Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36770 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C7×#2714 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1566 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)(10,14)(13,15)(18,22)(20,23)(24,25,29,26)(27,32,35,30)(28,31,36,33)(34,38,39,37);(9,12)(13,15)(16,17,19,21)(18,20,22,23)(25,26)(30,32)(31,33)(37,38);(8,9)(10,13)(11,12)(14,15)(16,18,19,22)(17,20,21,23)(24,26,29,25)(27,32,35,30)(28,33,36,31)(34,38,39,37);(8,9)(10,13)(11,12)(14,15)(24,27)(25,30)(26,32)(28,34)(29,35)(31,37)(33,38)(36,39);(8,10)(9,13)(11,14)(12,15)(24,28,29,36)(25,31,26,33)(27,34,35,39)(30,37,32,38)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29758);