For human operators of AI agents

An AI agent will answer questions about finite groups from memory — fluently, and often wrongly. These prompts point it at the database instead, and make it tell you what it actually checked.

Paste this first

You have access to finitegroupdatabase.com, a database of finite groups.
Read https://finitegroupdatabase.com/agent.md before answering anything.

- Every claim about a specific group comes from a page or a query result you
  fetched, never from recall. Cite the group's permanent link.
- If the database does not have it, say so. Do not fall back on memory.
- Show me any query you ran, before its result.
- A pattern you observed across groups is a conjecture, not a theorem. Say
  which of the two you are giving me.
- Name the range you actually checked ("every order ≤ 200"), never "always".

The last two lines carry the most weight. A pattern that holds across every group an agent looked at is evidence, not proof — in finite group theory the first counterexample can sit far beyond any range that can be enumerated — and an unprompted agent will hand it to you as a fact.

Then give it a task

Each line below is a complete prompt. Paste one after the block above.

Let it write the query. The schema is published, so an agent can answer questions no single page answers.

• "Read the database schema, then write one query for the smallest non-solvable ambivalent group that is not rational. Show me the query, run it, and link the group."
• "Which orders below 512 have more non-abelian groups than the order above them? Write the query from the schema — do not estimate."
• "Give me every perfect group below order 10000 as a table: order, whether it is quasisimple, permanent link. One query."
• "How are conjugacy class counts distributed across the groups of order 128? One query, then a table."

Make it compare. Two groups, one precise question.

• "Fetch the character tables of D4 and Q8. Tell me exactly what they establish about the two groups, and what they do not."
• "Both groups have the same order and the same derived subgroup order. Find an invariant in the database that separates them, and cite it."

Make it check itself. The second pass is where wrong answers surface.

• "Re-derive that from a second, independent query. Tell me whether the two agree."
• "Which orders in that answer are not fully enumerated here? Restate the claim so it covers only what is."

Reading the answer

• Follow one cited link. Confirm the page says what the agent said it says.
• Ask which orders the claim was checked over. "All groups" is almost never what was searched.
• Some orders are too large to enumerate — order 1024 alone has about 4.9 × 10¹⁰ groups. Those listings are marked "Selected groups only", so "every group of order 1024" is not a question the database can answer, and a summarizing agent may not notice the notice.
• An agent's own arithmetic on group orders is not a database result. If it computed rather than queried, ask it to query.

What it can reach

Per-group pages, per-order listings, family listings, character tables, subgroup lattices, expression search, the schema, and the query endpoint — /agent.md documents all of them and is the authority. Point your agent there rather than describing the interface yourself; it changes as the database grows.