Finite Group Databasebeta

← Group #337167

Character table — Group #337167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882222444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-1-1-11-11
χ3111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1
χ51111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-11-1
χ61111111111111111111111-1-111-1-1-1-1111111-1-1-1-11111-1111-1-11111-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1111111-1
χ11111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-111
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-11
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-11-1-1-1-111-1-111-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-111-1-111-1-1-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111111-1-1
χ17222222222-2-222-22-2-2-200002200-2-2220022-2-200000000-200000000000000
χ18222222222-2-222-22-2-2-200002200-2-2-2-200-2-22200000000200000000000000
χ19222222222-2-222-22-2-2-20000-2-200222200-2-22200000000-200000000000000
χ20222222222-2-222-22-2-2-20000-2-20022-2-20022-2-200000000200000000000000
χ2122222222-222-2-22-22-2-2222200220000-2-20000000000000-22-200000000000
χ2222222222-222-2-22-22-2-2222200-2-20000-2-200000000000002-2200000000000
χ2322222222-222-2-22-22-2-2-2-2-2-200220000220000000000000-2-2200000000000
χ2422222222-222-2-22-22-2-2-2-2-2-200-2-2000022000000000000022-200000000000
χ2522-22-2-22-2-2-2-2222-222-200000000000000000022-2-2000000002i−2i002i−2i00000
χ2622-22-2-22-2-2-2-2222-222-200000000000000000022-2-200000000−2i2i00−2i2i00000
χ2722-22-2-22-2-2-2-2222-222-2000000000000000000-2-222000000002i−2i00−2i2i00000
χ2822-22-2-22-2-2-2-2222-222-2000000000000000000-2-22200000000−2i2i002i−2i00000
χ292-2-22-22-222002-20-200022−2−200002i−2i2-22−2002i−2ii2−i2i2−i2i2i2−i2−i200000000002−2000
χ302-2-22-22-222002-20-200022−2−200002i−2i-222−200−2i2ii2−i2i2−i2−i2−i2i2i20000000000−22000
χ312-2-22-22-222002-20-200022−2−20000−2i2i2-22−200−2i2i−i2i2−i2i2−i2−i2i2i200000000002−2000
χ322-2-22-22-222002-20-200022−2−20000−2i2i-222−2002i−2i−i2i2−i2i2i2i2−i2−i20000000000−22000
χ332-2-22-22-222002-20-2000−2−22200002i−2i2-2−22002i−2i−i2i2−i2i2−i2−i2i2i20000000000−22000
χ342-2-22-22-222002-20-2000−2−22200002i−2i-22−2200−2i2i−i2i2−i2i2i2i2−i2−i200000000002−2000
χ352-2-22-22-222002-20-2000−2−2220000−2i2i2-2−2200−2i2ii2−i2i2−i2i2i2−i2−i20000000000−22000
χ362-2-22-22-222002-20-2000−2−2220000−2i2i-22−22002i−2ii2−i2i2−i2−i2−i2i2i200000000002−2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ3844-44-4-44-4444-4-4-44-44-400000000000000000000000000000000000000000
χ3944-44-4-44-44-4-4-4-4444-4400000000000000000000000000000000000000000
χ4044-44-4-44-4-44444-4-4-4-4400000000000000000000000000000000000000000
χ4144-4-44-4-4400000000002i2−2i22i2−2i2000000000022−220000002i−2i2i−2i000000000000000
χ4244-4-44-4-4400000000002i2−2i22i2−2i20000000000−2222000000−2i2i−2i2i000000000000000
χ4344-4-44-4-440000000000−2i22i2−2i22i2000000000022−22000000−2i2i−2i2i000000000000000
χ4444-4-44-4-440000000000−2i22i2−2i22i20000000000−22220000002i−2i2i−2i000000000000000
χ454-4444-4-4-4400-440-400000004-400000000000000000000000000000000000
χ464-4444-4-4-4400-440-40000000-4400000000000000000000000000000000000
χ474-4444-4-4-4-4004-4040000000000000000000002i2−2i2−2i22i20000000000000000000
χ484-4444-4-4-4-4004-404000000000000000000000−2i22i22i2−2i20000000000000000000
χ494-44-4-4-44404-40040-4004i−4i−4i4i0000000000000000000000000000000000000
χ504-44-4-4-44404-40040-400−4i4i4i−4i0000000000000000000000000000000000000
χ514-44-4-4-4440-4400-40400000000000000000000000022−22−2222000000000000000
χ524-44-4-4-4440-4400-404000000000000000000000000−222222−22000000000000000
χ534-4-44-44-44-400-44040002222−22−2200000000−2222000000000000000000000000000
χ544-4-44-44-44-400-4404000−22−2222220000000022−22000000000000000000000000000
χ554-4-4-4444-404-400-404000000004-4000000000000000000000000000000000
χ564-4-4-4444-404-400-40400000000-44000000000000000000000000000000000
χ574-4-4-4444-40-440040-400000000000000000000000000000000002i2−2i20000000
χ584-4-4-4444-40-440040-40000000000000000000000000000000000−2i22i20000000
χ59888-8-88-8-8000000000000000000000000000000000000000000000000000

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