Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32×C9 · Schur multiplier (H2) = C23×C33 |
| direct product | C23×C3×C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C33 | C32 |
| commutator | C3 | C23×C32×C9 |
| Frattini, cosocle | C32 | C23×C33 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C23×C33 ◁ G | |
1440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1944 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2)(7,8,9);(3,4)(11,13,16)(14,18,17)(19,20,22,21,23,25,24,26,27);(5,6)(10,11,14,12,13,17,15,16,18)792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2948);