Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C53 · Schur multiplier (H2) = C34 |
| direct product | C53×#10624887 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C53 | C34 |
| commutator, Frattini, cosocle | C32 | C34×C53 |
| prime radical | C3×H(3,𝔽3)×C53 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ G | |
698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 12879 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2,4,3,6,8,7,5,9)(11,14,16)(12,18,27)(15,23,21)(17,25,22)(19,29,28)(33,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(10,11,15)(12,17,24)(13,14,21)(16,23,20)(18,22,30)(19,26,33)(25,32,27)(28,31,35)(29,34,36);(2,5,6)(4,8,9)(11,16,14)(15,21,23)(17,25,22)(24,30,32)(26,34,31)(33,35,36);(10,12,19,13,18,28,20,27,29)(11,17,26,14,22,31,16,25,34)(15,24,33,21,30,35,23,32,36)5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 447);