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) = C3 |
| direct product | C8×#6864 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C8×C9 | C32 |
| commutator | C3 | C8×C92 |
| Frattini, cosocle | C3×C4×C9 | C2×C32 |
| socle, prime radical | C2×C32 | C3×C4×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C8×C9 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 1944 |
A minimal faithful permutation representation — 2 generators on 44 points:
(1,2,3,4,5,6,7,8)(18,19,22,20,24,30,26,33,38,21,25,29,27,34,37,35,41,43,28,23,31,36,32,39,42,40,44);(9,10,12,11,13,15,14,16,17)(19,23,25)(22,29,31)(24,32,34)(30,37,39)(33,40,41)(38,43,44)792 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 80);