Finite Group Databasebeta

← Group #288156

Character table — Group #288156

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882244444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-1-11-1-1-1111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-111-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-11-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-11111-1-1-11
χ91111111111111111-1-1-1-111111111-1-11111-1-1-1-111111111-1-11-11-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-1-11-1-1-11111-1-11-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-111-1-11-1-1-1-111-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11-1-111-111-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1111-1-111-1-11-1
χ172222222222-22-2-2-222222-2-2000000-2-20022000000-2-200000002000-200000000
χ182222222222-22-2-2-222222-2-2000000-2-200-2-2000000220000000-2000200000000
χ192222222222-22-2-2-22-2-2-2-2-2-2000000220022000000-2-20000000-2000200000000
χ202222222222-22-2-2-22-2-2-2-2-2-20000002200-2-20000002200000002000-200000000
χ2122222222-2-22-2222-20000-2-22222220022000000-2-200000000-20-200000000000
χ2222222222-2-22-2222-20000-2-22222-2-200-2-2000000-2-20000000020200000000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-22200-2-2000000220000000020-200000000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-2-2-200220000002200000000-20200000000000
χ25222-2-2-22-200-20-22200000002i2i−2i−2i2-2002i−2i2−20000002−2i2i2−i2−i200000000002−2i2−i200
χ26222-2-2-22-200-20-22200000002i2i−2i−2i2-2002i−2i−22000000−22−i2−i2i2i20000000000−22−i2i200
χ27222-2-2-22-200-20-22200000002i2i−2i−2i-2200−2i2i2−20000002−2i2i2−i2−i20000000000−22−i2i200
χ28222-2-2-22-200-20-22200000002i2i−2i−2i-2200−2i2i−22000000−22−i2−i2i2i200000000002−2i2−i200
χ29222-2-2-22-200-20-2220000000−2i−2i2i2i2-200−2i2i2−20000002−2−i2−i2i2i200000000002−2−i2i200
χ30222-2-2-22-200-20-2220000000−2i−2i2i2i2-200−2i2i−22000000−22i2i2−i2−i20000000000−22i2−i200
χ31222-2-2-22-200-20-2220000000−2i−2i2i2i-22002i−2i2−20000002−2−i2−i2i2i20000000000−22i2−i200
χ32222-2-2-22-200-20-2220000000−2i−2i2i2i-22002i−2i−22000000−22i2i2−i2−i200000000002−2−i2i200
χ332-2-22-2-222222-2-22-2-22i2i−2i−2i-220000002i−2i0000000000002-22-2000000002i−2i000000
χ342-2-22-2-222222-2-22-2-22i2i−2i−2i-220000002i−2i000000000000-22-2200000000−2i2i000000
χ352-2-22-2-222222-2-22-2-2−2i−2i2i2i-22000000−2i2i0000000000002-22-200000000−2i2i000000
χ362-2-22-2-222222-2-22-2-2−2i−2i2i2i-22000000−2i2i000000000000-22-22000000002i−2i000000
χ372-2-22-2-22222-2-22-22-22i2i−2i−2i2-22-22-200−2i2i00002i2i−2i−2i2-20000000000000000000000
χ382-2-22-2-22222-2-22-22-22i2i−2i−2i2-2-22-2200−2i2i0000−2i−2i2i2i-220000000000000000000000
χ392-2-22-2-22222-2-22-22-2−2i−2i2i2i2-22-22-2002i−2i0000−2i−2i2i2i2-20000000000000000000000
χ402-2-22-2-22222-2-22-22-2−2i−2i2i2i2-2-22-22002i−2i00002i2i−2i−2i-220000000000000000000000
χ412-2-22-2-222-2-2-222-2220000-222-22-2000000000000-220000002-20002-2000000000
χ422-2-22-2-222-2-2-222-2220000-222-22-2000000000000-22000000-22000-22000000000
χ432-2-22-2-222-2-2-222-2220000-22-22-220000000000002-20000002-2000-22000000000
χ442-2-22-2-222-2-2-222-2220000-22-22-220000000000002-2000000-220002-2000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-4-4-44-400404-4-40000000000000000022−22000000−222200000000000000000000
χ47444-4-4-44-400404-4-400000000000000000−222200000022−2200000000000000000000
χ4844-444-4-4-44-404000-400000000000000000022−2222−22000000000000000000000000
χ4944-444-4-4-44-404000-4000000000000000000−2222−2222000000000000000000000000
χ5044-444-4-4-4-440-400044i−4i4i−4i000000000000000000000000000000000000000000
χ5144-444-4-4-4-440-40004−4i4i−4i4i000000000000000000000000000000000000000000
χ524-444-44-4-44-40-400040000000000000000002i2−2i2−2i22i2000000000000000000000000
χ534-444-44-4-44-40-40004000000000000000000−2i22i22i2−2i2000000000000000000000000
χ544-444-44-4-4-4404000-44-4-44000000000000000000000000000000000000000000
χ554-444-44-4-4-4404000-4-444-4000000000000000000000000000000000000000000
χ564-4-44-4-444-4-444-44-4400004-40000000000000000000000000000000000000000
χ574-4-4-4444-40040-4-4400000004i−4i−4i4i000000000000000000000000000000000000
χ584-4-4-4444-40040-4-440000000−4i4i4i−4i000000000000000000000000000000000000
χ594-4-4-4444-400-4044-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ604-4-4-4444-400-4044-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ6188-8-8-88-88000000000000000000000000000000000000000000000000000000
χ628-88-88-8-88000000000000000000000000000000000000000000000000000000

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