Finite Group Databasebeta

← Group #449641

Character table — Group #449641

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222222222224444444422224444444444444444444444444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ311111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111
χ9111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ11111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111
χ12111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111
χ13111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ14111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-20000-2-2000000000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222220000-2-2000000000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-2000022000000000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222000022000000000000000000000000000000000000
χ212222-2-2-2-2222-2-2-22-22-2-2-2222-2000000000000002i2i−2i−2i00000000002i2i−2i−2i000022-2-20000000000000000
χ222222-2-2-2-2222-2-2-22-22-2-2-2222-2000000000000002i2i−2i−2i0000000000−2i−2i2i2i0000-2-2220000000000000000
χ232222-2-2-2-2222-2-2-22-22-2-2-2222-200000000000000−2i−2i2i2i00000000002i2i−2i−2i0000-2-2220000000000000000
χ242222-2-2-2-2222-2-2-22-22-2-2-2222-200000000000000−2i−2i2i2i0000000000−2i−2i2i2i000022-2-20000000000000000
χ25222-22-2-2-2-2-2-22-2222-22-2-222-220000000000000000000022-2-222-2-200000000000022-2-2000000000000
χ26222-22-2-2-2-2-2-22-2222-22-2-222-220000000000000000000022-2-2-2-222000000000000-2-222000000000000
χ27222-22-2-2-2-2-2-22-2222-22-2-222-2200000000000000000000-2-22222-2-2000000000000-2-222000000000000
χ28222-22-2-2-2-2-2-22-2222-22-2-222-2200000000000000000000-2-222-2-22200000000000022-2-2000000000000
χ2922-2-2-22-2-22-22222-2-20000000022-2-22i2i−2i−2i2i−2i0000000000000000000000i2i2−i2−i2i2−i2i2−i22−22−222−2−200000000
χ3022-2-2-22-2-22-22222-2-20000000022-2-22i2i−2i−2i2i−2i0000000000000000000000−i2−i2i2i2−i2i2−i2i2−22−22−2−22200000000
χ3122-2-2-22-2-22-22222-2-20000000022-2-2−2i−2i2i2i−2i2i0000000000000000000000i2i2−i2−i2i2−i2i2−i2−22−22−2−22200000000
χ3222-2-2-22-2-22-22222-2-20000000022-2-2−2i−2i2i2i−2i2i0000000000000000000000−i2−i2i2i2−i2i2−i2i22−22−222−2−200000000
χ3322-2-2-22-2-22-22222-2-200000000-2-2222i2i−2i−2i−2i2i0000000000000000000000i2i2−i2−i2−i2i2−i2i22−22−2−2−22200000000
χ3422-2-2-22-2-22-22222-2-200000000-2-2222i2i−2i−2i−2i2i0000000000000000000000−i2−i2i2i2i2−i2i2−i2−22−2222−2−200000000
χ3522-2-2-22-2-22-22222-2-200000000-2-222−2i−2i2i2i2i−2i0000000000000000000000i2i2−i2−i2−i2i2−i2i2−22−2222−2−200000000
χ3622-2-2-22-2-22-22222-2-200000000-2-222−2i−2i2i2i2i−2i0000000000000000000000−i2−i2i2i2i2−i2i2−i22−22−2−2−22200000000
χ372-2-222-22-2-2-2222-22-22-22-22-2-2200002i−2i2i−2i00002i−2i00000000002i−2i2i−2i00000000000000000000002-20000
χ382-2-222-22-2-2-2222-22-22-22-22-2-2200002i−2i2i−2i00002i−2i0000000000−2i2i−2i2i0000000000000000000000-220000
χ392-2-222-22-2-2-2222-22-22-22-22-2-220000−2i2i−2i2i0000−2i2i00000000002i−2i2i−2i0000000000000000000000-220000
χ402-2-222-22-2-2-2222-22-22-22-22-2-220000−2i2i−2i2i0000−2i2i0000000000−2i2i−2i2i00000000000000000000002-20000
χ412-2-222-22-2-2-2222-22-2-22-22-222-200002i−2i2i−2i0000−2i2i000000000000002i−2i2i−2i000000000000000000002-200
χ422-2-222-22-2-2-2222-22-2-22-22-222-200002i−2i2i−2i0000−2i2i00000000000000−2i2i−2i2i00000000000000000000-2200
χ432-2-222-22-2-2-2222-22-2-22-22-222-20000−2i2i−2i2i00002i−2i000000000000002i−2i2i−2i00000000000000000000-2200
χ442-2-222-22-2-2-2222-22-2-22-22-222-20000−2i2i−2i2i00002i−2i00000000000000−2i2i−2i2i000000000000000000002-200
