Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C2×C4 |
| direct product | C7×#11963 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C4×C8 | C23×C7 |
| prime radical | C7×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,10,13,11,12,14,15)(16,17,21,26,19,28,35,25,22,27,38,43,36,24,20,37)(18,29,32,41,34,42,47,45,33,44,46,23,30,40,31,39);(9,12)(10,14)(16,18)(17,23)(19,30)(20,32)(21,31)(22,33)(24,39)(25,42)(26,44)(27,41)(28,45)(29,43)(34,36)(35,46)(37,40)(38,47);(9,12)(13,15)(16,19,22,36)(17,24,27,28)(18,30,33,34)(20,21,35,38)(23,39,41,45)(25,26,37,43)(29,42,44,40)(31,46,47,32)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4951);