Finite Group Databasebeta

← Group #345049

Character table — Group #345049

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-1-11-1-11-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-1111111-1-1-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1111-1-11111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-1-1-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-1111-1-11-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1111111-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1111-1111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-111111-111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111
χ172222222222-22-2-2-22-2-2000000002222-2-2-2-200000000220000-2-22000000-20000000000
χ182222222222-22-2-2-22-2-2000000002222-2-2-2-200000000-2-2000022-200000020000000000
χ192222222222-22-2-2-22-2-200000000-2-2-2-222220000000022000022-2000000-20000000000
χ202222222222-22-2-2-22-2-200000000-2-2-2-2222200000000-2-20000-2-2200000020000000000
χ2122222222-2-22-2222-2-2-22222-2-2-2-20000000000000000002222000-200-20000000000000
χ2222222222-2-22-2222-2-2-22222-2-2-2-2000000000000000000-2-2-2-200020020000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2222200000000000000000022-2-2000200-20000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-22222000000000000000000-2-222000-20020000000000000
χ2522-2-2-2-22200202-2-20002i2i−2i−2i000022−2−222−2−2i2i2i2i2−i2−i2−i2−i2002i−2i2-200000000000000i2−i22−200
χ2622-2-2-2-22200202-2-20002i2i−2i−2i000022−2−222−2−2i2i2i2i2−i2−i2−i2−i200−2i2i-2200000000000000−i2i2−2200
χ2722-2-2-2-22200202-2-20002i2i−2i−2i0000−2−222−2−222−i2−i2−i2−i2i2i2i2i2002i−2i2-200000000000000−i2i2−2200
χ2822-2-2-2-22200202-2-20002i2i−2i−2i0000−2−222−2−222−i2−i2−i2−i2i2i2i2i200−2i2i-2200000000000000i2−i22−200
χ2922-2-2-2-22200202-2-2000−2i−2i2i2i000022−2−222−2−2−i2−i2−i2−i2i2i2i2i2002i−2i-2200000000000000i2−i2−2200
χ3022-2-2-2-22200202-2-2000−2i−2i2i2i000022−2−222−2−2−i2−i2−i2−i2i2i2i2i200−2i2i2-200000000000000−i2i22−200
χ3122-2-2-2-22200202-2-2000−2i−2i2i2i0000−2−222−2−222i2i2i2i2−i2−i2−i2−i2002i−2i-2200000000000000−i2i22−200
χ3222-2-2-2-22200202-2-2000−2i−2i2i2i0000−2−222−2−222i2i2i2i2−i2−i2−i2−i200−2i2i2-200000000000000i2−i2−2200
χ332-22-2-22-22222-2-2-22-2-22000000000000000022-2-222-2-200000000002i−2i02i−2i00000000000
χ342-22-2-22-22222-2-2-22-2-22000000000000000022-2-222-2-20000000000−2i2i0−2i2i00000000000
χ352-22-2-22-22222-2-2-22-2-220000000000000000-2-222-2-22200000000002i−2i0−2i2i00000000000
χ362-22-2-22-22222-2-2-22-2-220000000000000000-2-222-2-2220000000000−2i2i02i−2i00000000000
χ372-2-22-222-22-202000-2002−22−222−2−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i22-200002i−2i000000002−2i2−i2000000
χ382-2-22-222-22-202000-2002−22−222−2−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2-220000−2i2i00000000−22−i2i2000000
χ392-2-22-222-22-202000-2002−22−222−2−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22-20000−2i2i000000002−2−i2i2000000
χ402-2-22-222-22-202000-2002−22−222−2−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2-2200002i−2i00000000−22i2−i2000000
χ412-2-22-222-22-202000-200−22−22−2−22200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i22-200002i−2i00000000−22−i2i2000000
χ422-2-22-222-22-202000-200−22−22−2−22200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2-220000−2i2i000000002−2i2−i2000000
χ432-2-22-222-22-202000-200−22−22−2−2220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i22-20000−2i2i00000000−22i2−i2000000
χ442-2-22-222-22-202000-200−22−22−2−2220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2-2200002i−2i000000002−2−i2i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-40000000000000022−2222−2222−2222−2200002-2-22-222-200000000000000000000000000
χ474444-4-4-4-40000000000000022−2222−22−2222−22220000-222-22-2-2200000000000000000000000000
χ484444-4-4-4-400000000000000−2222−222222−2222−220000-222-22-2-2200000000000000000000000000
χ494444-4-4-4-400000000000000−2222−2222−2222−222200002-2-22-222-200000000000000000000000000
χ5044-4-444-4-44-40-400040000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ5144-4-444-4-44-40-40004000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ5244-4-444-4-4-4404000-400000000004-4-4400000000000000000000000000000000000000
χ5344-4-444-4-4-4404000-40000000000-444-400000000000000000000000000000000000000
χ5444-4-4-4-44400-40-444000000000002222−22−22−22−2222220000000000000000000000000000000000
χ5544-4-4-4-44400-40-44400000000000−22−2222222222−22−220000000000000000000000000000000000
χ564-44-44-44-400000000002i2−2i2−2i22i2000000002i2−2i2−2i22i2-22-222-22-200000000000000000000000000
χ574-44-44-44-400000000002i2−2i2−2i22i200000000−2i22i22i2−2i22-22-2-22-2200000000000000000000000000
χ584-44-44-44-40000000000−2i22i22i2−2i2000000002i2−2i2−2i22i22-22-2-22-2200000000000000000000000000
χ594-44-44-44-40000000000−2i22i22i2−2i200000000−2i22i22i2−2i2-22-222-22-200000000000000000000000000
χ604-44-4-44-4444-4-444-4-44-400000000000000000000000000000000000000000000000000
χ614-44-4-44-44-4-444-4-4444-400000000000000000000000000000000000000000000000000
χ624-44-4-44-44-4-4-4444-44-4400000000000000000000000000000000000000000000000000
χ634-4-444-4-440040-44-400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ644-4-444-4-440040-44-40000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ654-4-444-4-4400-404-4400000004-4-44000000000000000000000000000000000000000000
χ664-4-444-4-4400-404-440000000-444-4000000000000000000000000000000000000000000
χ674-4-44-444-4-440-400040022−2222−22−22−222222000000000000000000000000000000000000000000
χ684-4-44-444-4-440-4000400−2222−22222222−22−22000000000000000000000000000000000000000000

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