Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13370 |
| 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 | |
358 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)(8,9,11,13)(10,14,15,12)(16,17)(18,27)(19,33)(20,25)(21,38)(22,26)(23,29)(24,36)(28,43)(30,40)(31,47)(32,45)(34,42)(35,41)(37,44)(39,46);(8,10,11,15)(9,12,13,14)(16,17)(18,28)(19,24)(20,38)(21,25)(22,26)(23,30)(27,43)(29,40)(31,39)(32,42)(33,36)(34,45)(35,44)(37,41)(46,47);(16,18,22,32)(17,23,26,39)(19,34,37,43)(20,31,21,30)(24,40,41,47)(25,42,38,28)(27,44,45,33)(29,35,46,36)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6358);