Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23903 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23989 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C7×#534 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1210 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17)(18,22)(19,23)(20,24)(21,25)(26,36)(27,34)(28,35)(29,37)(30,38)(31,39)(32,40)(33,42)(41,46)(43,45)(44,47);(8,10,11,15)(9,12,13,14)(16,18)(17,22)(19,26)(20,27)(21,28)(23,36)(24,34)(25,35)(29,41)(30,42)(31,43)(32,44)(33,38)(37,46)(39,45)(40,47);(16,19,21,30)(17,23,25,38)(18,26,28,42)(20,31,32,29)(22,33,35,36)(24,39,40,37)(27,43,44,41)(34,46,47,45);(9,13)(12,14)(16,20,21,32)(17,24,25,40)(18,27,28,44)(19,29,30,31)(22,34,35,47)(23,37,38,39)(26,41,42,43)(33,45,36,46)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16977);