Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60191 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C8 | C24 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C22×C7 | C24×C4 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C8 ◁ G | |
1810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,15)(11,13)(12,14)(16,17,20,25,21,24,31,37)(18,22,28,34,27,33,40,44)(19,23,29,36,30,35,41,45)(26,32,39,43,38,42,46,47);(8,10,12,11)(9,13,14,15)(16,18)(17,22)(19,26)(20,28)(21,27)(23,32)(24,33)(25,34)(29,39)(30,38)(31,40)(35,42)(36,43)(37,44)(41,46)(45,47);(8,11,12,10)(9,13,14,15)(16,19,20,29,21,30,31,41)(17,23,25,36,24,35,37,45)(18,26,28,39,27,38,40,46)(22,32,34,43,33,42,44,47);(18,27)(22,33)(26,38)(28,40)(32,42)(34,44)(39,46)(43,47);(17,24)(22,33)(23,35)(25,37)(32,42)(34,44)(36,45)(43,47)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53179);