Finite Group Databasebeta

← Group #477180

Character table — Group #477180

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111111111111122222222888888888888888888888888888816161616161616161616161616161616
order12222222222222224444444422444444444488888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ9111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1
χ10111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111
χ11111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ12111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ13111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1
χ16111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000000000
χ212222-2-2-2-222-2-2-2-222222-22-2-2-20000000000000000000000002i2i−2i−2i2i−2i0000000000002-2
χ222222-2-2-2-222-2-2-2-222222-22-2-2-20000000000000000000000002i2i−2i−2i−2i2i000000000000-22
χ232222-2-2-2-222-2-2-2-222222-22-2-2-2000000000000000000000000−2i−2i2i2i2i−2i000000000000-22
χ242222-2-2-2-222-2-2-2-222222-22-2-2-2000000000000000000000000−2i−2i2i2i−2i2i0000000000002-2
χ25222-2-2-2-2-2-2-22222-222-2-2-2222-2000000000000000022-2-200000000002-22-20000000000
χ26222-2-2-2-2-2-2-22222-222-2-2-2222-2000000000000000022-2-20000000000-22-220000000000
χ27222-2-2-2-2-2-2-22222-222-2-2-2222-20000000000000000-2-22200000000002-2-220000000000
χ28222-2-2-2-2-2-2-22222-222-2-2-2222-20000000000000000-2-2220000000000-222-20000000000
χ2922-2-222-2-22-22-22-22-20000000000002-22i−2i002i−2ii2i2−i2−i22−22−2i2i2−i2−i22−22−20000000000000000
χ3022-2-222-2-22-22-22-22-20000000000002-22i−2i002i−2i−i2−i2i2i2−22−22−i2−i2i2i2−22−220000000000000000
χ3122-2-222-2-22-22-22-22-20000000000002-2−2i2i00−2i2ii2i2−i2−i2−22−22i2i2−i2−i2−22−220000000000000000
χ3222-2-222-2-22-22-22-22-20000000000002-2−2i2i00−2i2i−i2−i2i2i22−22−2−i2−i2i2i22−22−20000000000000000
χ3322-2-222-2-22-22-22-22-2000000000000-222i−2i00−2i2ii2i2−i2−i2−22−22−i2−i2i2i22−22−20000000000000000
χ3422-2-222-2-22-22-22-22-2000000000000-222i−2i00−2i2i−i2−i2i2i22−22−2i2i2−i2−i2−22−220000000000000000
χ3522-2-222-2-22-22-22-22-2000000000000-22−2i2i002i−2ii2i2−i2−i22−22−2−i2−i2i2i2−22−220000000000000000
χ3622-2-222-2-22-22-22-22-2000000000000-22−2i2i002i−2i−i2−i2i2i2−22−22i2i2−i2−i22−22−20000000000000000
χ372-2-222-22-2-2-2-2-22222-22-2-222-220000000000002-22-20000000000000000002-2002-20000
χ382-2-222-22-2-2-2-2-22222-22-2-222-220000000000002-22-2000000000000000000-2200-220000
χ392-2-222-22-2-2-2-2-22222-22-2-222-22000000000000-22-220000000000000000002-200-220000
χ402-2-222-22-2-2-2-2-22222-22-2-222-22000000000000-22-22000000000000000000-22002-20000
χ412-2-2-22-22-22222-2-2-2222-22-22-2-2000000000000000000002i−2i2i−2i0000000000002i−2i002-200
χ422-2-2-22-22-22222-2-2-2222-22-22-2-2000000000000000000002i−2i2i−2i000000000000−2i2i00-2200
χ432-2-2-22-22-22222-2-2-2222-22-22-2-200000000000000000000−2i2i−2i2i0000000000002i−2i00-2200
χ442-2-2-22-22-22222-2-2-2222-22-22-2-200000000000000000000−2i2i−2i2i000000000000−2i2i002-200
χ454444-4-4-4-444-4-4-4-444-4-4-44-444400000000000000000000000000000000000000000000
χ46444-44444-4-4-4-4-4-4-444-4-444-4-4400000000000000000000000000000000000000000000
χ47444-44444-4-4-4-4-4-4-44-444-4-444-400000000000000000000000000000000000000000000
χ48444-4-4-4-4-4-4-44444-44-4444-4-4-4400000000000000000000000000000000000000000000
χ4944-4444-4-4-44-44-44-4-400000000004-40000000000000000000000000000000000000000
χ5044-4444-4-4-44-44-44-4-40000000000-440000000000000000000000000000000000000000
χ5144-44-4-444-444-44-4-4-400000000000000000000000022−22−2222000000000000000000000000
χ5244-44-4-444-444-44-4-4-4000000000000000000000000−222222−22000000000000000000000000
χ5344-4-4-4-4444-4-44-444-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ5444-4-4-4-4444-4-44-444-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ554-4444-4-444-44-4-44-4-4000000000000000000000000000022−22−222200000000000000000000
χ564-4444-4-444-44-4-44-4-40000000000000000000000000000−222222−2200000000000000000000
χ574-444-444-44-4-444-4-4-4000000004-4000000000000000000000000000000000000000000
χ584-444-444-44-4-444-4-4-400000000-44000000000000000000000000000000000000000000
χ594-44-44-4-44-44-444-44-4000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ604-44-44-4-44-44-444-44-400000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ614-44-4-444-4-444-4-444-400000000000000004i−4i0000000000000000000000000000000000
χ624-44-4-444-4-444-4-444-40000000000000000−4i4i0000000000000000000000000000000000
χ634-4-444-44-4-4-4-4-444444-444-4-44-400000000000000000000000000000000000000000000
χ644-4-44-44-44-4-444-4-4444-44-4-44-4400000000000000000000000000000000000000000000
χ654-4-44-44-44-4-444-4-444-44-444-44-400000000000000000000000000000000000000000000
χ664-4-4-44-44-44444-4-4-44-4-44-44-44400000000000000000000000000000000000000000000
χ674-4-4-4-44-4444-4-444-4444-4-4-4-44400000000000000000000000000000000000000000000
χ684-4-4-4-44-4444-4-444-44-4-44444-4-400000000000000000000000000000000000000000000

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