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×#19051 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3545 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(13,15)(16,17,22,27)(18,28,31,40)(19,32,33,41)(20,26,21,25)(23,35,38,30)(24,36,39,34)(29,37,43,47)(42,44,46,45);(10,14)(12,15)(16,18)(17,23)(19,29)(20,35)(21,30)(22,31)(24,37)(25,40)(26,28)(27,38)(32,46)(33,43)(34,45)(36,44)(39,47)(41,42);(8,9)(10,15)(11,13)(12,14)(16,19)(17,24)(18,29)(20,34)(21,36)(22,33)(23,37)(25,32)(26,41)(27,39)(28,42)(30,44)(31,43)(35,45)(38,47)(40,46);(19,33)(24,39)(29,43)(32,41)(34,36)(37,47)(42,46)(44,45)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12039);