Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18977 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,19)(11,16)(12,17)(13,22)(14,18)(15,20)(21,23)(24,25,30,33)(26,36,32,39)(27,37,31,38)(28,35,29,34);(8,10,14,11)(9,15,18,23)(12,20,13,21)(16,22,19,17)(24,26,30,32)(25,31,33,27)(28,38,29,37)(34,39,35,36);(8,11,14,10)(9,16,18,19)(12,20,13,21)(15,22,23,17)(24,27,30,31)(25,32,33,26)(28,36,29,39)(34,37,35,38);(8,12,14,13)(9,17,18,22)(10,20,11,21)(15,16,23,19)(25,33)(27,31)(34,35)(36,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11965);