Finite Group Databasebeta

← Group #436218

Character table — Group #436218

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111111111112222222244448888888888888888888888888888888888161616161616161616161616
order12222222222222224444444444442244444444444444448888888888888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1
χ9111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ10111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111
χ11111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ12111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ14111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ16111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ172222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-20000-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222220000-2-200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-200002200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22200002200000000000000000000000000000000
χ212222-2-2-2-2-2222-2-22-2222-2-2-2-222i2i−2i−2i0000000000002i−2i000000002i2i−2i−2i000022-2-2000000000000
χ222222-2-2-2-2-2222-2-22-2222-2-2-2-222i2i−2i−2i0000000000002i−2i00000000−2i−2i2i2i0000-2-222000000000000
χ232222-2-2-2-2-2222-2-22-2222-2-2-2-22−2i−2i2i2i000000000000−2i2i000000002i2i−2i−2i0000-2-222000000000000
χ242222-2-2-2-2-2222-2-22-2222-2-2-2-22−2i−2i2i2i000000000000−2i2i00000000−2i−2i2i2i000022-2-2000000000000
χ252222-2-2-2-2-2222-2-22-2-2-2-22222-22i2i−2i−2i000000000000−2i2i000022-2-200002i2i−2i−2i0000000000000000
χ262222-2-2-2-2-2222-2-22-2-2-2-22222-22i2i−2i−2i000000000000−2i2i0000-2-2220000−2i−2i2i2i0000000000000000
χ272222-2-2-2-2-2222-2-22-2-2-2-22222-2−2i−2i2i2i0000000000002i−2i000022-2-20000−2i−2i2i2i0000000000000000
χ282222-2-2-2-2-2222-2-22-2-2-2-22222-2−2i−2i2i2i0000000000002i−2i0000-2-22200002i2i−2i−2i0000000000000000
χ2922-2-22-222-222-22-2-2-22-2-22-22-220000000000000000002i2i−2i−2i000000002-22-200002i−2i0000000000
χ3022-2-22-222-222-22-2-2-22-2-22-22-220000000000000000002i2i−2i−2i00000000-22-220000−2i2i0000000000
χ3122-2-22-222-222-22-2-2-22-2-22-22-22000000000000000000−2i−2i2i2i000000002-22-20000−2i2i0000000000
χ3222-2-22-222-222-22-2-2-22-2-22-22-22000000000000000000−2i−2i2i2i00000000-22-2200002i−2i0000000000
χ3322-2-2-22-2-2222-2-22-22-2222-22-2-200000000000022-2-2000000000000002i−2i−2i2i0000002i−2i00000000
χ3422-2-2-22-2-2222-2-22-22-2222-22-2-200000000000022-2-200000000000000−2i2i2i−2i000000−2i2i00000000
χ3522-2-2-22-2-2222-2-22-22-2222-22-2-2000000000000-2-222000000000000002i−2i−2i2i000000−2i2i00000000
χ3622-2-2-22-2-2222-2-22-22-2222-22-2-2000000000000-2-22200000000000000−2i2i2i−2i0000002i−2i00000000
χ372-22-22-2-2-222-2-2222-222-22-2-22-20000000000002i−2i2i−2i0000000000000000002i−2i2i−2i00000000002-2
χ382-22-22-2-2-222-2-2222-222-22-2-22-20000000000002i−2i2i−2i000000000000000000−2i2i−2i2i0000000000-22
χ392-22-22-2-2-222-2-2222-222-22-2-22-2000000000000−2i2i−2i2i0000000000000000002i−2i2i−2i0000000000-22
χ402-22-22-2-2-222-2-2222-222-22-2-22-2000000000000−2i2i−2i2i000000000000000000−2i2i−2i2i00000000002-2
χ412-22-2-2222-22-2-2-2-22222-2-222-2-20000000000000000002-22-20000000000002i−2i−2i2i00002i−2i000000
