Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#19718 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3207 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
712 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)(8,9,13,16)(10,17,15,12)(11,14,19,21)(18,23,22,20)(24,25,29,33)(26,31,34,39)(27,36,35,30)(28,38,37,32);(8,10,12,9,13,15,17,16)(11,18,20,14,19,22,23,21)(24,26,28,35,29,34,37,27)(25,30,32,31,33,36,38,39);(8,11,13,19)(9,14,16,21)(10,18,15,22)(12,20,17,23)(24,27,37,34,29,35,28,26)(25,31,38,30,33,39,32,36);(11,19)(14,21)(18,22)(20,23)(26,34)(27,35)(30,36)(31,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12706);