Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24378 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#29431 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C43×C7 ◁ G | |
670 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)(24,25,27,30,28,31,36,39)(26,32,34,37,33,38,35,29);(8,10,11,15)(9,12,13,14)(16,17)(18,21)(19,20)(22,23)(26,33)(29,37)(32,38)(34,35);(17,20)(21,23)(24,26,28,33)(25,29,31,37)(27,35,36,34)(30,38,39,32);(9,13)(12,14)(16,18,19,22)(17,21,20,23)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 22419);