Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61210 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#532 ◁ G | |
2014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,14,15,12)(16,17,22,26)(18,23,29,39)(19,30,32,40)(20,25,21,34)(24,35,41,31)(27,42,45,47)(28,37,33,38)(36,43,46,44);(8,10)(9,12)(11,15)(13,14)(16,18)(17,23)(19,27)(20,33)(21,28)(22,29)(24,36)(25,38)(26,39)(30,42)(31,44)(32,45)(34,37)(35,43)(40,47)(41,46);(16,19,22,32)(17,24,26,41)(18,27,29,45)(20,31,21,35)(23,36,39,46)(25,40,34,30)(28,43,33,44)(37,42,38,47);(10,15)(12,14)(16,18)(17,23)(19,27)(20,33)(21,28)(22,29)(24,36)(25,38)(26,39)(30,42)(31,44)(32,45)(34,37)(35,43)(40,47)(41,46);(16,20,22,21)(17,25,26,34)(18,28,29,33)(19,31,32,35)(23,37,39,38)(24,40,41,30)(27,43,45,44)(36,42,46,47)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54198);