Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#18429 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3561 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
932 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(11,18)(13,19)(14,21)(16,22)(24,25,29,33)(26,34,36,39)(27,32,28,31)(30,37,38,35);(8,9)(10,13)(11,14)(12,15)(16,20)(17,19)(18,21)(22,23)(24,26,29,36)(25,30,33,38)(27,35,28,37)(31,34,32,39);(8,10)(9,13)(11,16)(12,17)(14,20)(15,19)(18,22)(21,23)(27,28)(31,32)(34,39)(35,37);(8,11,12,18)(9,14,15,21)(10,16,17,22)(13,20,19,23)(24,27,29,28)(25,31,33,32)(26,35,36,37)(30,34,38,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11417);