Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×#6899 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C11 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C11 |
| prime radical | C33×C11 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C11 ◁ G | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 891 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16,14)(17,18,19)(21,22,26)(23,30,42)(24,28,36)(25,29,37)(27,38,33)(31,41,45)(32,43,35)(34,40,46)(39,47,44);(12,13,17,20,14,18,15,16,19)(21,23,31,25,32,44,34,33,24)(22,27,39,29,30,28,40,43,41)(26,35,36,37,38,45,46,42,47);(12,14,19,20,16,17,15,13,18)(21,24,33,34,44,32,25,31,23)(22,28,27,40,39,43,29,41,30)(26,36,38,46,47,35,37,45,42)561 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 46);