Finite Group Databasebeta

← Group #337150

Character table — Group #337150

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888444444888888244
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-1-111-1
χ3111111111111111111111111-1-1111111111111111111-1-1-1-1-11-1-1-1-111-1-1-1
χ4111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-11111-1-1-1-11
χ51111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11
χ61111111111111111111111-1-111-1-1-1-1111111-1-1-1-111111-1-111-11111-1-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1111-1111-1-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-11111-111
χ11111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-11-11
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-11-111-1-1111-1-1
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-11-1-111-1-11-1-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1-111-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-11-1-1-11111-11-1
χ172222222222-2-22-2-22-2-2222200220000-2-2000000000000-200-220000000000
χ182222222222-2-22-2-22-2-2222200-2-20000-2-20000000000002002-20000000000
χ192222222222-2-22-2-22-2-2-2-2-2-20022000022000000000000200-2-20000000000
χ202222222222-2-22-2-22-2-2-2-2-2-200-2-2000022000000000000-200220000000000
χ2122222222-2-222-222-2-2-20000220022-2-20022-2-20000000000000-2000000000
χ2222222222-2-222-222-2-2-200002200-2-2-2-200-2-22200000000000002000000000
χ2322222222-2-222-222-2-2-20000-2-200222200-2-2220000000000000-2000000000
χ2422222222-2-222-222-2-2-20000-2-200-2-2220022-2-200000000000002000000000
χ25222-2-22-2-2-2-2222-2-222-200000000000000000022-2-2000002i−2i000002i−2i00000
χ26222-2-22-2-2-2-2222-2-222-200000000000000000022-2-200000−2i2i00000−2i2i00000
χ27222-2-22-2-2-2-2222-2-222-2000000000000000000-2-222000002i−2i00000−2i2i00000
χ28222-2-22-2-2-2-2222-2-222-2000000000000000000-2-22200000−2i2i000002i−2i00000
χ2922-22-2-22-2002-202-2000i2i2−i2−i22-2002-200i2−i22-200i2−i2i2−i2i2i2−i2−i20000000000i2−i2000
χ3022-22-2-22-2002-202-2000i2i2−i2−i22-200-2200i2−i2-2200i2−i2i2−i2−i2−i2i2i20000000000−i2i2000
χ3122-22-2-22-2002-202-2000i2i2−i2−i2-22002-200i2−i2-2200−i2i2−i2i2−i2−i2i2i20000000000i2−i2000
χ3222-22-2-22-2002-202-2000i2i2−i2−i2-2200-2200i2−i22-200−i2i2−i2i2i2i2−i2−i20000000000−i2i2000
χ3322-22-2-22-2002-202-2000−i2−i2i2i22-2002-200−i2i22-200−i2i2−i2i2−i2−i2i2i20000000000−i2i2000
χ3422-22-2-22-2002-202-2000−i2−i2i2i22-200-2200−i2i2-2200−i2i2−i2i2i2i2−i2−i20000000000i2−i2000
χ3522-22-2-22-2002-202-2000−i2−i2i2i2-22002-200−i2i2-2200i2−i2i2−i2i2i2−i2−i20000000000−i2i2000
χ3622-22-2-22-2002-202-2000−i2−i2i2i2-2200-2200−i2i22-200i2−i2i2−i2−i2−i2i2i20000000000i2−i2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-44-4-44444-4-4-4-4-4400000000000000000000000000000000000000000
χ39444-4-44-4-444-4-4-444-44-400000000000000000000000000000000000000000
χ40444-4-44-4-4-4-4-4-44444-4400000000000000000000000000000000000000000
χ4144-44-4-44-400-440-440002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ4244-44-4-44-400-440-44000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ4344-4-44-4-44004-40-440000000000000000000002i2−2i2−2i22i20000000000000000000
χ4444-4-44-4-44004-40-44000000000000000000000−2i22i22i2−2i20000000000000000000
χ4544-4-44-4-4400-4404-400000000000004i−4i00000000000000000000000000000
χ4644-4-44-4-4400-4404-40000000000000−4i4i00000000000000000000000000000
χ474-4444-4-4-400000000002i2−2i22i2−2i20000000000002i2−2i200002-22-2000000000000000
χ484-4444-4-4-400000000002i2−2i22i2−2i2000000000000−2i22i20000-22-22000000000000000
χ494-4444-4-4-40000000000−2i22i2−2i22i20000000000002i2−2i20000-22-22000000000000000
χ504-4444-4-4-40000000000−2i22i2−2i22i2000000000000−2i22i200002-22-2000000000000000
χ514-4-44-44-444-400400-40000000000000000000000002i2−2i2−2i22i2000000000000000
χ524-4-44-44-444-400400-4000000000000000000000000−2i22i22i2−2i2000000000000000
χ534-4-44-44-44-4400-4004004-4-440000000000000000000000000000000000000
χ544-4-44-44-44-4400-400400-444-40000000000000000000000000000000000000
χ554-4-4-4444-44-400-4004000000000000000000000000000000000022−220000000
χ564-4-4-4444-44-400-40040000000000000000000000000000000000−22220000000
χ574-4-4-4444-4-4400400-4000000004i−4i000000000000000000000000000000000
χ584-4-4-4444-4-4400400-400000000−4i4i000000000000000000000000000000000
χ598-88-8-8-888000000000000000000000000000000000000000000000000000

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