Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#23363 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C22 | C23×C7×C8 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle, prime radical | C23×C7 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17,18,20,19,21,22,23)(24,25)(26,33)(27,31)(28,37)(29,32)(30,36)(34,39)(35,38);(10,15)(12,14)(24,26,29,36)(25,30,32,33)(27,35,28,34)(31,39,37,38);(8,10,11,15)(9,12,13,14)(24,27,29,28)(25,31,32,37)(26,34,36,35)(30,38,33,39);(9,13)(12,14)(24,28,29,27)(25,31,32,37)(26,35,36,34)(30,38,33,39)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16351);