Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#20671 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#117 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#380 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C7×M16 ◁ G | |
1324 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)(10,18)(11,22,24,15)(12,25)(13,17)(14,21)(16,26)(19,32,33,30)(20,31)(23,29,38,37)(27,34,36,39)(28,35);(8,10,12,21,13,20,26,35)(9,14,16,18,17,28,25,31)(11,19,23,34,24,33,38,39)(15,27,29,30,22,36,37,32);(8,11)(9,15)(10,19)(12,23)(13,24)(14,27)(16,29)(17,22)(18,30)(20,33)(21,34)(25,37)(26,38)(28,36)(31,32)(35,39);(10,20)(14,28)(18,31)(19,33)(21,35)(27,36)(30,32)(34,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13659);