Finite Group Databasebeta

← Group #168795

Character table — Group #168795

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444444444444444444888888882444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ411111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ51111111111111111111111-1-1-1-1111-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-111111-1-111111111-11-1-1-111111-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1111111
χ911111111-1-1-1-1-1-11-1-11111111-1-111-111-1-1-1-11111-1-1-1-1-111-11-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-11-1-11111111-1-111-111-1-1-1-1-1-1-1-11111-111-11-1-1-111-1-111-11
χ1111111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-111111111-1-1-1-11-11-1-11-1-11111-1-1-11
χ1211111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1111-1-1-1-1111-1
χ1311111111-1-1-1-1-1-11-1-111111-1-11111-1-1-111-1-11111-1-1-1-1-1-1-1111-1-111-1-1111-1
χ1411111111-1-1-1-1-1-11-1-111111-1-11111-1-1-111-1-1-1-1-1-11111-1-1-111111-1-111-1-1-11
χ1511111111-1-1-1-1-1-11-1-111111-1-111-1-1-111-1-1111111-1-1-1-111-11-1-111-1-1-1-111-11
χ1611111111-1-1-1-1-1-11-1-111111-1-111-1-1-111-1-111-1-1-1-1111111-11-1-1-1-11111-1-11-1
χ1722222222222222-2-2-22-2-2-22000000-2222200000000000-2000-20000000000
χ1822222222222222-2-2-22-2-2-22000000-2-2-2-2-200000000000200020000000000
χ19222222222222-2-22-2-2-2-2-22-2000022200002200000000-2000-200000000000
χ20222222222222-2-22-2-2-2-2-22-20000-2-220000-2-2000000002000200000000000
χ21222222222222-2-2-222-222-2-2222200-20000000000000000-2-2000000000000
χ22222222222222-2-2-222-222-2-2-2-2-2-200-2000000000000000022000000000000
χ2322222222-2-2-2-222222-2-2-22-2000022-20000-2-2000000002000-200000000000
χ2422222222-2-2-2-222222-2-2-22-20000-2-2-200002200000000-2000200000000000
χ2522222222-2-2-2-222-2-2-2-222-2-222-2-20020000000000000000-22000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2-2-22200200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2222-2-2-22000000222-2-200000000000-200020000000000
χ2822222222-2-2-2-2-2-2-2222-2-2-220000002-2-222000000000002000-20000000000
χ2922-2-22-22-22i2i−2i−2i0002i−2i02-2002-22i−2i000000000i2i2−i2−i222−2−20000000000i2−i22−200
χ3022-2-22-22-22i2i−2i−2i0002i−2i02-2002-22i−2i000000000−i2−i2i2i2−2−2220000000000−i2i2−2200
χ3122-2-22-22-22i2i−2i−2i0002i−2i02-200-22−2i2i000000000i2i2−i2−i222−2−20000000000−i2i2−2200
χ3222-2-22-22-22i2i−2i−2i0002i−2i02-200-22−2i2i000000000−i2−i2i2i2−2−2220000000000i2−i22−200
χ3322-2-22-22-2−2i−2i2i2i000−2i2i02-2002-2−2i2i000000000i2i2−i2−i2−2−2220000000000i2−i2−2200
χ3422-2-22-22-2−2i−2i2i2i000−2i2i02-2002-2−2i2i000000000−i2−i2i2i222−2−20000000000−i2i22−200
χ3522-2-22-22-2−2i−2i2i2i000−2i2i02-200-222i−2i000000000i2i2−i2−i2−2−2220000000000−i2i22−200
χ3622-2-22-22-2−2i−2i2i2i000−2i2i02-200-222i−2i000000000−i2−i2i2i222−2−20000000000i2−i2−2200
χ372-2-22-2-2222-22-22-20002000-200000002i−2i2i−2i002−22−22−22−2000000i2−i2i2−i2000000
χ382-2-22-2-2222-22-22-20002000-200000002i−2i2i−2i00−22−22−22−22000000−i2i2−i2i2000000
χ392-2-22-2-2222-22-22-20002000-20000000−2i2i−2i2i002−22−22−22−2000000−i2i2−i2i2000000
χ402-2-22-2-2222-22-22-20002000-20000000−2i2i−2i2i00−22−22−22−22000000i2−i2i2−i2000000
χ412-2-22-2-222-22-22-220002000-200000002i−2i−2i2i002−22−2−22−22000000i2−i2−i2i2000000
χ422-2-22-2-222-22-22-220002000-200000002i−2i−2i2i00−22−222−22−2000000−i2i2i2−i2000000
χ432-2-22-2-222-22-22-220002000-20000000−2i2i2i−2i002−22−2−22−22000000−i2i2i2−i2000000
χ442-2-22-2-222-22-22-220002000-20000000−2i2i2i−2i00−22−222−22−2000000i2−i2−i2i2000000
χ4544-44-44-4-4000000400000-4000004-40000000000000000000000000000000
χ4644-44-44-4-4000000400000-400000-440000000000000000000000000000000
χ4744-44-44-4-4000000-40000040000000000004i−4i000000000000000000000000
χ4844-44-44-4-4000000-4000004000000000000−4i4i000000000000000000000000
χ4944-4-44-44-44i4i−4i−4i000−4i4i0-44000000000000000000000000000000000000000
χ5044-4-44-44-4−4i−4i4i4i0004i−4i0-44000000000000000000000000000000000000000
χ514-44-4-444-44i−4i−4i4i000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ524-44-4-444-44i−4i−4i4i00000000000000000000000−2i2i2i−2i-222-20000000000000000
χ534-44-4-444-4−4i4i4i−4i000000000000000000000002i−2i−2i2i-222-20000000000000000
χ544-44-4-444-4−4i4i4i−4i00000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ554-4-44-4-4444-44-4-44000-400040000000000000000000000000000000000000
χ564-4-44-4-444-44-444-4000-400040000000000000000000000000000000000000
χ57888-8-8-8-88000000000000000000000000000000000000000000000000000
χ588-8888-8-8-8000000000000000000000000000000000000000000000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

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