Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C4 |
| direct product | C7×#60826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
2026 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)(16,17,21,26)(18,22,27,35)(19,24,30,38)(20,23,32,25)(28,34,40,45)(29,36,41,33)(31,37,43,39)(42,46,47,44);(8,10,11,15)(9,12,13,14)(16,18)(17,22)(19,28)(20,29)(21,27)(23,36)(24,34)(25,33)(26,35)(30,40)(31,42)(32,41)(37,46)(38,45)(39,44)(43,47);(10,15)(12,14)(17,23)(18,27)(20,32)(22,33)(24,37)(25,26)(28,40)(31,43)(34,44)(35,36)(38,39)(45,46);(9,13)(12,14)(16,19)(17,24)(18,28)(20,31)(21,30)(22,34)(23,37)(25,39)(26,38)(27,40)(29,42)(32,43)(33,44)(35,45)(36,46)(41,47);(19,30)(24,38)(28,40)(31,43)(34,45)(37,39)(42,47)(44,46)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53814);