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×#19027 |
| 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 | |
884 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)(8,9,12,15)(10,16,17,23)(11,19,21,14)(13,20,22,18)(26,32)(27,34)(29,37)(30,35)(33,36)(38,39);(8,10,12,17)(9,13,15,22)(11,20,21,18)(14,23,19,16)(24,25,28,31)(26,29,33,38)(27,35,34,30)(32,39,36,37);(11,21)(14,19)(16,23)(18,20)(24,26)(25,29)(27,36)(28,33)(30,39)(31,38)(32,34)(35,37);(10,17)(13,22)(16,23)(18,20)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12015);