Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14715 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×C4⋊#401 |
| unambiguous semidirect product | C4⋊(C7×#401) |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1106 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)(9,11)(13,15)(17,18)(20,21,25,23)(22,27,24,26)(28,29,32,35)(30,33,34,31);(12,13,16,15)(14,18,19,17)(20,22,25,24)(21,26,23,27)(28,30,32,34)(29,33,35,31);(12,14,16,19)(13,17,15,18)(20,23,25,21)(22,27,24,26)(28,29)(30,33)(31,34)(32,35);(8,9,10,11)(12,15,16,13)(14,18,19,17)(20,24,25,22)(21,27,23,26)(28,31,32,33)(29,34,35,30)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 8142);