Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#10541 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,17,19)(14,15,18,16)(21,25)(22,28)(23,31)(26,34)(27,32)(29,33);(12,14)(13,15)(16,19)(17,18)(20,21,24,27)(22,29,28,26)(23,32,31,25)(30,33,35,34);(9,11)(13,18)(14,19)(15,16)(20,22,23,30,24,28,31,35)(21,26,25,33,27,29,32,34)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3529);