Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9331 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9332 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C7×#3194 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,14,17)(10,13,16,12)(11,18)(15,19)(20,22)(21,23)(24,25)(26,29,33,37)(27,34,35,30)(28,31)(32,36)(38,39);(8,10,12,9,14,16,13,17)(11,18,20,15,21,23,19,22)(24,26,28,33)(25,29)(27,32,35,38)(30,36)(31,37)(34,39);(8,11)(9,15)(10,18)(12,20)(13,19)(14,21)(16,23)(17,22)(24,27)(25,30)(26,32)(28,35)(29,36)(31,34)(33,38)(37,39)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2320);