Finite Group Databasebeta

← Group #277669

Character table — Group #277669

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-1-1-111-1-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-11-1111-1-1-1-1-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111111-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-1-11111-1-111-11
χ9111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111-1-1-1-111
χ12111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-111-11-1-1-1-1-111-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1111-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-1-111-11111-1-1-1-111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-11-1-111-1-111-1-11-1
χ172222222222-2-22-2-22-2-2222200000000-2-2-2-20000000022-2-20000200-200000000000000
χ182222222222-2-22-2-22-2-2222200000000-2-2-2-200000000-2-2220000-200200000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-20000000022220000000022-2-20000-200200000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-200000000222200000000-2-2220000200-200000000000000
χ2122222222-2-222-222-2-2-200002222-2-2-2-2000000000000000022220000-2-2000000000000
χ2222222222-2-222-222-2-2-200002222-2-2-2-20000000000000000-2-2-2-2000022000000000000
χ2322222222-2-222-222-2-2-20000-2-2-2-22222000000000000000022-2-20000-22000000000000
χ2422222222-2-222-222-2-2-20000-2-2-2-222220000000000000000-2-22200002-2000000000000
χ2522-2-22-22-2002-202-2000i2i2−i2−i222-2-20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200002-22-2000000000000i2−i2i2−i200
χ2622-2-22-22-2002-202-2000i2i2−i2−i222-2-20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i20000-22-22000000000000−i2i2−i2i200
χ2722-2-22-22-2002-202-2000i2i2−i2−i2-2-2220000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i200002-2-22000000000000i2−i2−i2i200
χ2822-2-22-22-2002-202-2000i2i2−i2−i2-2-2220000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i20000-222-2000000000000−i2i2i2−i200
χ2922-2-22-22-2002-202-2000−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200002-22-2000000000000−i2i2−i2i200
χ3022-2-22-22-2002-202-2000−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i20000-22-22000000000000i2−i2i2−i200
χ3122-2-22-22-2002-202-2000−i2−i2i2i2-2-2220000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i200002-2-22000000000000−i2i2i2−i200
χ3222-2-22-22-2002-202-2000−i2−i2i2i2-2-2220000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i20000-222-2000000000000i2−i2−i2i200
χ332-222-2-22-222-2-2-222-22-200002-22-222-2-20000000000000000000002i−2i0002i−2i0000000000
χ342-222-2-22-222-2-2-222-22-200002-22-222-2-2000000000000000000000−2i2i000−2i2i0000000000
χ352-222-2-22-222-2-2-222-22-20000-22-22-2-2220000000000000000000002i−2i000−2i2i0000000000
χ362-222-2-22-222-2-2-222-22-20000-22-22-2-222000000000000000000000−2i2i0002i−2i0000000000
χ372-222-2-22-2-2-2222-2-222-200000000000000002i2i−2i−2i2i2i−2i−2i2-22-2000000000000002i−2i000000
χ382-222-2-22-2-2-2222-2-222-200000000000000002i2i−2i−2i2i2i−2i−2i-22-2200000000000000−2i2i000000
χ392-222-2-22-2-2-2222-2-222-20000000000000000−2i−2i2i2i−2i−2i2i2i2-22-200000000000000−2i2i000000
χ402-222-2-22-2-2-2222-2-222-20000000000000000−2i−2i2i2i−2i−2i2i2i-22-22000000000000002i−2i000000
χ412-222-2-22-2-2-2-2-22222-2200002-22-2-2-2220000000000002-2-220000000000002-200000000
χ422-222-2-22-2-2-2-2-22222-2200002-22-2-2-222000000000000-222-2000000000000-2200000000
χ432-222-2-22-2-2-2-2-22222-220000-22-2222-2-20000000000002-2-22000000000000-2200000000
χ442-222-2-22-2-2-2-2-22222-220000-22-2222-2-2000000000000-222-20000000000002-200000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-44-400400-400000000000000000022−2222−2222−2222−2200000000000000000000000000
χ47444-4-44-4-44-400400-4000000000000000000−2222−2222−2222−222200000000000000000000000000
χ48444-4-44-4-4-4400-4004004i−4i4i−4i0000000000000000000000000000000000000000000000
χ49444-4-44-4-4-4400-400400−4i4i−4i4i0000000000000000000000000000000000000000000000
χ5044-44-4-4-44000000000022−22−222200002i2−2i22i2−2i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5144-44-4-4-44000000000022−22−22220000−2i22i2−2i22i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5244-44-4-4-440000000000−222222−2200002i2−2i22i2−2i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5344-44-4-4-440000000000−222222−220000−2i22i2−2i22i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5444-4-44-44-400-440-440002i22i2−2i2−2i200000000−2i2−2i22i22i20000000000000000000000000000000000
χ5544-4-44-44-400-440-44000−2i2−2i22i22i2000000002i22i2−2i2−2i20000000000000000000000000000000000
χ564-444-4-44-44444-4-4-4-4-4400000000000000000000000000000000000000000000000000
χ574-44-44-4-444-400-4004000000000000004-44-40000000000000000000000000000000000
χ584-44-44-4-444-400-400400000000000000-44-440000000000000000000000000000000000
χ594-44-44-4-44-4400400-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ604-44-44-4-44-4400400-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ614-4-4444-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i22-2-22-222-200000000000000000000000000
χ624-4-4444-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2-222-22-2-2200000000000000000000000000
χ634-4-4444-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2-222-22-2-2200000000000000000000000000
χ644-4-4444-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i22-2-22-222-200000000000000000000000000
χ654-4-4-4-4444004-40-4400000000000000000002222−22−22−22−22222200000000000000000000000000
χ664-4-4-4-4444004-40-440000000000000000000−22−2222222222−22−2200000000000000000000000000
χ674-4-4-4-444400-4404-400000004-4-44000000000000000000000000000000000000000000
χ684-4-4-4-444400-4404-40000000-444-4000000000000000000000000000000000000000000

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