Finite Group Databasebeta

← Group #6574530

Character table — Group #6574530

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222222244444444444444442222224444444444444444888888882244444444444444444888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-11-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11-11-11-1
χ61111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-11-11-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-111-1-11111-1-11111-1-1-1-1-11-11-11
χ81111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11111-1-1-1-111-1-1-1-111111-11-11-1
χ9111111111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-111-1-111-1-1-1-1-1-111
χ10111111111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1111111-1-1
χ11111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-11111-111-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ12111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-111111111111-1-111-1-111-1-1-1-111
χ13111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111-1-11-1-1-11111-1-1-1-11111-1-1-1-111-11-111-1
χ14111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111-1-11-1-1-111-1-11111-1-1-1-11111-1-11-11-1-11
χ15111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-11111-1-1-1-1111-11-1-11
χ16111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-111-1-1111111-1-1-111-1-111-1-1-1-11111-1-1-11-111-1
χ1711111111-1-1-1-1111111-1-1-1-1111111-1-111111111-1-1-1-1111111-1-111111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ1811111111-1-1-1-1111111-1-1-1-1111111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ1911111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1111-111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ2011111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-111-1111111-1-1-1-11111111111-1-1-1-1
χ2111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-111111111-1-111-1-1-1-1-1-111111-1-11-11
χ2211111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-111-11-1
χ2311111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1-1-111-1-111-1111-1-11-1-1-1-11111-1-1-1-1-1-11111-111-11-1
χ2411111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1111-1-11-1-111-1-1-1-1111111-1-1-1-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-1
χ2611111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1111111-1-111-1-111-1-111
χ2711111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ2811111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-11111111111-1-111-1-1-1-111-1-1
χ2911111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1111-1-111-1-1-1-111-1-11111-1-1-111-1-11
χ3011111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1111-1-1-1-11111-1-111-1-1-1-1111-1-111-1
χ3111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-11-1-1-1-1-1111-1-111-1-111-1-11111-1-11-1-111-1
χ3211111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-111111-1-111-1-111-1-1-1-111-111-1-11
χ332222222222222222-2-222222222-2-2-2-20000-2-222-2-2220000-2-22200000000000000-200-200-2000000000000000000000000
χ342222222222222222-2-22222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-2000022-2-2000000000000002002002000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-22222-2-222000022-2-2-2-2220000-2-2-2-200000000000000200200-2000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22200002222-2-2-2-20000222200000000000000-200-2002000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-2-2-22222-2-2220000-2-22222-2-20000-2-2-2-200000000000000-2002002000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2220000-2-2-2-222220000222200000000000000200-200-2000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000022-2-222-2-20000-2-22200000000000000200-2002000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000022222222000022-2-200000000000000-200200-2000000000000000000000000
