Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#13456 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C23×C7 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
318 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)(8,9,12,14)(10,15,11,13)(16,17,19,24)(18,28,30,22)(20,23,33,39)(21,26,34,27)(25,41,40,35)(29,37,32,42)(31,46,45,38)(36,44,43,47);(8,10,12,11)(9,13,14,15)(16,18,19,30)(17,22,24,28)(20,31,33,45)(21,29,34,32)(23,38,39,46)(25,36,40,43)(26,42,27,37)(35,44,41,47);(8,11,12,10)(9,13,14,15)(17,23)(18,29)(20,35)(21,34)(22,36)(24,39)(25,27)(26,40)(28,43)(30,32)(31,45)(33,41)(37,46)(38,42)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6444);