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Table 1 The values of p and h(q)

From: A characterization of some alternating groups A p+8 of degree p + 8 by OD

p h(q) Condition p h(q) Condition
113 \(2^4.7\) None 139 2.3.23 None
181 \(2^2.3^2.5\) \(q\ne 19\) 181 4 \(q=19\)
199 \(2.3^2.11\) None 211 2.3.5.7 None
241 \(2^4.3.5\) None 283 2.3.47 None
293 \(2^2.73\) None 317 \(2^2.79\) \(q\ne 73\)
317 4 \(q=73\) 337 \(2^4.3.7\) None
409 \(2^3.3.17\) \(q\ne 31,53\) 409 8 \(q=31\)
409 3 \(q=53\) 421 \(2^2.3.5.7\) \(q\ne 29\)
421 4 \(q=29\) 467 2.233 None
509 \(2^2.127\) none 523 \(2.3^2.29\) \(q\ne 11,19,61\)
523 29 \(q=11\) 523 9 \(q=19\)
523 6 \(q=61\) 547 2.3.7.13 \(q\ne 11,13,41\)
547 39 \(q=11\) 547 21 \(q=13\)
547 6 \(q=41\) 577 \(2^6.3^2\) \(q\ne 23\)
577 8 \(q=23\) 619 2.3.103 None
631 \(2.3^2.5.7\) \(q\ne 43\) 631 3 \(q=43\)
661 \(2^3.3.5.11\) \(q\ne 11\) 661 33 \(q=11\)
691 2.3.5.23 \(q\ne 89\) 691 5 \(q=89\)
709 \(2^2.3.59\) \(q\ne 227\) 709 3 \(q=227\)
787 2.3.131 None 797 \(2^2.199\) None
811 \(2.3^4.5\) \(q\ne 131\) 811 6 \(q=131\)
829 \(2^2.3^2.23\) \(q\ne 11\) 829 23 \(q=11\)
839 2.419 None 863 2.431 None
887 2.443 None 919 \(2.3^3.17\) \(q\ne 53\)
919 6 \(q=53\) 953 \(2^3.7.17\) None
997 \(2^2.3.83\) None