Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#23751 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#400 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,16,13,17,19,28)(10,18,21,30,22,33,27,14)(11,23,26,37,25,15,31,32)(20,34,35,36,24,38,39,29);(8,10,19,21,13,22,12,27)(9,14,28,18,17,30,16,33)(11,24,31,39,25,20,26,35)(15,29,37,34,23,36,32,38);(8,11,12,26,13,25,19,31)(9,15,16,32,17,23,28,37)(10,20,21,35,22,24,27,39)(14,29,18,34,30,36,33,38);(11,25)(15,23)(20,24)(26,31)(29,36)(32,37)(34,38)(35,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16739);