Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62860 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| prime radical | C7×#3449 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(17,18)(21,34)(23,26)(24,27)(30,43)(32,44)(35,38)(41,47);(8,9)(10,13)(11,12)(14,15)(16,17,22,18)(19,23,31,26)(20,27,33,24)(21,25,34,28)(29,38,42,35)(30,36,43,39)(32,40,44,37)(41,46,47,45);(8,10,11,14)(9,13,12,15)(16,18,22,17)(19,23,31,26)(20,27,33,24)(21,28,34,25)(29,35,42,38)(30,36,43,39)(32,40,44,37)(41,45,47,46);(16,19)(17,23)(18,26)(20,29)(21,30)(22,31)(24,35)(25,36)(27,38)(28,39)(32,41)(33,42)(34,43)(37,45)(40,46)(44,47);(16,20,22,33)(17,24,18,27)(19,29,31,42)(21,32,34,44)(23,35,26,38)(25,37,28,40)(30,41,43,47)(36,45,39,46);(16,21)(17,25)(18,28)(19,30)(20,32)(22,34)(23,36)(24,37)(26,39)(27,40)(29,41)(31,43)(33,44)(35,45)(38,46)(42,47)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55848);