Finite Group Databasebeta

← Group #288597

Character table — Group #288597

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884448888888844448888888888888882244448888888824
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111-1-11-1-1-111-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1111111-1-1-1-1-1-1-111-1111-1-11-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-11-1-111111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-111-111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-11111-1-1
χ9111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-111-1-1-1-11-111-11-1-1-1111-1-11-1
χ10111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-111-1-1111111-1-1-1-111-111-11-1-1-1-1-111-11
χ11111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-11-1111-1-111-11
χ12111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11111-11-1-11-1111-111-1-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-11111-1-1-1-111-1-1-1-1-11-1-11-1-111111-1-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-11111-1-1-1-1-1-11-1-11111-1-1-1111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-1111111-111-1-1-1-11-1-1111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111111-111-111-1-1-111-1-1-11
χ172222222-2222-22222-2-2-2-2-22200000000-200220022000000000000-200-2000000
χ182222222-2222-22222-2-2-2-2-22200000000-200-2-200-2-20000000000002002000000
χ192222222-2222-2-2-2-2-2-2-2-222-2-2000000002002200-2-2000000000000200-2000000
χ202222222-2222-2-2-2-2-2-2-2-222-2-200000000200-2-20022000000000000-2002000000
χ21222222-2-2-2-2-2-200002-2200002i2i−2i−2i0000000002i−2i000022-2-200000002i−2i0000000
χ22222222-2-2-2-2-2-200002-2200002i2i−2i−2i0000000002i−2i0000-2-2220000000−2i2i0000000
χ23222222-2-2-2-2-2-200002-220000−2i−2i2i2i000000000−2i2i000022-2-20000000−2i2i0000000
χ24222222-2-2-2-2-2-200002-220000−2i−2i2i2i000000000−2i2i0000-2-22200000002i−2i0000000
χ252222-2-222-22-222222-2-2222-2-200000000-20000000000000002-20-220000000000
χ262222-2-222-22-222222-2-2222-2-200000000-2000000000000000-2202-20000000000
χ272222-2-222-22-22-2-2-2-2-2-22-2-222000000002000000000000000220-2-20000000000
χ282222-2-222-22-22-2-2-2-2-2-22-2-222000000002000000000000000-2-20220000000000
χ292222-2-22-2-22-2-2222222-2-2-2-2-22i2i−2i−2i2i2i−2i−2i20000−2i2i000000000000000000000000
χ302222-2-22-2-22-2-2222222-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i200002i−2i000000000000000000000000
χ312222-2-22-2-22-2-2-2-2-2-222-222222i2i−2i−2i−2i−2i2i2i-20000−2i2i000000000000000000000000
χ322222-2-22-2-22-2-2-2-2-2-222-22222−2i−2i2i2i2i2i−2i−2i-200002i−2i000000000000000000000000
χ332222-2-2-222-22200002-2-200002222000002200-2-200-2-20000-2002000000000000
χ342222-2-2-222-22200002-2-20000222200000-2-200-2-200220000200-2000000000000
χ352222-2-2-222-22200002-2-20000-2-2-2-20000022002200-2-20000200-2000000000000
χ362222-2-2-222-22200002-2-20000-2-2-2-200000-2-2002200220000-2002000000000000
χ372-22-2-22202-2-202i2i−2i−2i000002i−2i000000000i2−i22-2002i−2ii2−i22−22−20000000000i2−i22−200
χ382-22-2-22202-2-202i2i−2i−2i000002i−2i000000000i2−i2-2200−2i2ii2−i22−22−20000000000−i2i2−2200
χ392-22-2-22202-2-202i2i−2i−2i000002i−2i000000000−i2i22-2002i−2i−i2i2−22−220000000000−i2i2−2200
χ402-22-2-22202-2-202i2i−2i−2i000002i−2i000000000−i2i2-2200−2i2i−i2i2−22−220000000000i2−i22−200
χ412-22-2-22202-2-20−2i−2i2i2i00000−2i2i000000000i2−i22-200−2i2ii2−i2−22−220000000000i2−i2−2200
χ422-22-2-22202-2-20−2i−2i2i2i00000−2i2i000000000i2−i2-22002i−2ii2−i2−22−220000000000−i2i22−200
χ432-22-2-22202-2-20−2i−2i2i2i00000−2i2i000000000−i2i22-200−2i2i−i2i22−22−20000000000−i2i22−200
χ442-22-2-22202-2-20−2i−2i2i2i00000−2i2i000000000−i2i2-22002i−2i−i2i22−22−20000000000i2−i2−2200
χ45444444-44-4-4-440000-44-40000000000000000000000000000000000000000000
χ464444-4-4-4-44-44-40000-4440000000000000000000000000000000000000000000
χ474-44-44-440-4-4404i4i−4i−4i00000−4i4i000000000000000000000000000000000000000
χ484-44-44-440-4-440−4i−4i4i4i000004i−4i000000000000000000000000000000000000000
χ494-44-44-4-4044-40000000000000000000002i2−2i2000000−2i22i200000000000000000000
χ504-44-44-4-4044-4000000000000000000000−2i22i20000002i2−2i200000000000000000000
χ514-44-4-44-40-444000000000000000000000000000000022−22−22220000000000000000
χ524-44-4-44-40-4440000000000000000000000000000000−222222−220000000000000000
χ534-4-440004000-422−2222−2200022−22002i2−2i22i2−2i22i−2i2i−2i0000000000000000000000000000000
χ544-4-440004000-422−2222−2200022−2200−2i22i2−2i22i2−2i2i−2i2i0000000000000000000000000000000
χ554-4-440004000-4−2222−2222000−2222002i2−2i22i2−2i2−2i2i−2i2i0000000000000000000000000000000
χ564-4-440004000-4−2222−2222000−222200−2i22i2−2i22i22i−2i2i−2i0000000000000000000000000000000
χ574-4-44000-4000422−2222−22000−22220022−22−22222-2-220000000000000000000000000000000
χ584-4-44000-4000422−2222−22000−222200−222222−22-222-20000000000000000000000000000000
χ594-4-44000-40004−2222−222200022−220022−22−2222-222-20000000000000000000000000000000
χ604-4-44000-40004−2222−222200022−2200−222222−222-2-220000000000000000000000000000000
χ6188-8-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ6288-8-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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