Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10173 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,17)(10,18,21,22)(11,14,12,16)(15,19,23,20)(24,25,29,26)(27,34,35,39)(28,33,38,31)(30,37,32,36);(9,14)(10,19)(11,12)(16,17)(18,22)(20,21)(24,26,29,25)(27,32,35,30)(28,31,38,33)(34,37,39,36);(8,10,13,21)(9,15,17,23)(11,19,12,20)(14,18,16,22)(24,27)(25,30)(26,32)(28,37)(29,35)(31,39)(33,34)(36,38)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3161);