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×#36755 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1512 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)(16,17,19,21)(18,22,23,20)(24,25,28,29)(26,32,34,30)(27,31,35,36)(33,38,39,37);(9,12)(13,15)(25,29)(30,32)(31,36)(37,38);(8,9)(10,13)(11,12)(14,15)(16,18,19,23)(17,20,21,22)(24,25)(26,30)(27,31)(28,29)(32,34)(33,37)(35,36)(38,39);(8,9)(10,13)(11,12)(14,15)(24,26)(25,30)(27,33)(28,34)(29,32)(31,37)(35,39)(36,38);(8,10)(9,13)(11,14)(12,15)(24,27,28,35)(25,31,29,36)(26,33,34,39)(30,37,32,38)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29743);