Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#26990 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#537 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
766 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)(18,24)(19,32)(20,35)(21,28)(22,27)(23,30)(25,36)(26,33)(29,43)(31,39)(34,38)(37,42)(40,44)(41,47)(45,46);(8,10,11,15)(9,12,13,14)(16,18,21,30,22,19,33,31)(17,23,26,24,27,39,28,32)(20,29,36,44,37,34,47,45)(25,38,35,40,41,43,42,46);(9,13)(12,14)(16,19)(17,24)(18,22)(20,34)(21,31)(23,28)(25,40)(26,39)(27,32)(29,37)(30,33)(35,43)(36,45)(38,42)(41,46)(44,47);(9,13)(12,14)(16,20,33,47,22,37,21,36)(17,25,28,42,27,41,26,35)(18,29,31,45,19,34,30,44)(23,38,32,46,39,43,24,40)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 19978);