Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10035 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| socle | C22×C7 | #392 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C42×C7 ◁ G | |
498 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)(10,16)(11,19)(12,15)(13,18)(14,21)(17,23)(20,22)(24,25,29,33)(26,34,37,38)(27,32,28,31)(30,36,39,35);(13,22)(16,23)(24,26,29,37)(25,30,33,39)(27,36,28,35)(31,38,32,34);(8,10)(9,13)(11,20)(12,17)(14,23)(15,22)(16,19)(18,21)(26,35)(27,28)(30,34)(31,32)(36,37)(38,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3023);