Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24474 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,18,14,12,31,17)(10,19,23,21,24,33,22,15)(11,25,29,27,30,35,28,16)(20,32,37,39,38,36,26,34);(8,10)(9,15)(11,26)(12,21)(13,23)(14,24)(16,34)(17,33)(18,19)(20,29)(22,31)(25,32)(27,39)(28,38)(30,37)(35,36);(8,11,14,30)(9,16,12,27)(10,20,24,38)(13,28,31,29)(15,32,21,36)(17,25,18,35)(19,34,33,39)(22,37,23,26);(8,12)(9,14)(10,21)(11,27)(13,17)(15,24)(16,30)(18,31)(19,22)(20,36)(23,33)(25,28)(26,39)(29,35)(32,38)(34,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17462);