Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#24931 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
870 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,12)(11,13)(14,15)(16,17)(18,21)(19,26)(20,22)(23,27)(24,30)(25,29)(28,31);(8,10,11,14)(9,12,13,15)(17,22)(18,24)(20,30)(23,26)(25,31)(27,29);(9,13)(12,15)(16,18,21,17)(19,25,28,23)(20,22,30,24)(26,27,31,29);(16,19)(17,23)(18,25)(20,29)(21,28)(22,26)(24,31)(27,30)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17919);