Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6881 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C8×#6882 |
| 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×C32 | C4×H(3,𝔽3) |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C8 ◁ C32×C8 ◁ C3×C8×C9 ◁ G | |
76 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)(9,10,13,12,17,23,21,16,29)(11,18,22,19,15,27,30,28,35)(14,24,31,26,33,32,25,34,20);(10,14,15,17,26,28,16,25,18)(11,19,30)(13,22,33,29,35,24,23,27,34)(20,32,31)152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 98);