Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C53 · Schur multiplier (H2) = C3 |
| direct product | C53×#10624482 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C53 | #732 |
| commutator, Frattini, cosocle | C32×C9 | C32×C53 |
| prime radical | C33×C53 | H(3,𝔽3) |
| LCS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ C33×C53 ◁ C32×C9×C53 ◁ G | |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 4293 |
A minimal faithful permutation representation — 2 generators on 89 points:
(1,2,4)(3,5,8)(6,9,7)(10,11,16,15,12,19,14,22,31)(13,21,30,26,23,35,25,18,27)(17,28,29,20,32,34,33,24,36)(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);(2,5,6)(10,12,20,15,22,33,14,11,17)(13,23,16,26,18,19,25,21,31)(24,29,30,28,34,35,32,36,27)3021 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 42);