Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18938 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3207 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
892 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,17)(11,14)(12,16)(13,21)(15,19)(18,22)(20,23)(24,25)(26,32)(27,35)(28,30)(29,34)(31,36)(33,39)(37,38);(8,10)(9,15)(11,18)(12,19)(13,22)(14,20)(16,23)(17,21)(27,36)(31,35)(32,39)(34,37);(8,11,14,9)(10,18,20,15)(12,16,13,21)(17,19,23,22)(24,26)(25,29)(27,37)(28,33)(30,38)(31,39)(32,35)(34,36);(8,12,14,13)(9,16,11,21)(10,19,20,22)(15,23,18,17)(25,30)(29,38)(31,35)(32,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11926);