Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9×C11 · Schur multiplier (H2) = C32 |
| direct product | C11×#6903 |
| subgroup | G/H | |
|---|---|---|
| center | C11×C27 | C32 |
| commutator | C3 | C32×C9×C11 |
| Frattini, cosocle | C9 | C33×C11 |
| socle | C3×C11 | C32×C9 |
| prime radical | C11×H(3,𝔽3) | C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C11×C27 ◁ G | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 92 |
| transitive degree | μt(G) = 891 |
A minimal faithful permutation representation — 3 generators on 92 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,15,19,29,25,35,50,16,20,30,26,36,51,44,59,73,27,37,52,45,60,74,66,80,88)(14,18,28,23,33,48,42,57,71,24,34,49,43,58,72,65,79,87,22,32,47,41,56,70,64,78,86)(21,31,46,39,54,68,62,76,84,38,53,67,61,75,83,81,89,91,40,55,69,63,77,85,82,90,92);(12,14,21)(13,18,31)(15,23,39)(16,24,38)(17,28,46)(19,33,54)(20,34,53)(22,40,27)(25,42,62)(26,43,61)(29,48,68)(30,49,67)(32,55,37)(35,57,76)(36,58,75)(41,63,45)(44,65,81)(47,69,52)(50,71,84)(51,72,83)(56,77,60)(59,79,89)(64,82,66)(70,85,74)(73,87,91)(78,90,80)(86,92,88);(14,22,24)(18,32,34)(21,38,40)(23,41,43)(28,47,49)(31,53,55)(33,56,58)(39,61,63)(42,64,65)(46,67,69)(48,70,72)(54,75,77)(57,78,79)(62,81,82)(68,83,85)(71,86,87)(76,89,90)(84,91,92)1089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 50);