Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6909 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C4×#6913 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | C3×H(3,𝔽3) |
| commutator | C32 | C2×C33×C4 |
| Frattini, cosocle | C2×C32 | C22×C33 |
| socle | C22×C3 | C2×C3×H(3,𝔽3) |
| prime radical | C22×#6913 | C2 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C2×C3×C4×C9 ◁ G | |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2)(7,8,11)(9,13,18)(10,12,19)(14,23,17)(15,20,27)(16,22,28)(21,30,24)(25,29,32)(26,31,33);(3,4,5,6)(8,12,14)(9,15,24)(13,21,20)(16,26,25)(18,27,30)(28,33,32);(7,9,16,10,15,25,17,24,26)(8,13,22,12,20,29,14,21,31)(11,18,28,19,27,32,23,30,33)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2192);