Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23391 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#23785 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C43×C7 ◁ G | |
680 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,19,21)(18,22,23,20)(24,25,28,32)(26,34,37,30)(27,31,29,33)(35,39,36,38);(9,12)(13,15)(24,26,28,37)(25,30,32,34)(27,36,29,35)(31,39,33,38);(16,18,19,23)(17,20,21,22)(26,35)(27,29)(30,38)(31,33)(34,39)(36,37);(8,10,11,14)(9,13,12,15)(24,27,28,29)(25,31,32,33)(26,36,37,35)(30,39,34,38)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16773);