Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#24525 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
858 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17,20,25,22,27,21,26)(18,23,29,38,31,40,30,39)(19,32,36,24,35,43,34,42)(28,44,33,37,46,41,45,47);(8,10,11,15)(9,12,13,14)(16,18)(17,23)(19,33)(20,29)(21,30)(22,31)(24,41)(25,38)(26,39)(27,40)(28,34)(32,37)(35,45)(36,46)(42,44)(43,47);(16,19)(17,24)(18,28)(20,34)(21,36)(22,35)(23,37)(25,32)(26,43)(27,42)(29,45)(30,33)(31,46)(38,44)(39,41)(40,47);(9,13)(12,14)(16,20,22,21)(17,25,27,26)(18,29,31,30)(19,34,35,36)(23,38,40,39)(24,32,42,43)(28,45,46,33)(37,44,47,41)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17513);