Finite Group Databasebeta

← Group #309027

Character table — Group #309027

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-11-1-1-1-1-1111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-11-1-11111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-11111-1-11-1
χ911111111111111111-1-1-1-11111111-1-1111111-1-1-1-11111111-1-1-1-1-11-1-1-11111-1-1
χ1011111111111111111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-111-11-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-11-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1111-1-111-1-111-1-1-11
χ1722222222222-2-2-2-22-22222-2000000-2-20000220000-2-200000200000-200000000
χ1822222222222-2-2-2-22-22222-2000000-2-20000-2-200002200000-200000200000000
χ1922222222222-2-2-2-22-2-2-2-2-2-2000000220000220000-2-200000-200000200000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2000000220000-2-200002200000200000-200000000
χ2122222222-2-2-22222-2-20000-22222220022-2-2000000000000-200000-2000000000
χ2222222222-2-2-22222-2-20000-22222-2-200-2-2-2-20000000000002000002000000000
χ2322222222-2-2-22222-2-20000-2-2-2-2-22200-2-222000000000000-2000002000000000
χ2422222222-2-2-22222-2-20000-2-2-2-2-2-2-2002222000000000000200000-2000000000
χ2522-2-222-2-222-222-2-2-220000-222-2-20000002-2000000000000002-22-20000000000
χ2622-2-222-2-222-222-2-2-220000-222-2-20000002-200000000000000-22-220000000000
χ2722-2-222-2-222-222-2-2-220000-2-2-222000000-22000000000000002-2-220000000000
χ2822-2-222-2-222-222-2-2-220000-2-2-222000000-2200000000000000-222-20000000000
χ2922-2-222-2-2-2-2222-2-22-22i2i−2i−2i222-2-2002i−2i00-22002i2i−2i−2i0000000000000000000000
χ3022-2-222-2-2-2-2222-2-22-22i2i−2i−2i2-2-222002i−2i002-200−2i−2i2i2i0000000000000000000000
χ3122-2-222-2-2-2-2222-2-22-2−2i−2i2i2i222-2-200−2i2i00-2200−2i−2i2i2i0000000000000000000000
χ3222-2-222-2-2-2-2222-2-22-2−2i−2i2i2i2-2-22200−2i2i002-2002i2i−2i−2i0000000000000000000000
χ3322-2-222-2-2-2-22-2-222222i2i−2i−2i-2000000−2i2i0000000000002i2i−2i−2i000000002-2000000
χ3422-2-222-2-2-2-22-2-222222i2i−2i−2i-2000000−2i2i000000000000−2i−2i2i2i00000000-22000000
χ3522-2-222-2-2-2-22-2-22222−2i−2i2i2i-20000002i−2i0000000000002i2i−2i−2i00000000-22000000
χ3622-2-222-2-2-2-22-2-22222−2i−2i2i2i-20000002i−2i000000000000−2i−2i2i2i000000002-2000000
χ372-22-22-22-20002-22-200000002i−2i2i−2i2i−2i002-200i2−i20000i2−i22−22−200000000002−2i2−i200
χ382-22-22-22-20002-22-200000002i−2i2i−2i2i−2i002-200−i2i20000−i2i2−22−220000000000−22−i2i200
χ392-22-22-22-20002-22-200000002i−2i2i−2i−2i2i00-2200i2−i20000i2−i22−22−20000000000−22−i2i200
χ402-22-22-22-20002-22-200000002i−2i2i−2i−2i2i00-2200−i2i20000−i2i2−22−2200000000002−2i2−i200
χ412-22-22-22-20002-22-20000000−2i2i−2i2i2i−2i00-2200i2−i20000i2−i2−22−2200000000002−2−i2i200
χ422-22-22-22-20002-22-20000000−2i2i−2i2i2i−2i00-2200−i2i20000−i2i22−22−20000000000−22i2−i200
χ432-22-22-22-20002-22-20000000−2i2i−2i2i−2i2i002-200i2−i20000i2−i2−22−220000000000−22i2−i200
χ442-22-22-22-20002-22-20000000−2i2i−2i2i−2i2i002-200−i2i20000−i2i22−22−200000000002−2−i2i200
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ4644-4-444-4-444-4-4-444-4-4000040000000000000000000000000000000000000000
χ474-444-44-4-44-440000-404-44-400000000000000000000000000000000000000000
χ484-444-44-4-44-440000-40-44-4400000000000000000000000000000000000000000
χ494-444-44-4-4-44-400004000000000000000000002i2−2i22i2−2i20000000000000000000000
χ504-444-44-4-4-44-40000400000000000000000000−2i22i2−2i22i20000000000000000000000
χ514-44-44-44-4000-44-4400000000000000000002i2−2i20000−2i22i200000000000000000000
χ524-44-44-44-4000-44-440000000000000000000−2i22i200002i2−2i200000000000000000000
χ534-4-444-4-440004-4-4400000004i−4i−4i4i000000000000000000000000000000000000
χ544-4-444-4-440004-4-440000000−4i4i4i−4i000000000000000000000000000000000000
χ554-4-444-4-44000-444-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ564-4-444-4-44000-444-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ574-4-4-4-44444-4-4000040000000000000000000022−22−22220000000000000000000000
χ584-4-4-4-44444-4-40000400000000000000000000−222222−220000000000000000000000
χ594-4-4-4-4444-4440000-404i−4i−4i4i00000000000000000000000000000000000000000
χ604-4-4-4-4444-4440000-40−4i4i4i−4i00000000000000000000000000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ6288-88-8-88-8000000000000000000000000000000000000000000000000000000

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