Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C8 · Schur multiplier (H2) = C37 |
| direct product | C32×C8×H(3,𝔽3) |
| unambiguous semidirect product | (C32×C8)⋊C33 |
| subgroup | G/H | |
|---|---|---|
| center | C33×C8 | C32 |
| commutator | C3 | C34×C8 |
| Frattini, cosocle | C3×C4 | C2×C34 |
| socle | C2×C33 | C32×C4 |
| prime radical | C2×C32×H(3,𝔽3) | C4 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C8 ◁ G | |
1800 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(16,17,18,19,20,21,22,23);(4,5,6);(7,8,10)(9,12,14)(11,15,13);(8,11,12)(10,14,15)792 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2284);