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Order of twisted group 2F4(2^(2*n + 1)).
3

%I #17 Dec 22 2024 21:30:46

%S 35942400,264905352699586176614400,

%T 1318633155799591447702161609782722560000,

%U 6082094555322622967641341883296948240189833427183206400,27553065698713340677402960424984119640445544581637086693954488264294400,124270100714024486336082151164778648282667807904331482703587621226371097161732037017600

%N Order of twisted group 2F4(2^(2*n + 1)).

%D R. W. Carter, Simple Groups of Lie Type, Wiley 1972, Chap. 14.

%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.

%H Harry J. Smith, <a href="/A064586/b064586.txt">Table of n, a(n) for n = 0..40</a>

%F a(n) = (2^(2*n+1))^12*((2^(2*n+1))-1)*((2^(2*n+1))^3+1)*((2^(2*n+1))^4-1)*((2^(2*n+1))^6+1).

%o (PARI) a(n) = { my(q=2^(2*n + 1)); q^12*(q - 1)*(q^3 + 1)*(q^4 - 1)*(q^6 + 1) } \\ _Harry J. Smith_, Sep 19 2009

%Y Cf. A037252, A064585.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Oct 17 2001