Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C92 · Schur multiplier (H2) = C3 |
| direct product | Q8×#6864 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C2×C3×C9 | C22×C32 |
| commutator | C2×C3 | C22×C92 |
| socle, prime radical | C2×C32 | C22×C3×C9 |
| LCS | G ▷ C2×C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C9 ◁ G | |
180 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)(5,8,7,6)(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);(1,5,3,7)(2,6,4,8)(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)495 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 653);