Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C27 · Schur multiplier (H2) = C32 |
| direct product | C11×C32⋊C27 |
| unambiguous semidirect product | C32⋊(C11×C27) |
| unambiguous semidirect product | (C32×C11)⋊C27 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C11 | C32 |
| commutator | C3 | C3×C11×C27 |
| Frattini, cosocle | C3×C9 | C32×C11 |
| socle | C32×C11 | C3×C9 |
| prime radical | C33×C11 | C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C11 ◁ G | |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 891 |
A minimal faithful permutation representation — 2 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15)(14,17,19)(16,20,18)(21,22,25,23,26,31,28,33,38,24,27,32,29,34,39,36,41,44,30,35,40,37,42,45,43,46,47);(13,16,17)(15,19,20)1089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 12);