Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C22×C42 |
| direct product | C7×#13928 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1226 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,10,11)(13,16)(17,19)(20,21,24,22)(23,26,27,25)(30,34)(33,35);(21,22)(25,26)(28,29,32,31)(30,35,34,33);(12,13)(14,17)(15,16)(18,19)(20,22,24,21)(23,26,27,25)(28,30,32,34)(29,33,31,35);(12,14,15,18)(13,17,16,19)(20,23)(21,25)(22,26)(24,27)(28,31,32,29)(30,35,34,33)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6916);