Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C33 |
| direct product | C53×#10624585 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C53 | H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C53 |
| socle | C32×C53 | C3×H(3,𝔽3) |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C53 ◁ C32×C9×C53 ◁ G | |
256 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 12879 |
A minimal faithful permutation representation — 3 generators on 107 points:
(1,2,5)(3,7,12)(4,6,13)(8,17,11)(9,15,20)(10,14,21)(16,24,19)(18,22,26)(23,27,25)(28,29,32,31,34,41,39,45,51)(30,35,46,38,33,42,37,44,40)(36,43,50,48,53,54,49,47,52)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(2,6,8)(7,14,16)(15,22,23)(28,30,36)(29,33,43)(31,38,48)(32,40,50)(34,44,53)(35,47,45)(37,49,39)(41,46,54)(42,52,51);(1,3,9,4,10,18,11,19,25)(2,7,15,6,14,22,8,16,23)(5,12,20,13,21,26,17,24,27)5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 145);