Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C53 · Schur multiplier (H2) = C36 |
| direct product | C3×C53×#6891 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C53 | C33 |
| commutator, Frattini, cosocle | C32 | C34×C53 |
| prime radical | C35×C53 | C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C53 ◁ G | |
2636 conjugacy classes of subgroups.
| minimal degree | μ(G) = 74 |
| transitive degree | μt(G) = 4293 |
A minimal faithful permutation representation — 4 generators on 74 points:
(1,2,3)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74);(4,5,7,6,9,11,10,8,12)(13,14,16)(15,18,20)(17,21,19);(5,8,9)(7,11,12);(14,17,18)(16,20,21)8109 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 426);