Finite Group Databasebeta

← Group #436921

Character table — Group #436921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111111111112222222244448888888888888888888888888888888888161616161616161616161616
order12222222222222224444444444444444444444444444448888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1111111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ10111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ11111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ12111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ13111111111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ14111111111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ15111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ16111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ172222222222222222-2-2-2-2-2-2-2-222222222-2-20000-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2220000-2-22200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-20000222200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000022-2-200000000000000000000000000000000
χ2122222-2-2-222-2-2-22-2-222-2-2-22-220000000000000000002i2i−2i−2i2i2i−2i−2i0000000000002-20000000000
χ2222222-2-2-222-2-2-22-2-222-2-2-22-220000000000000000002i2i−2i−2i−2i−2i2i2i000000000000-220000000000
χ2322222-2-2-222-2-2-22-2-222-2-2-22-22000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000-220000000000
χ2422222-2-2-222-2-2-22-2-222-2-2-22-22000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000002-20000000000
χ25222-2-222-2-2-222-22-2-22-22-2-2-222000000000022-2-20000000000002i2i−2i−2i0000000000000000002i−2i
χ26222-2-222-2-2-222-22-2-22-22-2-2-222000000000022-2-2000000000000−2i−2i2i2i000000000000000000−2i2i
χ27222-2-222-2-2-222-22-2-22-22-2-2-2220000000000-2-2220000000000002i2i−2i−2i000000000000000000−2i2i
χ28222-2-222-2-2-222-22-2-22-22-2-2-2220000000000-2-222000000000000−2i−2i2i2i0000000000000000002i−2i
χ292-2-22-22222-2-2-2-222-22-2-22-222-22i2i−2i−2i00000000002i−2i00000000002-22-200002i2i−2i−2i000000000000
χ302-2-22-22222-2-2-2-222-22-2-22-222-22i2i−2i−2i00000000002i−2i0000000000-22-220000−2i−2i2i2i000000000000
χ312-2-22-22222-2-2-2-222-22-2-22-222-2−2i−2i2i2i0000000000−2i2i00000000002-22-20000−2i−2i2i2i000000000000
χ322-2-22-22222-2-2-2-222-22-2-22-222-2−2i−2i2i2i0000000000−2i2i0000000000-22-2200002i2i−2i−2i000000000000
χ332-2-22-22222-2-2-2-222-2-222-22-2-222i2i−2i−2i0000000000−2i2i0000002i−2i2i−2i000022-2-20000000000000000
χ342-2-22-22222-2-2-2-222-2-222-22-2-222i2i−2i−2i0000000000−2i2i000000−2i2i−2i2i0000-2-2220000000000000000
χ352-2-22-22222-2-2-2-222-2-222-22-2-22−2i−2i2i2i00000000002i−2i0000002i−2i2i−2i0000-2-2220000000000000000
χ362-2-22-22222-2-2-2-222-2-222-22-2-22−2i−2i2i2i00000000002i−2i000000−2i2i−2i2i000022-2-20000000000000000
χ372-2-22-2-2-2-22-22222-22-22-22-2-22200000000002-22-2000000002-2-220000000000000000002-20000
χ382-2-22-2-2-2-22-22222-22-22-22-2-22200000000002-22-200000000-222-2000000000000000000-220000
χ392-2-22-2-2-2-22-22222-22-22-22-2-2220000000000-22-22000000002-2-22000000000000000000-220000
χ402-2-22-2-2-2-22-22222-22-22-22-2-2220000000000-22-2200000000-222-20000000000000000002-20000
χ412-2-2-2222-2-22-2-222-2222-2-22-22-20000000000000000002-22-200002i−2i−2i2i00000000000000002i−2i00
χ422-2-2-2222-2-22-2-222-2222-2-22-22-20000000000000000002-22-20000−2i2i2i−2i0000000000000000−2i2i00
χ432-2-2-2222-2-22-2-222-2222-2-22-22-2000000000000000000-22-2200002i−2i−2i2i0000000000000000−2i2i00
χ442-2-2-2222-2-22-2-222-2222-2-22-22-2000000000000000000-22-220000−2i2i2i−2i00000000000000002i−2i00
χ452-2-2-22-2-22-2222-222-22222-2-2-2-200002-2002-2000000002i−2i−2i2i000000000000000000002i−2i000000
χ462-2-2-22-2-22-2222-222-22222-2-2-2-200002-2002-200000000−2i2i2i−2i00000000000000000000−2i2i000000
χ472-2-2-22-2-22-2222-222-22222-2-2-2-20000-2200-22000000002i−2i−2i2i00000000000000000000−2i2i000000
χ482-2-2-22-2-22-2222-222-22222-2-2-2-20000-2200-2200000000−2i2i2i−2i000000000000000000002i−2i000000
χ492-2-2-22-2-22-2222-222-2-2-2-2-2222200002-200-222-2-22000000000000000000000000002-200000000
χ502-2-2-22-2-22-2222-222-2-2-2-2-2222200002-200-22-222-200000000000000000000000000-2200000000
χ512-2-2-22-2-22-2222-222-2-2-2-2-222220000-22002-22-2-2200000000000000000000000000-2200000000
χ522-2-2-22-2-22-2222-222-2-2-2-2-222220000-22002-2-222-2000000000000000000000000002-200000000
χ5344444-4-4-444-4-4-44-4-4-4-4444-44-400000000000000000000000000000000000000000000000000
χ54444-4-444-4-4-444-44-4-4-44-4444-4-400000000000000000000000000000000000000000000000000
χ55444-4-4-4-44-4-4-4-444444-4-444-4-4400000000000000000000000000000000000000000000000000
χ56444-4-4-4-44-4-4-4-44444-444-4-444-400000000000000000000000000000000000000000000000000
χ5744-4444-44-4-44-44-4-4-4000000004-44-40000000000000000000000000000000000000000000000
χ5844-4444-44-4-44-44-4-4-400000000-44-440000000000000000000000000000000000000000000000
χ5944-444-44-4-4-4-44-4-444000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ6044-444-44-4-4-4-44-4-44400000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ6144-4-4-44-4-4444-4-4-44400000000000000000000000000000000000000000022−2222−22000000000000
χ6244-4-4-44-4-4444-4-4-444000000000000000000000000000000000000000000−2222−2222000000000000
χ6344-4-4-4-44444-444-4-4-40000000000000000000000004i−4i00000000000000000000000000000000
χ6444-4-4-4-44444-444-4-4-4000000000000000000000000−4i4i00000000000000000000000000000000
χ654-444-44-44-44-44-4-4-44000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ664-444-44-44-44-44-4-4-4400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-444-4-44-4-444-44-44-4000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ684-444-4-44-4-444-44-44-400000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ694-44-444-4-44-4-444-44-40000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ704-44-444-4-44-4-444-44-4000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ714-44-44-4444-44-4-4-4-44000000000000004i−4i000000000000000000000000000000000000000000
χ724-44-44-4444-44-4-4-4-4400000000000000−4i4i000000000000000000000000000000000000000000
χ734-4-44-4-4-4-44-44444-444-44-444-4-400000000000000000000000000000000000000000000000000
χ744-4-4-4444-4-44-4-444-44-4-444-44-4400000000000000000000000000000000000000000000000000

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