Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
846 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)(8,9,10,11)(12,13,17,23)(14,19,27,35)(15,28,31,37)(16,22,29,21)(18,26,33,25)(20,36,38,30)(24,39,42,32)(34,41,43,40);(12,14,16,25,17,27,29,26)(13,18,21,19,23,33,22,35)(15,24,30,40,31,42,36,41)(20,32,28,34,38,39,37,43);(9,11)(12,14)(13,19)(15,24)(16,25)(17,27)(18,22)(20,34)(21,33)(23,35)(26,29)(28,39)(30,40)(31,42)(32,37)(36,41)(38,43);(12,15,29,36,17,31,16,30)(13,20,22,37,23,38,21,28)(14,24,26,41,27,42,25,40)(18,32,35,43,33,39,19,34)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17786);