Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18466 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3558 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,19)(17,22)(18,20)(21,23)(24,25,29,32)(26,33,35,38)(27,31,28,36)(30,37,39,34);(9,13)(11,19)(14,20)(15,16)(18,23)(21,22)(24,26)(25,30)(27,34)(28,37)(29,35)(31,38)(32,39)(33,36);(8,10)(9,14)(11,18)(12,17)(13,20)(15,22)(16,21)(19,23)(27,28)(31,36)(33,38)(34,37);(9,15)(10,17)(13,16)(18,23)(24,27,29,28)(25,31,32,36)(26,34,35,37)(30,38,39,33)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11454);