Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C4 |
| direct product | C7×#60816 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C7×#117 ◁ G | |
2048 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17,22,26)(18,23,29,38)(19,31,33,39)(20,25,21,34)(24,35,40,32)(27,41,43,46)(28,37,30,44)(36,45,47,42);(8,10,11,15)(9,12,13,14)(16,18)(17,23)(19,27)(20,28)(21,30)(22,29)(24,36)(25,37)(26,38)(31,41)(32,42)(33,43)(34,44)(35,45)(39,46)(40,47);(10,15)(12,14)(16,19)(17,24)(18,27)(20,32)(21,35)(22,33)(23,36)(25,39)(26,40)(28,42)(29,43)(30,45)(31,34)(37,46)(38,47)(41,44);(9,13)(12,14)(16,20,22,21)(17,25,26,34)(18,28,29,30)(19,32,33,35)(23,37,38,44)(24,39,40,31)(27,42,43,45)(36,46,47,41);(18,29)(23,38)(27,43)(28,30)(36,47)(37,44)(41,46)(42,45)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53804);