Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19050 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19054 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3150 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(13,15)(16,17)(18,28)(19,33)(20,25)(21,26)(22,27)(23,31)(24,35)(29,37)(30,38)(32,41)(34,39)(36,40)(42,44)(43,46)(45,47);(10,14)(12,15)(16,18)(17,23)(19,29)(20,30)(21,31)(22,32)(24,37)(25,28)(26,41)(27,38)(33,46)(34,43)(35,44)(36,45)(39,47)(40,42);(8,9)(10,15)(11,13)(12,14)(16,19,22,36)(17,24,27,39)(18,29,32,45)(20,35,21,34)(23,37,38,47)(25,40,26,33)(28,42,41,46)(30,44,31,43);(16,20,22,21)(17,25,27,26)(18,30,32,31)(19,34,36,35)(23,28,38,41)(24,33,39,40)(29,43,45,44)(37,46,47,42)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12042);