Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#34629 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| prime radical | C24×C7 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
1558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,19,21)(18,20,22,23)(24,25)(26,29)(27,34)(28,30)(31,35)(32,37)(33,39)(36,38);(9,12)(13,15)(16,18,19,22)(17,20,21,23)(24,26,28,32)(25,29,30,37)(27,33,35,38)(31,36,34,39);(17,21)(20,23)(25,30)(26,32)(31,34)(33,38);(24,27,28,35)(25,31,30,34)(26,33,32,38)(29,36,37,39);(8,10,11,14)(9,13,12,15)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27617);