Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#18432 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3217 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
940 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)(9,13)(11,18)(14,20)(15,19)(17,22)(21,23)(27,34)(29,35)(30,37)(32,38);(8,9,12,15)(10,14,16,21)(11,19,18,13)(17,23,22,20)(24,25)(26,29)(27,30)(28,31)(32,36)(33,35)(34,37)(38,39);(8,10,12,16)(9,14,15,21)(11,17,18,22)(13,20,19,23)(24,26)(25,29)(27,32)(28,33)(30,36)(31,35)(34,38)(37,39);(10,16)(14,21)(17,22)(20,23)(24,27,28,34)(25,30,31,37)(26,32,33,38)(29,36,35,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11420);