Finite Group Databasebeta

← Group #428488

Character table — Group #428488

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111111111112222222244448888888888888888888888888888888888161616161616161616161616
order12222222222222224444444444442244444444444444448888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ9111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ10111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ11111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ12111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ172222222222222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2000000000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ212222-2-2-222-2-222-2-2-22-2-2-2222-20000000000000000002i2i−2i−2i0000000022-2-2000000002i−2i000000
χ222222-2-2-222-2-222-2-2-22-2-2-2222-20000000000000000002i2i−2i−2i00000000-2-22200000000−2i2i000000
χ232222-2-2-222-2-222-2-2-22-2-2-2222-2000000000000000000−2i−2i2i2i0000000022-2-200000000−2i2i000000
χ242222-2-2-222-2-222-2-2-22-2-2-2222-2000000000000000000−2i−2i2i2i00000000-2-222000000002i−2i000000
χ25222-2-2-2-2-2-2222-22-22-22-2-222-220000000000000022-2-20000000022-2-200000000000000002-200
χ26222-2-2-2-2-2-2222-22-22-22-2-222-220000000000000022-2-200000000-2-2220000000000000000-2200
χ27222-2-2-2-2-2-2222-22-22-22-2-222-2200000000000000-2-2220000000022-2-20000000000000000-2200
χ28222-2-2-2-2-2-2222-22-22-22-2-222-2200000000000000-2-22200000000-2-22200000000000000002-200
χ292-2-2222-2-2-22222-2-2-2-2-22-22-222000000000000002i−2i2i−2i0000000000002-22-2000000000000002i−2i
χ302-2-2222-2-2-22222-2-2-2-2-22-22-222000000000000002i−2i2i−2i000000000000-22-2200000000000000−2i2i
χ312-2-2222-2-2-22222-2-2-2-2-22-22-22200000000000000−2i2i−2i2i0000000000002-22-200000000000000−2i2i
χ322-2-2222-2-2-22222-2-2-2-2-22-22-22200000000000000−2i2i−2i2i000000000000-22-22000000000000002i−2i
χ332-2-22-2-22-2-2-2-2222222-22-2-22-2222-2-22-2000000000000000022-2-22-22-200000000000000000000
χ342-2-22-2-22-2-2-2-2222222-22-2-22-2222-2-22-20000000000000000-2-222-22-2200000000000000000000
χ352-2-22-2-22-2-2-2-2222222-22-2-22-22-2-222-22000000000000000022-2-2-22-2200000000000000000000
χ362-2-22-2-22-2-2-2-2222222-22-2-22-22-2-222-220000000000000000-2-2222-22-200000000000000000000
χ372-2-22-2-22-2-2-2-222222-22-222-22-222-2-2-220000000000000000000000002-2-2222-2-2000000000000
χ382-2-22-2-22-2-2-2-222222-22-222-22-222-2-2-22000000000000000000000000-222-2-2-222000000000000
χ392-2-22-2-22-2-2-2-222222-22-222-22-2-2-2222-20000000000000000000000002-2-22-2-222000000000000
χ402-2-22-2-22-2-2-2-222222-22-222-22-2-2-2222-2000000000000000000000000-222-222-2-2000000000000
χ412-2-2-222-222-2-22-22-22-2-2-22-22220000000000000000002-22-200002-2-22000000002-20000000000
χ422-2-2-222-222-2-22-22-22-2-2-22-22220000000000000000002-22-20000-222-200000000-220000000000
χ432-2-2-222-222-2-22-22-22-2-2-22-2222000000000000000000-22-2200002-2-2200000000-220000000000
χ442-2-2-222-222-2-22-22-22-2-2-22-2222000000000000000000-22-220000-222-2000000002-20000000000
χ452-2-2-2-2-2222222-2-22-22-2-222-2-2200000000002-22-22i−2i−2i2i000000000000000000000000002i−2i0000
χ462-2-2-2-2-2222222-2-22-22-2-222-2-2200000000002-22-2−2i2i2i−2i00000000000000000000000000−2i2i0000
χ472-2-2-2-2-2222222-2-22-22-2-222-2-220000000000-22-222i−2i−2i2i00000000000000000000000000−2i2i0000
χ482-2-2-2-2-2222222-2-22-22-2-222-2-220000000000-22-22−2i2i2i−2i000000000000000000000000002i−2i0000
χ492-2-2-2-2-2222222-2-22-2-222-2-222-200000000002-2-2200002i−2i−2i2i0000000000000000002i−2i00000000
χ502-2-2-2-2-2222222-2-22-2-222-2-222-200000000002-2-220000−2i2i2i−2i000000000000000000−2i2i00000000
χ512-2-2-2-2-2222222-2-22-2-222-2-222-20000000000-222-200002i−2i−2i2i000000000000000000−2i2i00000000
χ522-2-2-2-2-2222222-2-22-2-222-2-222-20000000000-222-20000−2i2i2i−2i0000000000000000002i−2i00000000
χ534444-4-4-444-4-444-4-4-4-4444-4-4-4400000000000000000000000000000000000000000000000000
χ54444-4444-4-4-4-44-4-44-444-4-4-4-44400000000000000000000000000000000000000000000000000
χ55444-4444-4-4-4-44-4-44-4-4-44444-4-400000000000000000000000000000000000000000000000000
χ56444-4-4-4-4-4-4444-44-444-444-4-44-400000000000000000000000000000000000000000000000000
χ5744-444-444-44-4-4-44-4-400000000000000000000000000000022−2222−22000000000000000000000000
χ5844-444-444-44-4-4-44-4-4000000000000000000000000000000−2222−2222000000000000000000000000
χ5944-44-44-44-4-44-4-4-444000000000000004-4000000000000000000000000000000000000000000
χ6044-44-44-44-4-44-4-4-44400000000000000-44000000000000000000000000000000000000000000
χ6144-4-44-44-44-44-44-4-4400000000000000000000000000000000000000000022−2222−22000000000000
χ6244-4-44-44-44-44-44-4-44000000000000000000000000000000000000000000−2222−2222000000000000
χ6344-4-4-44-4-444-4-4444-4000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ6444-4-4-44-4-444-4-4444-400000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ654-4444-4-4-444-4-4-4-44400000000000000004-40000000000000000000000000000000000000000
χ664-4444-4-4-444-4-4-4-4440000000000000000-440000000000000000000000000000000000000000
χ674-444-444-44-44-4-44-4-400000000000000000000000000000022−22−2222000000000000000000000000
χ684-444-444-44-44-4-44-4-4000000000000000000000000000000−222222−22000000000000000000000000
χ694-44-44-4-44-4-44-4444-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ704-44-44-4-44-4-44-4444-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ714-44-4-4444-44-4-44-4-4400000000000000000000000000000000000000000022−22−2222000000000000
χ724-44-4-4444-44-4-44-4-44000000000000000000000000000000000000000000−222222−22000000000000
χ734-4-4444-4-4-44444-4-4-444-44-44-4-400000000000000000000000000000000000000000000000000
χ744-4-4-444-444-4-44-44-44444-44-4-4-400000000000000000000000000000000000000000000000000

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