Finite Group Databasebeta

← Group #351413

Character table — Group #351413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444444444448888888888888888244444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-111111111-111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-111111111-111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-11-11
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-11-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-111111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-111-1-111-1-1-1-111-1-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-111-1-111-1-1-1-1-1-11111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111111111-1-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1111111-1-11111-1-11-1-11
χ1722222222222-2-2-2-22-2-222-2-20000000000000000-222222-2-2-2-200000000000000000000
χ1822222222222-2-2-2-22-2-222-2-20000000000000000-2-2-2-2-22222200000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2220000000000000000222-2-2-2-2-22200000000000000000000
χ2022222222222-2-2-2-22-2-2-2-22200000000000000002-2-222-222-2-200000000000000000000
χ2122222222-2-2-22222-2-2-222222222222200000000-20000-20000-2-2-2-20000000000000000
χ2222222222-2-2-22222-2-2-22222-2-2-2-2-2-2-2-200000000-20000-2000022220000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-22222-2-2-2-2000000002000020000-2-2220000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-2222200000000200002000022-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000002i2i2i2i−2i−2i−2i−2i20000-2000000002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000−2i−2i−2i−2i2i2i2i2i20000-200000000−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222000000002i2i2i2i−2i−2i−2i−2i-20000200000000−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000−2i−2i−2i−2i2i2i2i2i-200002000000002i2i−2i−2i000000000000
χ2922-2-222-2-200022-2-20002i−2i2i−2i2i2i−2i−2i22-2-200000000000000000000000000i2−i22−22−2i2−i20000
χ3022-2-222-2-200022-2-20002i−2i2i−2i2i2i−2i−2i22-2-200000000000000000000000000−i2i2−22−22−i2i20000
χ3122-2-222-2-200022-2-20002i−2i2i−2i−2i−2i2i2i-2-22200000000000000000000000000i2−i2−222−2−i2i20000
χ3222-2-222-2-200022-2-20002i−2i2i−2i−2i−2i2i2i-2-22200000000000000000000000000−i2i22−2−22i2−i20000
χ3322-2-222-2-200022-2-2000−2i2i−2i2i2i2i−2i−2i-2-22200000000000000000000000000i2−i22−2−22−i2i20000
χ3422-2-222-2-200022-2-2000−2i2i−2i2i2i2i−2i−2i-2-22200000000000000000000000000−i2i2−222−2i2−i20000
χ3522-2-222-2-200022-2-2000−2i2i−2i2i−2i−2i2i2i22-2-200000000000000000000000000i2−i2−22−22i2−i20000
χ3622-2-222-2-200022-2-2000−2i2i−2i2i−2i−2i2i2i22-2-200000000000000000000000000−i2i22−22−2−i2i20000
χ372-22-22-22-22-2-22-22-222-2000000002i−2i2i−2i0000000002i−2i0002i−2i00002i−2i2-22-2000000000000
χ382-22-22-22-22-2-22-22-222-2000000002i−2i2i−2i000000000−2i2i000−2i2i00002i−2i-22-22000000000000
χ392-22-22-22-22-2-22-22-222-200000000−2i2i−2i2i0000000002i−2i0002i−2i0000−2i2i-22-22000000000000
χ402-22-22-22-22-2-22-22-222-200000000−2i2i−2i2i000000000−2i2i000−2i2i0000−2i2i2-22-2000000000000
χ412-22-22-22-22-2-2-22-222-2200002-22-200002i2i−2i−2i2i2i−2i−2i02i−2i000−2i2i002-2000000000000000000
χ422-22-22-22-22-2-2-22-222-2200002-22-20000−2i−2i2i2i−2i−2i2i2i0−2i2i0002i−2i002-2000000000000000000
χ432-22-22-22-22-2-2-22-222-220000-22-2200002i2i−2i−2i2i2i−2i−2i0−2i2i0002i−2i00-22000000000000000000
χ442-22-22-22-22-2-2-22-222-220000-22-220000−2i−2i2i2i−2i−2i2i2i02i−2i000−2i2i00-22000000000000000000
χ452-22-22-22-2-2222-22-2-2-22000000002i−2i2i−2i22-2-2-2-2220002i−2i0002i−2i00−2i2i0000000000000000
χ462-22-22-22-2-2222-22-2-2-22000000002i−2i2i−2i-2-22222-2-2000−2i2i000−2i2i00−2i2i0000000000000000
χ472-22-22-22-2-2222-22-2-2-2200000000−2i2i−2i2i22-2-2-2-222000−2i2i000−2i2i002i−2i0000000000000000
χ482-22-22-22-2-2222-22-2-2-2200000000−2i2i−2i2i-2-22222-2-20002i−2i0002i−2i002i−2i0000000000000000
χ492-22-22-22-2-222-22-22-22-200002-22-20000000000000002i−2i000−2i2i-22002i−2i−2i2i000000000000
χ502-22-22-22-2-222-22-22-22-200002-22-2000000000000000−2i2i0002i−2i-2200−2i2i2i−2i000000000000
χ512-22-22-22-2-222-22-22-22-20000-22-220000000000000002i−2i000−2i2i2-200−2i2i2i−2i000000000000
χ522-22-22-22-2-222-22-22-22-20000-22-22000000000000000−2i2i0002i−2i2-2002i−2i−2i2i000000000000
χ5344-44-4-44-444-40000-40000000000000022−2222−2222−2222−22000000000000000000000000000000
χ5444-44-4-44-444-40000-400000000000000−2222−2222−2222−2222000000000000000000000000000000
χ5544-44-4-44-4-4-4400004000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ5644-44-4-44-4-4-440000400000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ5744-4-444-4-4000-4-4440004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5844-4-444-4-4000-4-444000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ594-4-444-4-440004-4-44000000000004i−4i−4i4i00000000000000000000000000000000000000
χ604-4-444-4-440004-4-4400000000000−4i4i4i−4i00000000000000000000000000000000000000
χ614-4-444-4-44000-444-400000004i−4i−4i4i000000000000000000000000000000000000000000
χ624-4-444-4-44000-444-40000000−4i4i4i−4i000000000000000000000000000000000000000000
χ634-4-4-4-44444-440000-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ644-4-4-4-44444-440000-400000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ654-4-4-4-4444-44-4000040000000000000022−22−2222−222222−22000000000000000000000000000000
χ664-4-4-4-4444-44-40000400000000000000−222222−2222−22−2222000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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