Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13452 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
382 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)(12,13,16,18)(14,19,15,17)(20,21,23,28)(22,30,25,26)(24,27,32,35)(29,31,34,33);(8,9)(10,11)(12,14,16,15)(13,17,18,19)(20,22,23,25)(21,26,28,30)(24,31,32,33)(27,29,35,34);(9,11)(12,15,16,14)(13,17,18,19)(21,27)(22,25)(24,33)(26,34)(28,35)(29,30)(31,32)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6440);