Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6878 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C8×#6878 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C8 | #732 |
| commutator | C3×C9 | C32×C8 |
| Frattini, cosocle | C3×C4×C9 | C2×C32 |
| socle | C2×C3 | C4×#732 |
| prime radical | C2×#732 | C3×C4 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C8 ◁ C32×C8 ◁ C3×C8×C9 ◁ G | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8)(9,10,13)(11,18,22)(12,17,23)(14,24,19)(15,28,20)(16,29,21)(25,33,31)(26,34,35)(27,32,30);(10,14,25,17,27,18,16,26,15)(13,22,24,29,33,34,23,28,32)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 94);