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×#24522 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
848 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)(18,23,29,38,30,39,36,43)(19,31,33,42,35,41,34,24)(28,40,32,46,44,47,45,37);(8,10,11,15)(9,12,13,14)(16,18)(17,23)(19,32)(20,29)(21,36)(22,30)(24,40)(25,38)(26,43)(27,39)(28,34)(31,46)(33,44)(35,45)(37,41)(42,47);(16,19,22,35)(17,24,27,42)(18,28,30,44)(20,34,21,33)(23,37,39,46)(25,41,26,31)(29,45,36,32)(38,47,43,40);(9,13)(12,14)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17510);