Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18269 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
924 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,15)(10,13,17,20)(11,14,18,21)(16,22,23,19)(25,30)(27,28)(31,38)(32,36)(33,34)(37,39);(8,10)(9,13)(11,16)(12,17)(14,19)(15,20)(18,23)(21,22)(24,25)(26,31)(27,30)(28,36)(29,32)(33,38)(34,37)(35,39);(8,11)(9,14)(10,16)(12,18)(13,19)(15,21)(17,23)(20,22)(24,26,29,35)(25,31,32,39)(27,34,28,33)(30,37,36,38);(24,27,29,28)(25,30,32,36)(26,33,35,34)(31,38,39,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11257);