Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C32 |
| direct product | C53×#10624575 |
| 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 | |
296 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 38637 |
A minimal faithful permutation representation — 3 generators on 80 points:
(1,2,6,5,7,9,4,8,3)(10,11,14,13,12,15,18,16,17)(19,20,21,23,24,27,22,25,26)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80);(1,3,8,4,9,7,5,6,2)(10,12,17,13,16,14,18,11,15)(20,24,25)(21,26,27);(2,7,8)(3,9,6)(11,16,12)(14,15,17)(19,21,25,22,26,24,23,27,20)5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 135);