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 | C11×#6908 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C11 | H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C33×C11 |
| socle | C3×C11 | C3×H(3,𝔽3) |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C11 ◁ C3×C9×C11 ◁ G | |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 297 |
A minimal faithful permutation representation — 3 generators on 38 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16)(14,18,23)(15,17,24)(19,28,22)(20,26,31)(21,25,32)(27,35,30)(29,33,37)(34,38,36);(13,17,19)(18,25,27)(26,33,34);(12,14,20,15,21,29,22,30,36)(13,18,26,17,25,33,19,27,34)(16,23,31,24,32,37,28,35,38)561 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 55);