Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18744 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3212 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
852 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)(10,16)(11,13)(12,20)(14,18)(15,22)(17,21)(19,23)(25,30)(26,33)(27,28)(32,36)(34,35)(37,38);(8,10,13,19)(9,14,11,17)(12,21,22,18)(15,23,20,16)(24,25,29,32)(26,31,35,39)(27,30,28,36)(33,37,34,38);(8,11,13,9)(10,17,19,14)(12,20,22,15)(16,18,23,21)(24,26,29,35)(25,31,32,39)(27,33,28,34)(30,37,36,38);(9,11)(14,17)(15,20)(16,23)(24,27,29,28)(25,30,32,36)(26,34,35,33)(31,38,39,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11732);