Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60367 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60566 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3455 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C7×#117 ◁ G | |
2002 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)(10,13)(11,12)(14,15)(16,17)(18,22)(19,29)(20,32)(21,24)(23,30)(25,34)(26,40)(27,36)(28,44)(31,39)(33,38)(35,42)(37,43)(41,47)(45,46);(9,12)(13,15)(16,18)(17,22)(19,26)(20,28)(21,27)(23,35)(24,36)(25,37)(29,40)(30,42)(31,41)(32,44)(33,45)(34,43)(38,46)(39,47);(16,19,21,31)(17,23,24,38)(18,26,27,41)(20,33,34,30)(22,35,36,46)(25,39,32,29)(28,45,43,42)(37,47,44,40);(8,10,11,14)(9,13,12,15)(18,27)(22,36)(26,41)(28,43)(35,46)(37,44)(40,47)(42,45);(17,24)(22,36)(23,38)(25,32)(29,39)(35,46)(37,44)(40,47)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53554);