Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19002 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3213 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
884 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)(8,9)(10,16)(11,19)(12,14)(13,17)(15,21)(18,23)(20,22)(26,32)(27,34)(29,37)(30,35)(33,36)(38,39);(8,10)(9,13)(11,20)(12,18)(14,22)(15,23)(16,19)(17,21)(24,25,28,31)(26,29,33,38)(27,35,34,30)(32,39,36,37);(11,21)(15,19)(16,23)(17,20)(24,26)(25,29)(27,36)(28,33)(30,39)(31,38)(32,34)(35,37);(9,14)(13,22)(15,19)(16,23)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11990);