Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C9 · Schur multiplier (H2) = C32 |
| direct product | C3×Q8×C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C9 | C22×C32 |
| commutator | C2×C3 | C22×C32×C9 |
| Frattini, cosocle | C2×C9 | C22×C33 |
| socle | C2×C32 | C22×C3×C9 |
| prime radical | C2×C33 | C22×C9 |
| LCS | G ▷ C2×C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C9 ◁ G | |
360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 3 generators on 38 points:
(1,2,3)(31,32,33,34)(35,38,37,36);(4,5,8,6,10,16,12,19,24,7,11,15,13,20,23,21,27,29,14,9,17,22,18,25,28,26,30)(31,35,33,37)(32,36,34,38);(5,9,11)(8,15,17)(10,18,20)(16,23,25)(19,26,27)(24,29,30)495 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2241);