Statements (60)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:musical_group
|
| gptkbp:discovered_by |
gptkb:1965
|
| gptkbp:has_a_center |
trivial
|
| gptkbp:has_a_character_table |
with 15 conjugacy classes
|
| gptkbp:has_a_normal_subgroup |
of order 60
|
| gptkbp:has_a_presentation |
with generators and relations
|
| gptkbp:has_a_subgroup_of_index |
336
|
| gptkbp:has_a_unique_nontrivial_normal_subgroup |
of order 60
|
| gptkbp:has_a_unique_subgroup |
of order 2
|
| gptkbp:has_subgroup |
gptkb:12
gptkb:30 the Monster group of order 2,880 the Janko group J1 |
| https://www.w3.org/2000/01/rdf-schema#label |
Janko subgroup
|
| gptkbp:is_a |
gptkb:musical_group
|
| gptkbp:is_a_finite_group_of |
degree 5
|
| gptkbp:is_a_member_of |
the family of Janko groups
|
| gptkbp:is_a_quotient_of |
the Monster group by a normal subgroup
|
| gptkbp:is_a_simple_group_of |
order 20,160
|
| gptkbp:is_associated_with |
the theory of group actions
|
| gptkbp:is_connected_to |
the theory of modular forms
|
| gptkbp:is_involved_in |
the classification of finite simple groups
|
| gptkbp:is_one_of |
the sporadic groups
|
| gptkbp:is_part_of |
the Monster group
|
| gptkbp:is_related_to |
the Leech lattice
the Thompson group |
| gptkbp:is_represented_in |
a permutation group
the symmetric group S_5 |
| gptkbp:is_studied_in |
algebraic topology
|
| gptkbp:is_used_in |
gptkb:musical_group
the study of finite groups |
| gptkbp:key_feature |
a sporadic group
|
| gptkbp:known_as |
J1
|
| gptkbp:members |
acts on a set of 5 elements
can be represented as a permutation group has a nontrivial center has a unique subgroup of order 10 has a unique subgroup of order 120 has a unique subgroup of order 122880 has a unique subgroup of order 15 has a unique subgroup of order 15360 has a unique subgroup of order 1920 has a unique subgroup of order 20 has a unique subgroup of order 240 has a unique subgroup of order 3 has a unique subgroup of order 30 has a unique subgroup of order 30720 has a unique subgroup of order 3840 has a unique subgroup of order 4 has a unique subgroup of order 480 has a unique subgroup of order 5 has a unique subgroup of order 6 has a unique subgroup of order 60 has a unique subgroup of order 61440 has a unique subgroup of order 7680 has a unique subgroup of order 960 |
| gptkbp:named_after |
Zvonimir Janko
|
| gptkbp:order |
20,160
|
| gptkbp:scientific_classification |
a sporadic simple group
|