Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23876 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23959 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1192 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)(10,14)(11,13)(12,15)(16,17)(18,19)(20,24)(21,25)(22,26)(23,29)(27,31)(28,30);(8,10,11,15)(9,12,13,14)(16,18,22,28)(17,19,26,30)(20,23,21,27)(24,29,25,31);(16,19)(17,23)(18,25)(20,29)(21,31)(22,30)(24,28)(26,27);(9,13)(12,14)(16,20,22,21)(17,24,26,25)(18,23,28,27)(19,29,30,31)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16947);