Finite Group Databasebeta

← Group #97539

Character table — Group #97539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111111111111144444444444488888888888888888888888888888888888816161616161616161616
order12222222222222224444444444444444444444448888888888888888888888884444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1
χ9111-1-1-1-1-1-1-11111-1111-111-111-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−i1-1
χ10111-1-1-1-1-1-1-11111-1111-111-111-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii1-1
χ11111-1-1-1-1-1-1-11111-1111-111-111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-11−i−iii1-1
χ12111-1-1-1-1-1-1-11111-1111-111-111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-11ii−i−i1-1
χ13111-1-1-1-1-1-1-11111-1111-111-111-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11−i−iii-11
χ14111-1-1-1-1-1-1-11111-1111-111-111-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11ii−i−i-11
χ15111-1-1-1-1-1-1-11111-1111-111-111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1ii−i−i-11
χ16111-1-1-1-1-1-1-11111-1111-111-111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-1−i−iii-11
χ172222222222222222222-2-2-2-2-2-22-2-222220000000000000000000000000000000000000000-2-2
χ182222222222222222222-2-2-2-2-2-22-2-2-2-2-2-2000000000000000000000000000000000000000022
χ192222222222222222-2-2-2222-2-2-2-22-200000000222200000000000000000000000000-2-2000000
χ202222222222222222-2-2-2222-2-2-2-22-200000000-2-2-2-20000000000000000000000000022000000
χ212222222222222222-2-2-2-2-2-2222-2-22000022220000000000000000000000000000-2-200000000
χ222222222222222222-2-2-2-2-2-2222-2-220000-2-2-2-200000000000000000000000000002200000000
χ23222-2-2-2-2-2-2-22222-2222-2-2-22-2-22-22222-2-20000000000000000000000000000000000000000-22
χ24222-2-2-2-2-2-2-22222-2222-2-2-22-2-22-222-2-22200000000000000000000000000000000000000002-2
χ25222-2-2-2-2-2-2-22222-22-2-2222-2-2-222-220000000022-2-200000000000000000000000000-22000000
χ26222-2-2-2-2-2-2-22222-22-2-2222-2-2-222-2200000000-2-222000000000000000000000000002-2000000
χ27222-2-2-2-2-2-2-22222-22-2-22-2-2222-222-2000022-2-20000000000000000000000000000-2200000000
χ28222-2-2-2-2-2-2-22222-22-2-22-2-2222-222-20000-2-22200000000000000000000000000002-200000000
χ2922-22222-2-2-222-2-2-2-22-22000000-2002-22-20000000022−2−222−2−222−2−222−2−2000000000000000000
χ3022-22222-2-2-222-2-2-2-22-22000000-2002-22-200000000−2−222−2−222−2−222−2−222000000000000000000
χ3122-22222-2-2-222-2-2-2-22-22000000-200-22-220000000022−2−222−2−2−2−222−2−222000000000000000000
χ3222-22222-2-2-222-2-2-2-22-22000000-200-22-2200000000−2−222−2−22222−2−222−2−2000000000000000000
χ3322-222-2-222-2-2-222-2-20002-2-2000020000000002i−2i2i−2i00000000i2−i2i2−i2i2−i2i2−i222−2−222−2−20000000000
χ3422-222-2-222-2-2-222-2-20002-2-2000020000000002i−2i2i−2i00000000−i2i2−i2i2−i2i2−i2i2−2−222−2−2220000000000
χ3522-222-2-222-2-2-222-2-20002-2-200002000000000−2i2i−2i2i00000000i2−i2i2−i2i2−i2i2−i2−2−222−2−2220000000000
χ3622-222-2-222-2-2-222-2-20002-2-200002000000000−2i2i−2i2i00000000−i2i2−i2i2−i2i2−i2i222−2−222−2−20000000000
χ3722-2-2-222-2-22-2-2222-20002-220000-20000000002i−2i−2i2i000000002−22−2−22−22−i2−i2i2i2i2i2−i2−i20000000000
χ3822-2-2-222-2-22-2-2222-20002-220000-20000000002i−2i−2i2i00000000−22−222−22−2i2i2−i2−i2−i2−i2i2i20000000000
χ3922-2-2-222-2-22-2-2222-20002-220000-2000000000−2i2i2i−2i000000002−22−2−22−22i2i2−i2−i2−i2−i2i2i20000000000
