Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#23297 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C23×C4 |
| prime radical | C22×C7×D4 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
726 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(9,13)(14,15)(16,17)(18,22)(19,21)(20,23)(24,25,29,26,28,31,37,33)(27,34,36,39,35,30,38,32);(8,9)(10,14)(11,15)(12,13)(16,18)(17,20)(19,23)(21,22)(24,26,29,31,28,33,37,25)(27,32,36,34,35,39,38,30);(8,10,12,11)(9,14,13,15)(17,21)(20,22)(24,27)(25,30)(26,32)(28,35)(29,36)(31,34)(33,39)(37,38);(8,11,12,10)(9,14,13,15)(18,23)(20,22)(27,35)(30,34)(32,39)(36,38)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16285);