Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C4×C7×#400 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C7 | C23 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| socle, prime radical | C24×C7 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C7 ◁ G | |
1398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4)(25,26,27,28,29,30,31);(11,15)(13,16)(17,18,20,22)(19,23,24,21);(6,8)(9,10,12,14)(11,16,15,13)(17,18)(19,23)(20,22)(21,24);(5,6)(7,8)(9,11)(10,13)(12,15)(14,16)(17,19,20,24)(18,21,22,23)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6852);