Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36698 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
1484 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,20)(19,21)(22,23)(24,25,28,29)(26,30,33,36)(27,31,35,37)(32,38,34,39);(16,18,19,23)(17,20,21,22)(25,29)(30,36)(31,37)(38,39);(9,12)(13,15)(16,17)(18,22)(19,21)(20,23)(24,26,28,33)(25,30,29,36)(27,34,35,32)(31,39,37,38);(17,21)(20,22)(24,27,28,35)(25,31,29,37)(26,32,33,34)(30,38,36,39);(8,10,11,14)(9,13,12,15)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29686);