χ422-22-2-2222-22-2-2-2-22222-2-222-2-20000000000000000002-22-2000000000000−2i2i2i−2i0000−2i2i000000
χ432-22-2-2222-22-2-2-2-22222-2-222-2-2000000000000000000-22-220000000000002i−2i−2i2i0000−2i2i000000
χ442-22-2-2222-22-2-2-2-22222-2-222-2-2000000000000000000-22-22000000000000−2i2i2i−2i00002i−2i000000
χ452-2-22-2-22222-22-22-2-22-22-2-222-200002-200002-20000002i−2i−2i2i0000000000000000000000002i−2i00
χ462-2-22-2-22222-22-22-2-22-22-2-222-200002-200002-2000000−2i2i2i−2i000000000000000000000000−2i2i00
χ472-2-22-2-22222-22-22-2-22-22-2-222-20000-220000-220000002i−2i−2i2i000000000000000000000000−2i2i00
χ482-2-22-2-22222-22-22-2-22-22-2-222-20000-220000-22000000−2i2i2i−2i0000000000000000000000002i−2i00
χ492-2-22-2-22222-22-22-2-2-22-222-2-2200002-20000-222i−2i−2i2i00000000000000000000000000002i−2i0000
χ502-2-22-2-22222-22-22-2-2-22-222-2-2200002-20000-22−2i2i2i−2i0000000000000000000000000000−2i2i0000
χ512-2-22-2-22222-22-22-2-2-22-222-2-220000-2200002-22i−2i−2i2i0000000000000000000000000000−2i2i0000
χ522-2-22-2-22222-22-22-2-2-22-222-2-220000-2200002-2−2i2i2i−2i00000000000000000000000000002i−2i0000
χ53444-44-44-4-4-4-44-44-44000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ54444-44-44-4-4-4-44-44-4400000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ55444-4-44-444-4-444-4-4-4000000004-4-440000000000000000000000000000000000000000000000
χ56444-4-44-444-4-444-4-4-400000000-444-40000000000000000000000000000000000000000000000
χ5744-44444-44-4-4-4-4-44-400000000000000000000000000000022−2222−22000000000000000000000000
χ5844-44444-44-4-4-4-4-44-4000000000000000000000000000000−2222−2222000000000000000000000000
χ5944-44-4-4-44-4-4-4-4444400000000000000000000000000000022−22−2222000000000000000000000000
χ6044-44-4-4-44-4-4-4-44444000000000000000000000000000000−222222−22000000000000000000000000
χ6144-4-44-444-444-44-4-4-4-444-44-44-400000000000000000000000000000000000000000000000000
χ6244-4-4-44-4-4444-4-44-444-4-4-44-44400000000000000000000000000000000000000000000000000
χ634-44444-44-4-44-4-44-4-4000000000000000000000000000000000022−2222−2200000000000000000000
χ644-44444-44-4-44-4-44-4-40000000000000000000000000000000000−2222−222200000000000000000000
χ654-444-4-44-44-44-44-4-4400000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ664-444-4-44-44-44-44-4-440000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ674-44-44-4-4-444-4-4444-4-4-44-444-4400000000000000000000000000000000000000000000000000
χ684-44-4-4444-44-4-4-4-444-4-444-4-44400000000000000000000000000000000000000000000000000
χ694-4-4444-4-4-44-444-4-444-4444-4-4-400000000000000000000000000000000000000000000000000
χ704-4-4444-4-4-44-444-4-44-44-4-4-444400000000000000000000000000000000000000000000000000
χ714-4-4-44-4-444-444-4-444000000000000004-4000000000000000000000000000000000000000000
χ724-4-4-44-4-444-444-4-44400000000000000-44000000000000000000000000000000000000000000
χ734-4-4-4-444-4-4-444444-400000000000000004-40000000000000000000000000000000000000000
χ744-4-4-4-444-4-4-444444-40000000000000000-440000000000000000000000000000000000000000

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