Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23814 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C7×#376 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7)(12,13,15,16)(14,17,18,19)(20,21,24,28,25,29,39,45)(22,30,33,41,32,43,37,26)(23,34,35,42,36,44,38,27)(31,40,48,51,47,50,49,46);(8,9)(10,11)(13,16)(17,19)(20,22,25,32)(21,26,29,41)(23,31,36,47)(24,37,39,33)(27,40,42,50)(28,43,45,30)(34,46,44,51)(35,49,38,48);(9,11)(20,23,25,36)(21,27,29,42)(22,31,32,47)(24,38,39,35)(26,40,41,50)(28,44,45,34)(30,46,43,51)(33,49,37,48);(12,14,15,18)(13,17,16,19)(22,32)(26,41)(30,43)(31,47)(33,37)(40,50)(46,51)(48,49)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16802);