Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61221 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3497 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#532 ◁ G | |
2018 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)(16,17,21,24)(18,22,27,38)(19,29,32,41)(20,33,35,25)(23,34,40,31)(26,42,30,47)(28,45,44,37)(36,46,39,43);(8,10)(9,12)(11,15)(13,14)(16,18)(17,22)(19,30)(20,28)(21,27)(23,39)(24,38)(25,37)(26,32)(29,47)(31,46)(33,45)(34,43)(35,44)(36,40)(41,42);(16,19,21,32)(17,23,24,40)(18,26,27,30)(20,34,35,31)(22,36,38,39)(25,41,33,29)(28,46,44,43)(37,47,45,42);(10,15)(12,14)(16,18)(17,22)(19,26)(20,28)(21,27)(23,36)(24,38)(25,37)(29,42)(30,32)(31,43)(33,45)(34,46)(35,44)(39,40)(41,47);(17,24)(18,27)(23,40)(25,33)(26,30)(28,44)(29,41)(43,46)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54209);