Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18449 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
918 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)(8,9,12,14)(10,16,18,23)(11,19,21,15)(13,20,22,17)(24,25)(26,29)(27,30)(28,31)(32,38)(33,36)(34,37)(35,39);(8,10,12,18)(9,13,14,22)(11,20,21,17)(15,23,19,16)(24,26)(25,29)(27,32)(28,33)(30,35)(31,36)(34,39)(37,38);(8,9)(10,13)(11,15)(12,14)(16,17)(18,22)(19,21)(20,23)(24,27)(25,30)(26,32)(28,34)(29,35)(31,37)(33,39)(36,38);(9,14)(13,22)(15,19)(16,23)(25,31)(29,36)(30,37)(35,38)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11437);