Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#34919 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| prime radical | C7×#2540 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
2392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 27 points:
(1,2,3,4,5,6,7)(9,10)(12,13)(14,18)(15,17)(16,19);(8,9,11,10)(12,14,16,15)(13,17,19,18)(20,21)(22,26)(23,24)(25,27);(8,10,11,9)(12,14,16,15)(13,18,19,17)(21,24)(25,26);(20,22,23,27)(21,25,24,26);(12,15,16,14)(13,17,19,18)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27907);