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 | C3×C11×C27⋊C3 |
| unambiguous semidirect product | C27⋊(C32×C11) |
| unambiguous semidirect product | (C11×C27)⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C11 | C32 |
| commutator | C3 | C32×C9×C11 |
| Frattini, cosocle | C9 | C33×C11 |
| socle | C32×C11 | C3×C9 |
| prime radical | C33×C11 | C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C11 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 891 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3)(31,32,33,34,35,36,37,38,39,40,41);(4,5,8,6,10,16,12,19,24,7,11,15,13,20,23,21,27,29,14,9,17,22,18,25,28,26,30);(5,9,11)(8,15,17)(10,18,20)(16,23,25)(19,26,27)(24,29,30)1089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 49);