Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C32 |
| direct product | C53×#10624577 |
| 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) = 98 |
| transitive degree | μt(G) = 38637 |
A minimal faithful permutation representation — 3 generators on 98 points:
(2,6,8)(3,7,9)(10,11,14,18,12,15,13,16,17)(19,20,24,23,27,35,33,40,43)(21,28,41,22,26,34,32,25,36)(29,38,44,30,37,45,31,39,42)(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);(1,2,7,5,8,9,4,6,3)(10,12,17,18,16,14,13,11,15)(19,21,29,23,22,30,33,32,31)(20,25,37,27,28,39,40,26,38)(24,34,42,35,36,44,43,41,45);(1,3,6,4,9,8,5,7,2)(11,12,16)(14,17,15)(19,22,31,23,32,29,33,21,30)(20,26,39,27,25,38,40,28,37)(24,34,42,35,36,44,43,41,45)5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 137);