Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#21737 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C23×C7 | C2×#41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C4×C7×C8 ◁ G | |
662 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)(10,15)(11,13)(12,14)(16,17,23,27,21,26,22,38)(18,28,33,43,31,24,32,41)(19,34,37,42,36,46,20,25)(29,44,30,39,35,47,45,40);(8,10,12,11)(9,13,14,15)(16,18,21,31)(17,24,26,28)(19,35,36,29)(20,30,37,45)(22,32,23,33)(25,40,42,39)(27,41,38,43)(34,44,46,47);(16,19,22,20,21,36,23,37)(17,25,27,34,26,42,38,46)(18,29,32,45,31,35,33,30)(24,39,41,47,28,40,43,44);(8,11,12,10)(9,13,14,15)(16,20,22,36,21,37,23,19)(17,25,38,46,26,42,27,34)(18,30,32,29,31,45,33,35)(24,40,43,47,28,39,41,44)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14725);