2i−2i00000000000000002i−2i0000
χ502-2-22-22-2222-220000-2-22-200002-22-2-220-22000000000000−2i2i−2i2i0000000000000000−2i2i0000
χ512-2-22-22-2222-220000-2-22-20000-22-22-2202-20000000000002i−2i2i−2i0000000000000000−2i2i0000
χ522-2-22-22-2222-220000-2-22-20000-22-22-2202-2000000000000−2i2i−2i2i00000000000000002i−2i0000
χ53444-4-44-4-400-444i4i−4i−4i00-44−4i4i0000000000000000000000000000000000000000000000000
χ54444-4-44-4-400-44−4i−4i4i4i00-444i−4i0000000000000000000000000000000000000000000000000
χ5544-44-4-44-4-44004i−4i4i−4i-440000−4i4i00000000000000000000000000000000000000000000000
χ5644-44-4-44-4-4400−4i4i−4i4i-4400004i−4i00000000000000000000000000000000000000000000000
χ5744-4-44-4-4400004-4-440000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ5844-4-44-4-4400004-4-44000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ5944-4-44-4-440000-444-40000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ6044-4-44-4-440000-444-4000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ614-4444-4-4-44-4000000-440000004i−4i−4i4i0000000000000000000000000000000000000000000
χ624-4444-4-4-44-4000000-44000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ634-4444-4-4-4-440000004-4000000000000000004i−4i0000000000000000000000000000000000
χ644-4444-4-4-4-440000004-400000000000000000−4i4i0000000000000000000000000000000000
χ654-4-44-44-44-4-44-4000044-4400000000-4400000000000000000000000000000000000000000
χ664-4-44-44-44-4-4-440000444-4000000004-400000000000000000000000000000000000000000
χ674-4-4-4444-40044000000-4-40000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ684-4-4-4444-40044000000-4-4000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ694-4-4-4444-400-4-400000044000000000000000000000000022−22−22220000000000000000000000
χ704-4-4-4444-400-4-4000000440000000000000000000000000−222222−220000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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