Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#10377 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,11,15)(10,18,20,33)(12,26,24,16)(13,17,25,32)(14,29,30,37)(19,27,31,21)(22,35,23,36)(28,39,38,34);(8,9)(10,19,22,14)(11,15)(12,16)(13,17)(18,21,35,37)(20,31,23,30)(24,26)(25,32)(27,36,29,33)(28,34)(38,39);(8,10,11,23)(9,14,15,31)(12,27,24,37)(13,22,25,20)(16,33,26,35)(17,19,32,30)(18,34,36,39)(21,28,29,38)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3365);