Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19014 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3561 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
896 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)(9,14)(10,17)(11,12)(16,19)(18,20)(21,23)(24,25,28,31)(26,32,33,39)(27,35,37,30)(29,36,38,34);(8,9)(10,15)(11,19)(12,14)(13,16)(17,23)(18,22)(20,21)(24,26,28,33)(25,29,31,38)(27,36,37,34)(30,39,35,32);(8,10)(9,15)(11,17)(12,20)(13,18)(14,21)(16,22)(19,23)(27,37)(30,35)(32,39)(34,36);(9,16)(14,19)(15,22)(21,23)(26,33)(29,38)(32,39)(34,36)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12020);