χ41222-22-2-2-222-2-222-2-22222-2-20000-2-22-222-2-22-2002-20000000000000000002-22-20002-20000000000000000000000000000
χ42222-22-2-2-222-2-222-2-22222-2-20000-2-22-2-2-2222-2002-2000000000000000000-22-22000-220000000000000000000000000000
χ43222-22-2-2-222-2-222-2-2-2-222-2-2000022-220000-2200-22002i2i−2i−2i00000000000000002i−2i00002i−2i02i−2i0000000000000000000000
χ44222-22-2-2-222-2-222-2-2-2-222-2-2000022-220000-2200-2200−2i−2i2i2i0000000000000000−2i2i0000−2i2i0−2i2i0000000000000000000000
χ45222-22-2-2-222-2-2-2-22222-2-2220000-2-2-2222-2-2-22002-20000000000000000002-2-22000-220000000000000000000000000000
χ46222-22-2-2-222-2-2-2-22222-2-2220000-2-2-22-2-222-22002-2000000000000000000-222-20002-20000000000000000000000000000
χ47222-22-2-2-222-2-2-2-222-2-2-2-2220000222-200002-200-22002i2i−2i−2i0000000000000000−2i2i00002i−2i0−2i2i0000000000000000000000
χ48222-22-2-2-222-2-2-2-222-2-2-2-2220000222-200002-200-2200−2i−2i2i2i00000000000000002i−2i0000−2i2i02i−2i0000000000000000000000
χ49222-22-2-2-2-2-22222-2-222-2-2220000-2-2-2222-2-22-200-22000000000000000000-222-2000-220000000000000000000000000000
χ50222-22-2-2-2-2-22222-2-222-2-2220000-2-2-22-2-2222-200-220000000000000000002-2-220002-20000000000000000000000000000
χ51222-22-2-2-2-2-22222-2-2-2-2-2-2220000222-20000-22002-2002i2i−2i−2i00000000000000002i−2i0000−2i2i0−2i2i0000000000000000000000
χ52222-22-2-2-2-2-22222-2-2-2-2-2-2220000222-20000-22002-200−2i−2i2i2i0000000000000000−2i2i00002i−2i02i−2i0000000000000000000000
χ53222-22-2-2-2-2-222-2-2222222-2-20000-2-22-222-2-2-2200-22000000000000000000-22-220002-20000000000000000000000000000
χ54222-22-2-2-2-2-222-2-2222222-2-20000-2-22-2-2-222-2200-220000000000000000002-22-2000-220000000000000000000000000000
χ55222-22-2-2-2-2-222-2-222-2-222-2-2000022-2200002-2002-2002i2i−2i−2i0000000000000000−2i2i0000−2i2i02i−2i0000000000000000000000
χ56222-22-2-2-2-2-222-2-222-2-222-2-2000022-2200002-2002-200−2i−2i2i2i00000000000000002i−2i00002i−2i0−2i2i0000000000000000000000
χ5722-2-2-222-22-22-22i−2i2i−2i002i−2i2i−2i22-2-200000000002i−2i002-20000002i−2ii2i2−i2−i2i2i2−i2−i200000000000000000002−22−2i2−i22−2i2−i22−2000000
χ5822-2-2-222-22-22-22i−2i2i−2i002i−2i2i−2i22-2-200000000002i−2i002-20000002i−2i−i2−i2i2i2−i2−i2i2i20000000000000000000−22−22−i2i2−22−i2i2−22000000
χ5922-2-2-222-22-22-22i−2i2i−2i002i−2i2i−2i-2-2220000000000−2i2i00-22000000−2i2ii2i2−i2−i2−i2−i2i2i200000000000000000002−2−22i2−i22−2−i2i2−22000000
χ6022-2-2-222-22-22-22i−2i2i−2i002i−2i2i−2i-2-2220000000000−2i2i00-22000000−2i2i−i2−i2i2i2i2i2−i2−i20000000000000000000−222−2−i2i2−22i2−i22−2000000
χ6122-2-2-222-22-22-2−2i2i−2i2i00−2i2i−2i2i22-2-20000000000−2i2i002-2000000−2i2ii2i2−i2−i2i2i2−i2−i20000000000000000000−22−22i2−i2−22i2−i2−22000000
χ6222-2-2-222-22-22-2−2i2i−2i2i00−2i2i−2i2i22-2-20000000000−2i2i002-2000000−2i2i−i2−i2i2i2−i2−i2i2i200000000000000000002−22−2−i2i22−2−i2i22−2000000
χ6322-2-2-222-22-22-2−2i2i−2i2i00−2i2i−2i2i-2-22200000000002i−2i00-220000002i−2ii2i2−i2−i2−i2−i2i2i20000000000000000000−222−2i2−i2−22−i2i22−2000000
χ6422-2-2-222-22-22-2−2i2i−2i2i00−2i2i−2i2i-2-22200000000002i−2i00-220000002i−2i−i2−i2i2i2i2i2−i2−i200000000000000000002−2−22−i2i22−2i2−i2−22000000
