Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C9 |
| direct product | Q8×#6896 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C2×C32 | C22×C33 |
| prime radical | C2×C33 | C22×C32 |
| LCS | G ▷ C2×C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2,3,4)(5,8,7,6)(10,14,16)(11,15,17)(19,20,24)(22,25,23);(1,5,3,7)(2,6,4,8)(9,10,15,13,16,17,12,14,11)(18,19,22,21,20,23,26,24,25);(9,11,14,12,17,16,13,15,10)(18,20,25,21,24,22,26,19,23)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2235);