Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C33 |
| direct product | C53×#10624570 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C53 | C33 |
| commutator, Frattini, cosocle | C33 | C33×C53 |
| prime radical | C34×C53 | C32 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C33×C53 ◁ G | |
428 conjugacy classes of subgroups.
| minimal degree | μ(G) = 98 |
| transitive degree | μt(G) = 12879 |
A minimal faithful permutation representation — 3 generators on 98 points:
(2,5,3)(6,7,8)(19,20,24)(21,28,40)(22,26,34)(23,27,35)(25,36,31)(29,39,43)(30,41,33)(32,38,44)(37,45,42)(46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98);(1,2,6,9,3,7,4,5,8)(10,11,13)(12,15,17)(14,18,16)(19,21,29,23,30,42,32,31,22)(20,25,37,27,28,26,38,41,39)(24,33,34,35,36,43,44,40,45);(1,3,8,9,5,6,4,2,7)(11,14,15)(13,17,18)(19,22,31,32,42,30,23,29,21)(20,26,25,38,37,41,27,39,28)(24,34,36,44,45,33,35,43,40)5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 130);