Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C3 |
| direct product | C53×#10624828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C53 | #6895 |
| commutator, Frattini, cosocle | C3×C9 | C33×C53 |
| prime radical | C33×C53 | 3−1+2 |
| LCS | G ▷ C3×C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C53 ◁ C3×C9×C53 ◁ G | |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 1431 |
A minimal faithful permutation representation — 3 generators on 80 points:
(1,2,5,3,9,16,11,17,25,4,6,15,12,18,26,24,20,27,13,8,21,10,22,14,23,7,19)(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);(2,6,8)(7,17,20)(9,18,22);(2,7,9,8,20,22,6,17,18)(3,10,12)(5,14,25,15,16,27,21,26,19)(11,24,23)3021 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 388);