Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6881 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×#6882 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C11 | #732 |
| commutator, Frattini, cosocle | C3×C9 | C32×C11 |
| prime radical | C32×C11 | H(3,𝔽3) |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C11 ◁ C32×C11 ◁ C3×C9×C11 ◁ G | |
38 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)(12,13,16,15,20,26,24,19,32)(14,21,25,22,18,30,33,31,38)(17,27,34,29,36,35,28,37,23);(13,17,18,20,29,31,19,28,21)(14,22,33)(16,25,36,32,38,27,26,30,37)(23,35,34)209 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 29);