χ4022-2-2-222-2-22-2-2222-20002-220000-2000000000−2i2i2i−2i00000000−22−222−22−2−i2−i2i2i2i2i2−i2−i20000000000
χ4122-2-2-2-2-222222-2-22-22-2-20000002002-2-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000
χ4222-2-2-2-2-222222-2-22-22-2-20000002002-2-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000
χ4322-2-2-2-2-222222-2-22-22-2-2000000200-222-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000
χ4422-2-2-2-2-222222-2-22-22-2-2000000200-222-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000
χ452-2-22-22-22-22-22-22-220000002-2200-200002-22-20000i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i20000000000
χ462-2-22-22-22-22-22-22-220000002-2200-200002-22-20000−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i20000000000
χ472-2-22-22-22-22-22-22-220000002-2200-20000-22-220000i2−i2i2−i2i2−i2i2−i200000000−i2i2−i2i2−i2i2−i2i20000000000
χ482-2-22-22-22-22-22-22-220000002-2200-20000-22-220000−i2i2−i2i2−i2i2−i2i200000000i2−i2i2−i2i2−i2i2−i20000000000
χ492-2-2-22-22-22-2-22-22220000002-2-200200002-2-2200002−22−2−22−22000000002−22−2−22−220000000000
χ502-2-2-22-22-22-2-22-22220000002-2-200200002-2-220000−22−222−22−200000000−22−222−22−20000000000
χ512-2-2-22-22-22-2-22-22220000002-2-20020000-222-200002−22−2−22−2200000000−22−222−22−20000000000
χ522-2-2-22-22-22-2-22-22220000002-2-20020000-222-20000−22−222−22−2000000002−22−2−22−220000000000
χ5344444-4-4-4-44-4-4-4-444000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ5444444-4-4-4-44-4-4-4-44400000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ55444-4-44444-4-4-4-4-4-44000000000000000000000000000000002-2-22-222-2000000000000000000
χ56444-4-44444-4-4-4-4-4-4400000000000000000000000000000000-222-22-2-22000000000000000000
χ5744-44444-4-4-444-4-4-4-4-44-40000004000000000000000000000000000000000000000000000000
χ5844-444-4-444-4-4-444-4-4000-4440000-400000000000000000000000000000000000000000000000
χ5944-4-4-444-4-44-4-4444-4000-44-40000400000000000000000000000000000000000000000000000
χ6044-4-4-4-4-444444-4-44-4-444000000-4000000000000000000000000000000000000000000000000
χ614-444-44-4-44-4-444-44-40000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ624-444-44-4-44-4-444-44-4000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ634-444-4-444-4-44-4-444-400000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ644-444-4-444-4-44-4-444-40000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ654-44-444-4-4444-4-44-4-400000000000000000000000000000000000000002-2-22-222-20000000000
χ664-44-444-4-4444-4-44-4-40000000000000000000000000000000000000000-222-22-2-220000000000
χ674-44-44-444-44-444-4-4-40000000000000000000000002-2-22-222-200000000000000000000000000
χ684-44-44-444-44-444-4-4-4000000000000000000000000-222-22-2-2200000000000000000000000000
χ694-4-44-44-44-44-44-44-44000000-44-40040000000000000000000000000000000000000000000000
χ704-4-44-4-44-4444-44-4-4400000000000000000000000000000000000000000000000000002i−2i2i−2i00
χ714-4-44-4-44-4444-44-4-440000000000000000000000000000000000000000000000000000−2i2i−2i2i00
χ724-4-4-444-44-4-44-44-44400000000000000000000000000000000000000000000000000002-2-2200
χ734-4-4-444-44-4-44-44-4440000000000000000000000000000000000000000000000000000-222-200
χ744-4-4-44-44-44-4-44-4444000000-44400-40000000000000000000000000000000000000000000000

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