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×#18433 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#121 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
872 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)(24,25,30,27)(26,34,37,39)(28,33,29,32)(31,38,35,36);(8,9)(10,13)(11,14)(12,15)(16,20)(17,19)(18,21)(22,23)(24,26,30,37)(25,31,27,35)(28,36,29,38)(32,34,33,39);(8,10)(9,13)(11,16)(12,17)(14,20)(15,19)(18,22)(21,23)(24,27,30,25)(26,35,37,31)(28,32,29,33)(34,38,39,36);(8,11,12,18)(9,14,15,21)(10,16,17,22)(13,20,19,23)(24,28,30,29)(25,32,27,33)(26,36,37,38)(31,34,35,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11421);