Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#9370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#3219 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
424 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)(10,16)(11,19,21,14)(12,18)(13,15)(17,20,23,22)(24,25,28,31)(26,29)(27,32,36,37)(30,35)(33,39)(34,38);(8,10,16,9,13,18,12,15)(11,17,20,14,21,23,22,19)(24,26)(25,29,31,39)(27,35)(28,33)(30,37,38,32)(34,36);(8,11)(9,14)(10,17)(12,22)(13,21)(15,19)(16,20)(18,23)(24,26)(25,30)(27,35)(28,33)(29,37)(31,38)(32,39)(34,36)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2358);