χ6522-2-2-222-2-22-222i−2i2i−2i00−2i2i−2i2i22-2-200000000002i−2i00-22000000−2i2ii2i2−i2−i2i2i2−i2−i200000000000000000002−22−2−i2i2−22−i2i2−22000000
χ6622-2-2-222-2-22-222i−2i2i−2i00−2i2i−2i2i22-2-200000000002i−2i00-22000000−2i2i−i2−i2i2i2−i2−i2i2i20000000000000000000−22−22i2−i22−2i2−i22−2000000
χ6722-2-2-222-2-22-222i−2i2i−2i00−2i2i−2i2i-2-2220000000000−2i2i002-20000002i−2ii2i2−i2−i2−i2−i2i2i200000000000000000002−2−22−i2i2−22i2−i22−2000000
χ6822-2-2-222-2-22-222i−2i2i−2i00−2i2i−2i2i-2-2220000000000−2i2i002-20000002i−2i−i2−i2i2i2i2i2−i2−i20000000000000000000−222−2i2−i22−2−i2i2−22000000
χ6922-2-2-222-2-22-22−2i2i−2i2i002i−2i2i−2i22-2-20000000000−2i2i00-220000002i−2ii2i2−i2−i2i2i2−i2−i20000000000000000000−22−22−i2i22−2−i2i22−2000000
χ7022-2-2-222-2-22-22−2i2i−2i2i002i−2i2i−2i22-2-20000000000−2i2i00-220000002i−2i−i2−i2i2i2−i2−i2i2i200000000000000000002−22−2i2−i2−22i2−i2−22000000
χ7122-2-2-222-2-22-22−2i2i−2i2i002i−2i2i−2i-2-22200000000002i−2i002-2000000−2i2ii2i2−i2−i2−i2−i2i2i20000000000000000000−222−2−i2i22−2i2−i2−22000000
χ7222-2-2-222-2-22-22−2i2i−2i2i002i−2i2i−2i-2-22200000000002i−2i002-2000000−2i2i−i2−i2i2i2i2i2−i2−i200000000000000000002−2−22i2−i2−22−i2i22−2000000
χ732-2-2-22-222000000002-200002-22-2-22002-22-2000000002-22-22-2002-22-22-22-20000000000000002-22-2000000000000000000
χ742-2-2-22-222000000002-200002-22-2-22002-22-2000000002-22-22-200-22-22-22-22000000000000000-22-22000000000000000000
χ752-2-2-22-222000000002-200002-22-2-2200-22-2200000000-22-222-2002-22-22-22-2000000000000000-22-22000000000000000000
χ762-2-2-22-222000000002-200002-22-2-2200-22-2200000000-22-222-200-22-22-22-220000000000000002-22-2000000000000000000
χ772-2-2-22-222000000002-20000-22-22-22002-22-200000000-22-22-22002-22-2-22-220000000000000002-2-22000000000000000000
χ782-2-2-22-222000000002-20000-22-22-22002-22-200000000-22-22-2200-22-222-22-2000000000000000-222-2000000000000000000
χ792-2-2-22-222000000002-20000-22-22-2200-22-22000000002-22-2-22002-22-2-22-22000000000000000-222-2000000000000000000
χ802-2-2-22-222000000002-20000-22-22-2200-22-22000000002-22-2-2200-22-222-22-20000000000000002-2-22000000000000000000
χ8144-44-4-4-444-4-444i−4i−4i4i004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000
χ8244-44-4-4-444-4-44−4i4i4i−4i00−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000
χ8344-44-4-4-44-444-44i−4i−4i4i00−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000
χ8444-44-4-4-44-444-4−4i4i4i−4i004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000
χ854-444-4-44-4000000000000004-4-440000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ864-444-4-44-4000000000000004-4-44000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ874-444-4-44-400000000000000-444-40000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000
χ884-444-4-44-400000000000000-444-4000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000
χ894-4-4444-4-4000000004-4000000004-4004-4-440000000000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-4000000004-4000000004-400-444-40000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-4-400000000-4400000000-44000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ924-4-4444-4-400000000-4400000000-4400000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ934-4-4-44-44400000000-4400004-44-44-4000000000000000000-4400000000000000000000000000000000000000000000000
χ944-4-4-44-44400000000-440000-44-444-40000000000000000004-400000000000000000000000000000000000000000000000
χ958-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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