Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C11 · Schur multiplier (H2) = C33 |
| direct product | C3×C11×AΣL(1,𝔽27) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C11 | H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C33×C11 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C11 ◁ C33×C11 ◁ G | |
252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 297 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(13,14,15,16,17,18,19,20,21,22,23);(4,5,7)(6,8,11)(9,12,10);(5,8,9)561 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 51);