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×#61207 |
| 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 ◁ C7×#532 ◁ G | |
2046 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)(8,9,11,13)(10,14,15,12)(16,17)(18,23)(19,25)(20,26)(21,35)(22,27)(24,31)(28,37)(29,38)(30,40)(32,41)(33,39)(34,42)(36,44)(43,46)(45,47);(8,10)(9,12)(11,15)(13,14)(16,18,22,30)(17,23,27,40)(19,28,32,45)(20,33,21,29)(24,36,42,46)(25,37,41,47)(26,39,35,38)(31,44,34,43);(16,19)(17,24)(18,28)(20,31)(21,34)(22,32)(23,36)(25,35)(26,41)(27,42)(29,43)(30,45)(33,44)(37,38)(39,47)(40,46);(10,15)(12,14)(16,19)(17,25)(18,28)(20,34)(21,31)(22,32)(23,37)(24,35)(26,42)(27,41)(29,44)(30,45)(33,43)(36,38)(39,46)(40,47);(16,20,22,21)(17,26,27,35)(18,29,30,33)(19,31,32,34)(23,38,40,39)(24,41,42,25)(28,43,45,44)(36,37,46,47)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54195);