Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8×C9 · Schur multiplier (H2) = C32 |
| direct product | C8×#6866 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C8 | H(3,𝔽3) |
| commutator | C32 | C3×C8×C9 |
| Frattini, cosocle | C33×C4 | C2×C32 |
| socle | C2×C32 | C4×H(3,𝔽3) |
| prime radical | C2×C34 | C3×C4 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C8 ◁ C33×C8 ◁ G | |
360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5,6,7,8)(9,10,12,11,13,15,14,16,17)(18,19,21)(20,22,25)(23,26,24);(19,22,23)408 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 82);