Finite Group Databasebeta

← Group #170378

Character table — Group #170378

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1111111-1-1
χ911111111-1-1-1-11-1-11-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-1-11-1
χ1011111111-1-1-1-11-1-11-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-111-11
χ1111111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-111-11-1-111-11
χ1211111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11-111-1111-1-11-1
χ1311111111-1-1-1-11-1-11-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1111-1-1-11
χ1411111111-1-1-1-11-1-11-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-11-111-1-1-11-1-1111-1
χ1511111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-11-11-111-1-1-1111-1
χ1611111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-11-11-111-111-1-1-11
χ172222222222222-2-2-222-2-2-2-22-2000000000000000000000000022000-2-2000000
χ182222222222222-2-2-222-2-2-2-22-20000000000000000000000000-2-200022000000
χ19222222222222-2222-2-2-2-2-2-2-22000022220000000000000000-20000-200000000
χ20222222222222-2222-2-2-2-2-2-2-220000-2-2-2-2000000000000000020000200000000
χ21222222222222-2-2-2-2-2-22222-2-2222200000000000000000000000-2-2000000000
χ22222222222222-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000022000000000
χ2322222222-2-2-2-2222-2-2-222-2-22-200000000000000000000000002-2000-22000000
χ2422222222-2-2-2-2222-2-2-222-2-22-20000000000000000000000000-220002-2000000
χ2522222222-2-2-2-2-222-222-2-222-2-222-2-2000000000000000000000002-2000000000
χ2622222222-2-2-2-2-222-222-2-222-2-2-2-22200000000000000000000000-22000000000
χ2722222222-2-2-2-2-2-2-222222-2-2-22000022-2-20000000000000000-20000200000000
χ2822222222-2-2-2-2-2-2-222222-2-2-220000-2-222000000000000000020000-200000000
χ2922-2-222-2-222-2-202-2-20000000200002i−2i2i−2i22−2−222−2−20000000000000000i2−i2i2−i200
χ3022-2-222-2-222-2-202-2-20000000200002i−2i2i−2i−2−222−2−2220000000000000000−i2i2−i2i200
χ3122-2-222-2-222-2-202-2-2000000020000−2i2i−2i2i22−2−222−2−20000000000000000−i2i2−i2i200
χ3222-2-222-2-222-2-202-2-2000000020000−2i2i−2i2i−2−222−2−2220000000000000000i2−i2i2−i200
χ3322-2-222-2-2-2-2220-22-20000000200002i−2i−2i2i22−2−2−2−2220000000000000000i2−i2−i2i200
χ3422-2-222-2-2-2-2220-22-20000000200002i−2i−2i2i−2−22222−2−20000000000000000−i2i2i2−i200
χ3522-2-222-2-2-2-2220-22-2000000020000−2i2i2i−2i22−2−2−2−2220000000000000000−i2i2i2−i200
χ3622-2-222-2-2-2-2220-22-2000000020000−2i2i2i−2i−2−22222−2−20000000000000000i2−i2−i2i200
χ372-22-22-22-22i−2i2i−2i0000002i−2i2-2002-22i−2i0000i2−i2i2−i22−22−2i2i2−i2−i222−2−200000000000000
χ382-22-22-22-22i−2i2i−2i0000002i−2i2-2002-22i−2i0000−i2i2−i2i2−22−22−i2−i2i2i2−2−22200000000000000
χ392-22-22-22-22i−2i2i−2i0000002i−2i2-200-22−2i2i0000i2−i2i2−i22−22−2−i2−i2i2i2−2−22200000000000000
χ402-22-22-22-22i−2i2i−2i0000002i−2i2-200-22−2i2i0000−i2i2−i2i2−22−22i2i2−i2−i222−2−200000000000000
χ412-22-22-22-2−2i2i−2i2i000000−2i2i2-2002-2−2i2i0000i2−i2i2−i2−22−22i2i2−i2−i2−2−22200000000000000
χ422-22-22-22-2−2i2i−2i2i000000−2i2i2-2002-2−2i2i0000−i2i2−i2i22−22−2−i2−i2i2i222−2−200000000000000
χ432-22-22-22-2−2i2i−2i2i000000−2i2i2-200-222i−2i0000i2−i2i2−i2−22−22−i2−i2i2i222−2−200000000000000
χ442-22-22-22-2−2i2i−2i2i000000−2i2i2-200-222i−2i0000−i2i2−i2i22−22−2i2i2−i2−i2−2−22200000000000000
χ4544-44-4-44-400004000000000-400000000000000000000022−2222−2200000000000000
χ4644-44-4-44-400004000000000-4000000000000000000000−2222−222200000000000000
χ4744-44-4-44-40000-40000000004000000000000000002i2−2i22i2−2i2000000000000000000
χ4844-44-4-44-40000-4000000000400000000000000000−2i22i2−2i22i2000000000000000000
χ4944-4-444-4-444-4-40-4440000000-400000000000000000000000000000000000000
χ5044-4-444-4-4-4-44404-440000000-400000000000000000000000000000000000000
χ514-44-44-44-44i−4i4i−4i000000−4i4i-440000000000000000000000000000000000000000
χ524-44-44-44-4−4i4i−4i4i0000004i−4i-440000000000000000000000000000000000000000
χ534-4-444-4-444i−4i−4i4i000000000000000000002i−2i−2i2i2-2-220000000000000000000000
χ544-4-444-4-444i−4i−4i4i00000000000000000000−2i2i2i−2i-222-20000000000000000000000
χ554-4-444-4-44−4i4i4i−4i000000000000000000002i−2i−2i2i-222-20000000000000000000000
χ564-4-444-4-44−4i4i4i−4i00000000000000000000−2i2i2i−2i2-2-220000000000000000000000
χ574-4-4-4-4444000000004-400000000000000000000002-2-222-2-2200000000000000
χ584-4-4-4-4444000000004-40000000000000000000000-222-2-222-200000000000000
χ594-4-4-4-444400000000-4400000000000000000000002-2-22-222-200000000000000
χ604-4-4-4-444400000000-440000000000000000000000-222-22-2-2200000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ628-888-88-8-8000000000000000000000000000000000000000000000000000000

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