Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×#6909 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C33 |
| direct product | Q8×#6912 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C22×C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C2×C32 | C22×C33 |
| prime radical | C2×C33 | C22×C32 |
| LCS | G ▷ C2×C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C33×Q8 ◁ G | |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4)(5,8,7,6)(9,10,13,12,16,23,21,15,27)(11,17,22,20,14,24,19,26,33)(18,29,32,30,28,34,31,25,35);(1,5,3,7)(2,6,4,8)(9,11,18,21,19,31,12,20,30)(10,14,25,15,17,28,16,26,29)(13,22,32,27,33,35,23,24,34);(11,19,20)(14,17,26)(18,30,31)(22,33,24)(25,29,28)(32,34,35)175 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2251);