Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18734 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3548 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
932 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)(10,15)(11,17)(12,16)(13,18)(14,19)(20,23)(21,22)(24,25,29,33)(26,34,37,38)(27,32,28,31)(30,35,39,36);(8,10)(9,14)(11,19)(12,21)(13,20)(15,16)(17,23)(18,22)(24,26,29,37)(25,30,33,39)(27,35,28,36)(31,38,32,34);(8,10)(9,15)(11,21)(12,19)(13,20)(14,16)(17,22)(18,23)(25,31)(27,28)(30,38)(32,33)(34,39)(35,36);(8,11,13,12)(9,16,18,17)(10,19,20,21)(14,15,22,23)(24,27,29,28)(25,31,33,32)(26,35,37,36)(30,38,39,34)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11722);