A066051 Maximal degree of an irreducible representation of the group of n X n signed permutation matrices.

1, 2, 3, 8, 20, 80, 210, 672, 2688, 10080, 44352, 236544, 960960, 4324320, 20270250, 104247000, 522762240, 3024552960, 15713497800, 108973522944, 625746401280, 3824005785600, 24049411386000, 160329409240000, 858907549500000, 5226869622374400

Offset

1,2

Comments

This group is also the automorphism group of the n-dimensional hypercube and the wreath product of the cyclic group C_2 and the symmetric group S_n.

The number of irreducible representations is given in A000712; the order of the group in A000165.

The group is also the Weyl group of type B_n. - Eric M. Schmidt, Sep 21 2013

References

Roger W. Carter, Finite Groups of Lie Type: Conjugacy Classes And Complex Characters. Wiley, 1985.

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..40

Prog

(GAP) to produce a(8): c := CyclicGroup(2); s := SymmetricGroup(8); w := WreathProduct(c, s); Display(CharacterTable(w));
(Sage) def A066051(n) : return factorial(n) // min(prod(A.hooks()) * prod(B.hooks()) for (A, B) in PartitionTuples(2, n)) # Eric M. Schmidt, Sep 21 2013

Crossrefs

Cf. A000712, A000165, A003040.

Sequence in context: A029895 A073268 A073190 * A056971 A108125 A175490

Adjacent sequences: A066048 A066049 A066050 * A066052 A066053 A066054

Keyword

nonn,nice

Author

Sharon Sela (sharonsela(AT)hotmail.com), Dec 29 2001

Extensions

More terms from Eric M. Schmidt, Sep 21 2013

Status

approved