Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C92 · Schur multiplier (H2) = C33 |
| direct product | C8×#6855 |
| subgroup | G/H | |
|---|---|---|
| center | C33×C8 | C32 |
| commutator | C3 | C8×C92 |
| Frattini, cosocle | C33×C4 | C2×C32 |
| socle, prime radical | C2×C33 | C32×C4 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C8 ◁ G | |
276 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1944 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8)(9,10,12)(11,14,16)(13,17,15)(18,19,21,20,22,24,23,25,26);(10,13,14)(12,16,17)(27,28,30,29,31,33,32,34,35)792 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 71);