Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#21484 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#120 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C4×#120 |
| prime radical | C7×#3025 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C7×C8 ◁ G | |
1306 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)(8,9,13,12,14,17,26,25)(10,15,21,19,20,28,35,34)(11,16,24,22,23,29,37,36)(18,30,33,39,32,27,38,31);(8,10)(9,15)(11,18)(12,19)(13,21)(14,20)(16,27)(17,28)(22,31)(23,32)(24,33)(25,34)(26,35)(29,30)(36,39)(37,38);(8,11)(9,16)(10,18)(12,22)(13,24)(14,23)(15,27)(17,29)(19,31)(20,32)(21,33)(25,36)(26,37)(28,30)(34,39)(35,38);(8,12,13,17,14,25,26,9)(10,19,21,28,20,34,35,15)(11,22,24,29,23,36,37,16)(18,31,33,30,32,39,38,27)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14472);