Finite Group Databasebeta

← Group #345592

Character table — Group #345592

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444224444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-11-1-1-11-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-1-11-1-1-11-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-111-1-1-1-111-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111-1-1-1-1-1-1-111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11111111-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-11-1-11111-1-1-1-1-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-111-1-111111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-11-1-111-1-1-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1111111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-11-1-11-1-1-11111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1
χ172222222222-2-222-2-2-2-2000000002222-2-2-2-20000000000220022000-2000-20000000000
χ182222222222-2-222-2-2-2-2000000002222-2-2-2-20000000000-2-200-2-2000200020000000000
χ192222222222-2-222-2-2-2-200000000-2-2-2-2222200000000002200-2-20002000-20000000000
χ202222222222-2-222-2-2-2-200000000-2-2-2-222220000000000-2-20022000-200020000000000
χ2122222222-2-222-2-222-2-22222-2-2-2-200000000000000002200220000-2000-200000000000
χ2222222222-2-222-2-222-2-22222-2-2-2-20000000000000000-2-200-2-200002000200000000000
χ2322222222-2-222-2-222-2-2-2-2-2-2222200000000000000002200-2-200002000-200000000000
χ2422222222-2-222-2-222-2-2-2-2-2-222220000000000000000-2-200220000-2000200000000000
χ25222-2-22-2-22222-2-2-2-2-2200000000000000002222-2-2-2-2000000002-2002-2000000000000
χ26222-2-22-2-22222-2-2-2-2-2200000000000000002222-2-2-2-200000000-2200-22000000000000
χ27222-2-22-2-22222-2-2-2-2-220000000000000000-2-2-2-22222000000002-200-22000000000000
χ28222-2-22-2-22222-2-2-2-2-220000000000000000-2-2-2-2222200000000-22002-2000000000000
χ2922-22-2-22-2002-2002-20022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22i−2i002i−2i00000000002−22−2000000
χ3022-22-2-22-2002-2002-20022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i00−2i2i0000000000−22−22000000
χ3122-22-2-22-2002-2002-20022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22i−2i002i−2i0000000000−22−22000000
χ3222-22-2-22-2002-2002-20022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2i2i00−2i2i00000000002−22−2000000
χ3322-22-2-22-2002-2002-200-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i00−2i2i00000000002−2−22000000
χ3422-22-2-22-2002-2002-200-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i002i−2i0000000000−222−2000000
χ3522-22-2-22-2002-2002-200-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22i−2i00−2i2i0000000000−222−2000000
χ3622-22-2-22-2002-2002-200-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2i2i002i−2i00000000002−2−22000000
χ372-222-2-2-222-2002-20000i2−i2i2−i2i2i2−i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i0000000000002−22−200
χ382-222-2-2-222-2002-20000i2−i2i2−i2i2i2−i2−i22-22-20000i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i000000000000−22−2200
χ392-222-2-2-222-2002-20000i2−i2i2−i2i2i2−i2−i2-22-220000−i2i2−i2i2−i2i2−i2i2002i−2i00−2i2i0000000000002−2−2200
χ402-222-2-2-222-2002-20000i2−i2i2−i2i2i2−i2−i2-22-220000−i2i2−i2i2−i2i2−i2i200−2i2i002i−2i000000000000−222−200
χ412-222-2-2-222-2002-20000−i2i2−i2i2−i2−i2i2i22-22-20000−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i000000000000−22−2200
χ422-222-2-2-222-2002-20000−i2i2−i2i2−i2−i2i2i22-22-20000−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i0000000000002−22−200
χ432-222-2-2-222-2002-20000−i2i2−i2i2−i2−i2i2i2-22-220000i2−i2i2−i2i2−i2i2−i2002i−2i00−2i2i000000000000−222−200
χ442-222-2-2-222-2002-20000−i2i2−i2i2−i2−i2i2i2-22-220000i2−i2i2−i2i2−i2i2−i200−2i2i002i−2i0000000000002−2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-444-4-4-4-4444-400000000000000000000000000000000000000000000000000
χ47444-4-44-4-4-4-44444-4-44-400000000000000000000000000000000000000000000000000
χ48444-4-44-4-4-4-4-4-44444-4400000000000000000000000000000000000000000000000000
χ4944-44-4-44-400-4400-4400000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ5044-44-4-44-400-4400-440000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ5144-4-44-4-44004-400-440000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5244-4-44-4-44004-400-44000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5344-4-44-4-4400-44004-40000004i−4i4i−4i000000000000000000000000000000000000000000
χ5444-4-44-4-4400-44004-4000000−4i4i−4i4i000000000000000000000000000000000000000000
χ554-444-4-4-44-4400-4400002i2−2i22i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ564-444-4-4-44-4400-440000−2i22i2−2i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ574-44-44-44-44-400-44000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ584-44-44-44-44-400-4400000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ594-44-44-44-4-44004-400000000000000004i−4i4i−4i0000000000000000000000000000000000
χ604-44-44-44-4-44004-40000000000000000−4i4i−4i4i0000000000000000000000000000000000
χ614-4-4444-4-400000000002i2−2i2−2i22i200002i2−2i2−2i22i20000-222-2-222-200000000000000000000000000
χ624-4-4444-4-400000000002i2−2i2−2i22i20000−2i22i22i2−2i200002-2-222-2-2200000000000000000000000000
χ634-4-4444-4-40000000000−2i22i22i2−2i200002i2−2i2−2i22i200002-2-222-2-2200000000000000000000000000
χ644-4-4444-4-40000000000−2i22i22i2−2i20000−2i22i22i2−2i20000-222-2-222-200000000000000000000000000
χ654-4-4-4-44440000000000000022−22−2222000022−22−22222-2-22-222-200000000000000000000000000
χ664-4-4-4-44440000000000000022−22−22220000−222222−22-222-22-2-2200000000000000000000000000
χ674-4-4-4-444400000000000000−222222−22000022−22−2222-222-22-2-2200000000000000000000000000
χ684-4-4-4-444400000000000000−222222−220000−222222−222-2-22-222-200000000000000000000000000

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