From 493d8d1dc6017c723e03fc3ffd68a2303427bbaf Mon Sep 17 00:00:00 2001
From: Alexander Hulpke <hulpke@math.colostate.edu>
Date: Sun, 7 Feb 2021 11:30:09 -0700
Subject: [PATCH] FIX: IntermediateGroup will not exit quietly if index is
 large

---
 lib/csetgrp.gi                                | 19 ++++++++++++++++---
 .../2021-02-07-IntermediateGroup.tst          |  5 +++++
 2 files changed, 21 insertions(+), 3 deletions(-)
 create mode 100644 tst/testbugfix/2021-02-07-IntermediateGroup.tst

diff --git a/lib/csetgrp.gi b/lib/csetgrp.gi
index 945c2c0f104..ed659446eb1 100644
--- a/lib/csetgrp.gi
+++ b/lib/csetgrp.gi
@@ -330,8 +330,6 @@ local o,b,img,G1,c,m,mt,hardlimit,gens,t,k,intersize;
     return fail;
   fi;
 
-  # old code -- obsolete
-
   c:=ValueOption("refineChainActionLimit");
   if IsInt(c) then
     hardlimit:=c;
@@ -339,7 +337,22 @@ local o,b,img,G1,c,m,mt,hardlimit,gens,t,k,intersize;
     hardlimit:=1000000;
   fi;
 
-  if Index(G,U)>hardlimit then return fail;fi;
+  if Index(G,U)>hardlimit/10
+   and ValueOption("callinintermediategroup")<>true then
+    # try the `AscendingChain` mechanism
+    c:=AscendingChain(G,U:cheap,refineIndex:=QuoInt(IndexNC(G,U),2),
+      callinintermediategroup);
+    if Length(c)>2 then
+      return First(c,x->Size(x)>Size(U));
+    fi;
+  fi;
+
+  if Index(G,U)>hardlimit then 
+    Info(InfoWarning,1,
+      "will have to use permutation action of degree bigger than ", hardlimit);
+  fi;
+
+  # old code -- obsolete
 
   if IsPermGroup(G) and Length(GeneratorsOfGroup(G))>3 then
     G1:=Group(SmallGeneratingSet(G));
diff --git a/tst/testbugfix/2021-02-07-IntermediateGroup.tst b/tst/testbugfix/2021-02-07-IntermediateGroup.tst
new file mode 100644
index 00000000000..0aa2cba47d6
--- /dev/null
+++ b/tst/testbugfix/2021-02-07-IntermediateGroup.tst
@@ -0,0 +1,5 @@
+# IntermediateGroup in large index, reported in Forum (Breuer/Anvita) on 2/7/21
+gap> L:=PSL(2,7^3);;
+gap> S:=SylowSubgroup(L,2);;
+gap> IntermediateGroup(L,S);
+<permutation group of size 344 with 4 generators>