Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C53 · Schur multiplier (H2) = C34 |
| direct product | C53×#10624886 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C53 | C34 |
| commutator, Frattini, cosocle | C32 | C34×C53 |
| prime radical | C34×C53 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ G | |
728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 4293 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2,4,3,6,8,7,5,9)(10,11,14)(12,16,22)(13,17,21)(15,23,20)(18,26,30)(19,25,32)(24,31,27)(28,34,35)(29,33,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(11,15,17)(12,18,27)(14,21,23)(19,29,28)(22,31,30)(25,34,33);(2,5,6)(4,8,9)(10,12,19,13,18,28,20,27,29)(11,16,25,17,26,34,15,24,33)(14,22,32,21,30,35,23,31,36);(11,15,17)(14,21,23)(16,24,26)(22,30,31)(25,33,34)(32,35,36)5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 446);