Table 1 Finite non-abelian simple groups S with \(\pi (S)\subseteq \{2,3,5,7\}\)
From: A characterization of L 3(4) by its character degree graph and order
S | Order of S | Out(S) | S | Order of S | Out(S) |
|---|---|---|---|---|---|
\(A_5\) | \(2^2\cdot 3\cdot 5\) | 2 | \(L_2(49)\) | \(2^4\cdot 3\cdot 5^2\cdot 7^2\) | \(2^2\) |
\(L_2(7)\) | \(2^3\cdot 3\cdot 7\) | 2 | \(U_3(5)\) | \(2^4\cdot 3^2\cdot 5^3\cdot 7\) | \(S_3\) |
\(A_6\) | \(2^3\cdot 3^2\cdot 5\) | \(2^2\) | \(A_9\) | \(2^6\cdot 3^4\cdot 5\cdot 7\) | 2 |
\(L_2(8)\) | \(2^3\cdot 3^2\cdot 7\) | 3 | \(J_2\) | \(2^7\cdot 3^3\cdot 5^2\cdot 7\) | 2 |
\(A_7\) | \(2^3\cdot 3^2\cdot 5\cdot 7\) | 2 | \(S_6(2)\) | \(2^9\cdot 3^4\cdot 5\cdot 7\) | 1 |
\(U_3(3)\) | \(2^5\cdot 3^3\cdot 7\) | 2 | \(A_{10}\) | \(2^7\cdot 3^4\cdot 5^2\cdot 7\) | 2 |
\(A_8\) | \(2^6\cdot 3^2\cdot 5\cdot 7\) | 2 | \(U_4(3)\) | \(2^7\cdot 3^6\cdot 5\cdot 7\) | \(D_8\) |
\(L_3(4)\) | \(2^6\cdot 3^2\cdot 5\cdot 7\) | \(D_{12}\) | \(S_4(7)\) | \(2^8\cdot 3^2\cdot 5^2\cdot 7^4\) | 2 |
\(U_4(2)\) | \(2^6\cdot 3^4\cdot 5\) | 2 | \(O_{8}^+(2)\) | \(2^{12}\cdot 3^5\cdot 5^2\cdot 7\) | \(S_3\) |