Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10273 |
| 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 | |
542 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)(12,13,15,18)(14,16,19,17)(20,21,26,23)(22,30,34,31)(24,29,25,28)(27,33,35,32);(9,11)(20,22,26,34)(21,27,23,35)(24,33,25,32)(28,31,29,30);(13,16)(14,19)(17,18)(20,23,26,21)(22,31,34,30)(24,28,25,29)(27,32,35,33)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3261);