Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9279 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9284 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,13,15,18)(10,16,17,19)(24,25,29,33,30,32,28,26)(27,34,35,31,36,39,37,38);(8,9,11,18,12,15,20,13)(10,14,19,22,17,23,16,21)(24,26,29,32,30,33,28,25)(27,34,35,38,36,39,37,31);(8,10)(9,14)(11,19)(12,17)(13,21)(15,23)(16,20)(18,22)(24,27,30,36)(25,31,32,38)(26,34,33,39)(28,37,29,35)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2272);