Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7734 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#7794 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(13,15)(16,17)(18,20)(19,22)(21,23)(24,25,28,31)(26,29,33,36)(27,30,34,37)(32,38,39,35);(8,9,11,13)(10,15,14,12)(24,26)(25,29)(27,32)(28,33)(30,35)(31,36)(34,39)(37,38);(17,20)(18,23)(21,22)(24,27,28,34)(25,30,31,37)(26,32,33,39)(29,35,36,38)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 782);