Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10207 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #127 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,14,19)(10,20,11,22)(12,18,13,17)(15,23,16,21)(25,30)(27,28)(31,34)(32,33)(35,36)(38,39);(8,10,14,11)(9,15,19,16)(12,23,13,21)(17,22,18,20)(24,25,29,33)(26,34,37,38)(27,32,28,30)(31,35,39,36);(8,11,14,10)(9,16,19,15)(12,23,13,21)(17,22,18,20)(24,26,29,37)(25,31,33,39)(27,36,28,35)(30,34,32,38)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3195);