Janko group

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In mathematics, a Janko group is one of the four sporadic simple groups named for Zvonimir Janko. Janko constructed the first of these groups, J1, in 1965 and predicted the existence of J2 and J3. In 1976, he suggested the existence of J4. J2, J3 and J4 were all later shown to exist.

Janko groups[edit]

  • The Janko group J1 has order 175 560 = 23 ···· 11 · 19. It is the only Janko group whose existence was proved by Janko himself.
  • The Hall–Janko group has order 604 800 = 27 · 33 · 52 · 7. It is also known as J2, HJ, or the Hall–Janko–Wales group. It was constructed by Marshall Hall, Jr. and David Wales.
  • The Janko group J3 has order 50 232 960 = 27 · 35 ·· 17 · 19. It is also known as the Higman–Janko–McKay group. It was constructed by Graham Higman and John McKay.
  • The Janko group J4 has order 86 775 571 046 077 562 880 = 221 · 33 ··· 113 · 23 · 29 · 31 · 37 · 43. It was constructed by Simon P. Norton.