{
  "ambient_quotient": "O^+(L) -> Aut(chamber) times {+1,-1}, via chamber action and determinant",
  "ambient_quotient_image_order": 96,
  "hypergeometric_image_order": 8,
  "index_of_preimage_overgroup": 12,
  "implication": "The projective hypergeometric subgroup has index at least 12; if finite, its index is a multiple of 12.",
  "all_eight_wall_reflections_have_determinant": -1,
  "both_projective_companion_generators_have_determinant": 1,
  "wall_reflections_in_projective_hypergeometric_group": false,
  "qualification": "The determinant obstruction distinguishes the groups, but does not establish infinite index; finite-index orientation-preserving subgroups exist."
}