χ452-2-22-22-22-2-22-2-2222-2-22-2-2222000000000000000000002-22-200002-2-220000000000002-22-200000000
χ462-2-22-22-22-2-22-2-2222-2-22-2-2222000000000000000000002-22-20000-222-2000000000000-22-2200000000
χ472-2-22-22-22-2-22-2-2222-2-22-2-222200000000000000000000-22-2200002-2-22000000000000-22-2200000000
χ482-2-22-22-22-2-22-2-2222-2-22-2-222200000000000000000000-22-220000-222-20000000000002-22-200000000
χ492-2-2-222-2222-22-2-22-2-2-2-222-222000000000000002i−2i2i−2i0000002i−2i−2i2i00002-22-200000000000000000000
χ502-2-2-222-2222-22-2-22-2-2-2-222-222000000000000002i−2i2i−2i000000−2i2i2i−2i0000-22-2200000000000000000000
χ512-2-2-222-2222-22-2-22-2-2-2-222-22200000000000000−2i2i−2i2i0000002i−2i−2i2i0000-22-2200000000000000000000
χ522-2-2-222-2222-22-2-22-2-2-2-222-22200000000000000−2i2i−2i2i000000−2i2i2i−2i00002-22-200000000000000000000
χ532-2-2-2-2-22-222-2-222222-2-22-22-222-22-2000000000000002-22-2-220000000000000000000000000000002-2
χ542-2-2-2-2-22-222-2-222222-2-22-22-222-22-2000000000000002-2-222-2000000000000000000000000000000-22
χ552-2-2-2-2-22-222-2-222222-2-22-22-22-22-2200000000000000-222-2-22000000000000000000000000000000-22
χ562-2-2-2-2-22-222-2-222222-2-22-22-22-22-2200000000000000-22-222-20000000000000000000000000000002-2
χ572-2-2-2-2-22-222-2-22222-222-22-22-22-22-200000000002-2-22-2200000000000000000000000000002-2000000
χ582-2-2-2-2-22-222-2-22222-222-22-22-22-22-20000000000-222-2-220000000000000000000000000000-22000000
χ592-2-2-2-2-22-222-2-22222-222-22-22-2-22-2200000000002-2-222-20000000000000000000000000000-22000000
χ602-2-2-2-2-22-222-2-22222-222-22-22-2-22-220000000000-222-22-200000000000000000000000000002-2000000
χ614444-4-4-4-4444-4-4-44-4-4444-4-4-4400000000000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-4-44-44444-444-4-44-400000000000000000000000000000000000000000000000000000000
χ63444-4-4444-4-4-4-44-44-444-4-4-4-44400000000000000000000000000000000000000000000000000000000
χ64444-4-4444-4-4-4-44-44-4-4-44444-4-400000000000000000000000000000000000000000000000000000000
χ6544-4444-4-4-44-4-44-4-440000000000000000004i−4i00000000000000000000000000000000000000000000
χ6644-4444-4-4-44-4-44-4-44000000000000000000−4i4i00000000000000000000000000000000000000000000
χ6744-44-4-444-44-44-44-4-400000000000000000000000000000000000000000000000022−22−2222000000000000
χ6844-44-4-444-44-44-44-4-4000000000000000000000000000000000000000000000000−222222−22000000000000
χ6944-4-44-4444-44-4-4-4-44000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ7044-4-44-4444-44-4-4-4-4400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ714-4444-4-444-4-4-444-4-4000000004-4-440000000000000000000000000000000000000000000000000000
χ724-4444-4-444-4-4-444-4-400000000-444-40000000000000000000000000000000000000000000000000000
χ734-444-444-44-4-44-4-4-4400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ744-444-444-44-4-44-4-4-440000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ754-44-4444-4-444-4-44-4-4000000000000000000000000000000000000000000000000000022−22−222200000000
χ764-44-4444-4-444-4-44-4-40000000000000000000000000000000000000000000000000000−222222−2200000000
χ774-44-4-4-4-44-44444-4-440000000000004-4-44000000000000000000000000000000000000000000000000
χ784-44-4-4-4-44-44444-4-44000000000000-444-4000000000000000000000000000000000000000000000000
χ794-4-44-44-44-4-44-4-444444-444-4-4-400000000000000000000000000000000000000000000000000000000
χ804-4-4-444-4444-44-4-44-4444-4-44-4-400000000000000000000000000000000000000000000000000000000

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