Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6856 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C32 |
| direct product | C8×#6856 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C8 | H(3,𝔽3) |
| commutator | C33 | C32×C8 |
| Frattini, cosocle | C33×C4 | C2×C32 |
| socle | C2×C32 | C4×H(3,𝔽3) |
| prime radical | C2×#6856 | C4 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C8 ◁ C33×C8 ◁ G | |
188 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5,6,7,8)(9,10,12)(11,13,16)(14,17,15)(19,21,23);(10,13,14)(18,19,22)(20,23,26)(21,25,24)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 72);