Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9279 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,13,12,15,10,14)(16,17,21,25,22,26,20,36)(18,27,31,38,30,42,29,23)(19,32,34,40,35,24,33,39)(28,41,45,37,44,47,43,46);(9,13)(10,11)(14,15)(16,18)(17,23,26,38)(19,28)(20,29)(21,31)(22,30)(24,37,32,46)(25,27,36,42)(33,43)(34,45)(35,44)(39,47,40,41);(9,13)(10,11)(14,15)(16,19,22,35)(17,24,26,32)(18,28,30,44)(20,34,21,33)(23,37,38,46)(25,40,36,39)(27,41,42,47)(29,45,31,43)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2284);