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×#36838 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1526 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)(21,23)(24,25)(26,32)(27,33)(28,31)(29,30)(34,38)(35,39)(36,37);(9,12)(13,15)(16,17,20,19)(18,21,22,23)(25,30)(26,33)(31,37)(34,39);(8,9)(10,13)(11,12)(14,15)(16,18,20,22)(17,21,19,23)(24,26)(25,27)(28,34)(29,33)(30,32)(31,35)(36,39)(37,38);(8,9)(10,13)(11,12)(14,15)(16,19,20,17)(18,23,22,21)(24,27)(25,26)(28,35)(29,32)(30,33)(31,34)(36,38)(37,39);(8,10)(9,13)(11,14)(12,15)(24,28,29,36)(25,31,30,37)(26,34,33,39)(27,35,32,38)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29826);