Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C92×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×#6864 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C11 | C32 |
| commutator | C3 | C92×C11 |
| Frattini, cosocle | C3×C9 | C32×C11 |
| socle, prime radical | C32×C11 | C3×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C11 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2673 |
A minimal faithful permutation representation — 2 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(21,22,25,23,27,33,29,36,41,24,28,32,30,37,40,38,44,46,31,26,34,39,35,42,45,43,47);(12,13,15,14,16,18,17,19,20)(22,26,28)(25,32,34)(27,35,37)(33,40,42)(36,43,44)(41,46,47)1089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 11);