All connected cubic vertex-transitive graphs of order at most $1280$.

Id of the graph in the dataset. A graph is uniquely identified by the id and the order.

The number of vertices in the largest clique subgraph.

The greatest distance between any pair of vertices.

Length of the shortest cycle in the graph.

For every two ordered pairs of adjacent vertices, does there exist an authomorphism, mapping one to the other.

Can the vertices of the graph be partitioned into two sets, such that every edge connects a vertex in one set to a vertex in the other set.

Can the graph be constructed as a Cayley graph of some group for some generating set.

For any two vertices $v$ and $w$, the number of vertices at distance $j$ from $v$ and at distance $k$ from $w$ depends only upon $j$, $k$, and $i = d(v, w)$.

Given any two vertices $v$ and $w$ at any distance $i$, and any other two vertices $x$ and $y$ at the same distance, there is an automorphism of the graph that carries $v$ to $x$ and $w$ to $y$.

For every two edges, does there exist an authomorphism, mapping one to the other.

Does the graph have a cycle that visits each vertex exactly once.

Is the graph isometric to a subgraph of a hypercube.

Can the vertices of the graph be partitioned into a clique and an independent set.

Do there exists $\lambda$ and $\mu$ such that every two adjacent vertices have $\lambda$ common neighbours and every two non-adjacent vertices have $\mu$ common neighbours.

The number of cycles of length $3$ in the graph.

Does the graph belong to the Split Praeger-Xu family of graphs.

This is the full collection of extremal additive bases of up to $25$ elements.

A set $A$ of non-negative integers such that every non-negative integer can be written in at least one way as a sum of integers from $A$.

The number of elements in the additive basis.

The binary relation which holds between comparable elements that are immediate neighbours.

Can the lattice $L$ be equipped with a rank function $r$ from $L$ to $\mathbb{N}$ (or \mathbb{Z}), compatible with the ordering (so $r(x) < r(y)$ whenever $x < y$) such that whenever $y$ covers $x$, then $r(y) = r(x) + 1$.

All regular maniplexes of rank 3 with automorphism groups of order 200 or less.

The Schläfli symbol is a recursive description of regular polytopes or maniplexes. A polytope with the symbol ${p,q,r,...,y,z}$ has $z$ ${p,q,r,...,y}$-facets.

A list of additional relators in the finite representation of the polytope's automorphism group, expressed in terms of the standard flag-exchanging generators.

The dimension of the greatest face of the polytope.

The size of the polytope's automorphism group.

A vector representing the number of faces of each rank (starting with $0$).

All regular abstract polyhedra with automorphism groups of order 2000 or less.

Does the object satisfy the conditions for an abstract polytope.

Id of the group in the dataset. A group is uniquely identified by the id and the order.

Does the group have an upper central series that terminates with itself.

Does the group have an invariant normal series where all the factors are cyclic groups.

Can the group be constructed from abelian groups using extensions.

The pair $[order, id]$ of the group's Frattini factor in the Small Groups Library.

A short description of the group's structure as produced by GAP.

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