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Janko group

In mathematics, the Janko groups J1, J2, J3 and J4 are four of the twenty-six sporadic groups; their orderss are 23.3.5.7.11.19 (J1), 27.33.52.7 (J2), 27.35.5.17.19 (J3) and 221.33.5.7.113.23.29.31.37.43 (J4), respectively.

The Janko groups were first described by mathematician Zvonimir Janko in 1966; each of these groups has intricate matrix representationss as mapss into large general linear groups. For example, the matrix corresponding to J4 gives a representation of J4 in GL(112, 2).

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