Finite Group Databasebeta

← Group #284169

Character table — Group #284169

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882222444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111-1-1111111-1-111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-111-1111111-1-1-1-1
χ51111111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ61111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111111-1-11-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-11
χ11111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111111-1
χ12111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-111-11
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1111-1-111-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111111-1-1-111-1-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-111-1-111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-111111-1
χ172222222222-22-2-2-22-2-22222000022220000-2-2000000000000-200-20000000000
χ182222222222-22-2-2-22-2-222220000-2-2-2-20000-2-200000000000020020000000000
χ192222222222-22-2-2-22-2-2-2-2-2-2000022-2-2000022000000000000200-20000000000
χ202222222222-22-2-2-22-2-2-2-2-2-20000-2-222000022000000000000-20020000000000
χ2122222222-2-22-2222-2-2-2000022220000-2-2-2-200-2-2220000000000000000000000
χ2222222222-2-22-2222-2-2-2000022-2-20000-2-2220022-2-20000000000000000000000
χ2322222222-2-22-2222-2-2-20000-2-222000022-2-20022-2-20000000000000000000000
χ2422222222-2-22-2222-2-2-20000-2-2-2-20000222200-2-2220000000000000000000000
χ25222-2-2-22-22-20-200020022-2-200002i−2i2i−2i0000002−22−2000022−2−2000000i2−i2i2−i20000
χ26222-2-2-22-22-20-200020022-2-200002i−2i2i−2i000000−22−220000−2−222000000−i2i2−i2i20000
χ27222-2-2-22-22-20-200020022-2-20000−2i2i−2i2i0000002−22−2000022−2−2000000−i2i2−i2i20000
χ28222-2-2-22-22-20-200020022-2-20000−2i2i−2i2i000000−22−220000−2−222000000i2−i2i2−i20000
χ29222-2-2-22-22-20-2000200-2-22200002i−2i−2i2i0000002−22−20000−2−222000000i2−i2−i2i20000
χ30222-2-2-22-22-20-2000200-2-22200002i−2i−2i2i000000−22−22000022−2−2000000−i2i2i2−i20000
χ31222-2-2-22-22-20-2000200-2-2220000−2i2i2i−2i0000002−22−20000−2−222000000−i2i2i2−i20000
χ32222-2-2-22-22-20-2000200-2-2220000−2i2i2i−2i000000−22−22000022−2−2000000i2−i2−i2i20000
χ332-2-22-2-222222-2-22-2-2-222i−2i2i−2i0000000000002i−2i00000000000002i−2i02-200000000
χ342-2-22-2-222222-2-22-2-2-222i−2i2i−2i0000000000002i−2i0000000000000−2i2i0-2200000000
χ352-2-22-2-222222-2-22-2-2-22−2i2i−2i2i000000000000−2i2i00000000000002i−2i0-2200000000
χ362-2-22-2-222222-2-22-2-2-22−2i2i−2i2i000000000000−2i2i0000000000000−2i2i02-200000000
χ372-2-22-2-22222-2-22-22-22-22i−2i2i−2i002-20000002-2−2i2i00000000000000000000002i−2i00
χ382-2-22-2-22222-2-22-22-22-22i−2i2i−2i00-22000000-22−2i2i0000000000000000000000−2i2i00
χ392-2-22-2-22222-2-22-22-22-2−2i2i−2i2i002-20000002-22i−2i0000000000000000000000−2i2i00
χ402-2-22-2-22222-2-22-22-22-2−2i2i−2i2i00-22000000-222i−2i00000000000000000000002i−2i00
χ412-2-22-2-222-2-2-222-222-220000002-2000000-2200000022-2-22-22-200000000000000
χ422-2-22-2-222-2-2-222-222-220000002-2000000-22000000-2-222-22-2200000000000000
χ432-2-22-2-222-2-2-222-222-22000000-220000002-200000022-2-2-22-2200000000000000
χ442-2-22-2-222-2-2-222-222-22000000-220000002-2000000-2-2222-22-200000000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-44-4-4404000-40000000000000000000022−22−22220000000000000000000000
χ47444-4-4-44-4-4404000-400000000000000000000−222222−220000000000000000000000
χ4844-4-44-4-440040-4-440000000000000004i−4i000000000000000000000000000000
χ4944-4-44-4-440040-4-44000000000000000−4i4i000000000000000000000000000000
χ5044-4-44-4-4400-4044-400000000000000000000000002i2−2i22i2−2i2000000000000000000
χ5144-4-44-4-4400-4044-40000000000000000000000000−2i22i2−2i22i2000000000000000000
χ524-44-4-44-4400404-4-400000000000000000000000002i2−2i2−2i22i2000000000000000000
χ534-44-4-44-4400404-4-40000000000000000000000000−2i22i22i2−2i2000000000000000000
χ544-44-4-44-4400-40-44400000004-400000000000000000000000000000000000000
χ554-44-4-44-4400-40-4440000000-4400000000000000000000000000000000000000
χ564-4-44-4-444-4-444-44-444-400000000000000000000000000000000000000000000
χ574-4-4-4444-44-404000-4004i−4i−4i4i0000000000000000000000000000000000000000
χ584-4-4-4444-44-404000-400−4i4i4i−4i0000000000000000000000000000000000000000
χ594-4-4-4444-4-440-40004000000000000000000000000000022−22−222200000000000000
χ604-4-4-4444-4-440-400040000000000000000000000000000−222222−2200000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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