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×#61350 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3035 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#533 ◁ G | |
1746 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)(9,12)(13,14)(16,17,21,26)(18,28,30,23)(19,32,34,41)(20,27,22,25)(24,36,39,33)(29,43,44,47)(31,38,35,40)(37,46,42,45);(8,9,11,12)(10,14,15,13)(16,18,21,30)(17,23,26,28)(19,29,34,44)(20,35,22,31)(24,37,39,42)(25,40,27,38)(32,47,41,43)(33,46,36,45);(16,19)(17,24)(18,29)(20,33)(21,34)(22,36)(23,37)(25,32)(26,39)(27,41)(28,42)(30,44)(31,45)(35,46)(38,43)(40,47);(8,10,11,15)(9,13,12,14)(18,30)(23,28)(29,44)(31,35)(37,42)(38,40)(43,47)(45,46);(16,20,21,22)(17,25,26,27)(18,31,30,35)(19,33,34,36)(23,38,28,40)(24,32,39,41)(29,45,44,46)(37,43,42,47)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54338);