Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×#6869 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C11 | H(3,𝔽3) |
| commutator | C32 | C3×C9×C11 |
| Frattini, cosocle | C3×C9 | C32×C11 |
| socle | C3×C11 | C32⋊C9 |
| prime radical | C33×C11 | C9 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C11 ◁ C3×C9×C11 ◁ G | |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 297 |
A minimal faithful permutation representation — 2 generators on 38 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,14,19,24,20,28,32,15,17,23,21,25,31,29,33,37,22,18,26,30,27,34,36,35,38);(13,17,18)(19,25,27)(28,33,35)561 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 16);