Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C32 |
| direct product | C53×#10624576 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C33×C53 | C33 |
| commutator, Frattini, cosocle | C33 | C33×C53 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C33×C53 ◁ G | |
254 conjugacy classes of subgroups.
| minimal degree | μ(G) = 116 |
| transitive degree | μt(G) = 38637 |
A minimal faithful permutation representation — 3 generators on 116 points:
(1,2,6,4,3,9,5,7,8)(10,11,15)(12,19,32)(13,17,25)(14,18,26)(16,27,23)(20,29,35)(21,28,36)(22,30,33)(24,31,34)(37,38,41,40,44,49,47,43,53)(39,42,48,46,52,57,55,51,60)(45,50,56,54,59,62,61,58,63)(64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116);(2,7,3)(6,9,8)(10,12,20,14,13,21,24,23,22)(11,16,28,18,19,30,31,17,29)(15,25,33,26,27,35,34,32,36)(37,39,45,40,46,54,47,55,61)(38,42,50,44,52,59,43,51,58)(41,48,56,49,57,62,53,60,63);(1,3,6,4,7,9,5,2,8)(10,13,22,14,23,20,24,12,21)(11,17,30,18,16,29,31,19,28)(15,25,33,26,27,35,34,32,36)(38,43,44)(41,49,53)(42,51,52)(48,57,60)(50,58,59)(56,62,63)5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 136);