A389366 Indices of normal subgroups of the modular group (without repetition).

1, 2, 3, 6, 12, 18, 24, 42, 48, 54, 60, 72, 78, 96, 114, 120, 126, 144, 150, 162, 168, 180, 186, 192, 216, 222, 234, 240, 258, 288, 294, 312, 324, 336, 342, 360, 366, 378, 384, 402, 432, 438, 450, 456, 474, 486, 504, 546, 558, 576, 582, 600, 618, 624, 648

Offset

1,2

Comments

Apart from the first three terms, all terms are divisible by 6.

Links

Table of n, a(n) for n=1..55.

Marston Conder and Peter Dobcsányi, Normal subgroups of low index in the modular group and other Hecke groups, Combinatorial Group Theory, Discrete Groups, and Number Theory (Benjamin Fine, Anthony M. Gaglione, and Dennis Spellman, eds.), Contemporary Mathematics, vol. 421, Amer. Math. Soc., Providence, RI, (2006), 65-86.

Example

If Gamma denotes the modular group, and Gamma^n denotes the subgroup consisting of all n-th powers of elements of Gamma, then Gamma, Gamma^2, and Gamma^3 are normal subgroups of indices 1, 2, and 3. If Gamma(n) denotes the principal congruence subgroup of level n, then Gamma(2), Gamma(3), Gamma(4), and Gamma(5) are normal subgroups of indices 6, 12, 24, and 60. The quotient of Gamma by Gamma(5) is isomorphic to the group of rotations of the icosahedron.

Crossrefs

Cf. A389830, A390078.

Sequence in context: A328899 A093687 A000423 * A007335 A309311 A394760

Adjacent sequences: A389363 A389364 A389365 * A389367 A389368 A389369

Keyword

nonn

Author

William P. Orrick, Nov 02 2025

Status

approved