Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C92 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C4×#6855 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C33×C4 | C32 |
| commutator | C3 | C2×C4×C92 |
| Frattini, cosocle | C2×C33 | C22×C32 |
| socle, prime radical | C22×C33 | C2×C32 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C33×C4 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1944 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2)(7,8,10)(9,12,14)(11,15,13)(16,17,19,18,20,22,21,23,24);(3,4,5,6)(8,11,12)(10,14,15)(25,26,28,27,29,31,30,32,33)792 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 586);