A070953 Order of the group GU(n,2), the general unitary n X n matrices over the finite field GF(4).

3, 18, 648, 77760, 41057280, 82771476480, 683361309818880, 22304913152488243200, 2929259634489976002969600, 1534275894314621670931405209600, 3219180858829475639028172057057689600, 26997853423424927215248106646837737291776000, 906008220049901275850865613854890318362709065728000

Offset

1,1

Comments

Replacing 2 in the definition by a prime power q, the order of the group GU(n,q), the general unitary n X n matrices over the finite field GF(q^2) is (q+1) * q^(n(n-1)/2) * Product_{i=1..(n-1)} (q^(i+1) - (-1)^(i+1)).

References

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups, Oxford Univ. Press, 1985.

Links

Table of n, a(n) for n=1..13.

Index entries for sequences related to groups.

Formula

a(n) = 3 * 2^(n(n-1)/2) * Product_{i=1..(n-1)} (2^(i+1) - (-1)^(i+1)).

a(n) ~ c * 2^(n^2-1), where c = 3 * Product_{k>=1} (1 - (-1/2)^k) = 2.42144826060211836027... . - Amiram Eldar, Jul 11 2025

Mathematica

Table[3*2^(n*(n-1)/2) * Product[2^(k+1) - (-1)^(k+1), {k, 1, n-1}], {n, 1, 12}]
 (* or *) Table[I^(n*(n+3)) * 2^((n-1)*n/2) * QPochhammer[-2, -2, n], {n, 1, 12}] (* Vaclav Kotesovec, Jan 06 2021 *)

Prog

(PARI) a(n) = 3*2^(n*(n-1)/2)*prod(i=1, (n-1), (2^(i+1)-(-1)^(i+1)));

Crossrefs

Sequence in context: A304780 A265468 A365292 * A163261 A064846 A157544

Adjacent sequences: A070950 A070951 A070952 * A070954 A070955 A070956

Keyword

nonn

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 24 2002

Extensions

More terms from Benoit Cloitre, Jun 06 2002

Status

approved