Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23723 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#399 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
972 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)(8,9,12,16,13,17,19,27)(10,18,21,29,22,33,26,14)(11,23,25,37,24,15,30,32)(20,34,36,31,35,39,38,28);(8,10,19,21,13,22,12,26)(9,14,27,18,17,29,16,33)(11,20,30,36,24,35,25,38)(15,31,37,39,23,28,32,34);(8,11)(9,15)(10,20)(12,25)(13,24)(14,28)(16,32)(17,23)(18,34)(19,30)(21,36)(22,35)(26,38)(27,37)(29,31)(33,39);(11,24)(15,23)(20,35)(25,30)(28,31)(32,37)(34,39)(36,38)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16711);