Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24805 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24807 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
844 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(12,13,19,23,18,25,17,24)(14,26,35,22,16,34,28,20)(15,29,31,21,33,39,32,38)(27,37,41,40,30,36,42,43);(8,9)(10,11)(12,14,17,28,18,16,19,35)(13,20,23,26,25,22,24,34)(15,27,31,41,33,30,32,42)(21,36,29,40,38,37,39,43);(9,11)(12,15)(13,21)(14,27)(16,30)(17,31)(18,33)(19,32)(20,36)(22,37)(23,29)(24,39)(25,38)(26,40)(28,41)(34,43)(35,42);(12,16,19,28,18,14,17,35)(13,22,24,26,25,20,23,34)(15,30,32,41,33,27,31,42)(21,37,39,40,38,36,29,43)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17795);