Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#21559 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#121 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C4×#121 |
| prime radical | C7×#3067 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C7×C8 ◁ G | |
868 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)(8,9,13,19,15,20,14,18)(10,21,12,16,24,31,23,32)(11,25,27,17,28,33,29,34)(22,36,26,35,37,30,38,39);(8,10,13,12,15,24,14,23)(9,16,18,21,20,32,19,31)(11,22,27,26,28,37,29,38)(17,30,25,35,34,36,33,39);(8,11)(9,17)(10,22)(12,26)(13,27)(14,29)(15,28)(16,30)(18,25)(19,33)(20,34)(21,35)(23,38)(24,37)(31,39)(32,36);(8,12,13,24,15,23,14,10)(9,16,19,31,20,32,18,21)(11,26,27,37,28,38,29,22)(17,30,33,39,34,36,25,35)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14547);