Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18313 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3455 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
910 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)(8,9,13,16)(10,17,19,22)(11,15,12,20)(14,21,23,18)(25,30)(27,28)(31,38)(32,35)(33,36)(37,39);(8,10)(9,14)(11,18)(12,21)(13,19)(15,22)(16,23)(17,20)(24,25)(26,31)(27,30)(28,35)(29,32)(33,37)(34,39)(36,38);(8,11,13,12)(9,15,16,20)(10,18,19,21)(14,22,23,17)(24,26,29,34)(25,31,32,39)(27,33,28,36)(30,37,35,38);(24,27,29,28)(25,30,32,35)(26,33,34,36)(31,37,39,38)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11301);