Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#578 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
1302 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)(12,13,18,22)(14,24,27,34)(15,28,32,20)(16,26,19,35)(17,23,36,21)(25,41,43,38)(29,37,42,30)(31,39,33,40);(12,14,18,27)(13,19,22,16)(15,29,32,42)(17,35,36,26)(20,38,28,41)(21,34,23,24)(25,31,43,33)(30,39,37,40);(9,11)(12,15,18,32)(13,20,22,28)(14,25,27,43)(16,30,19,37)(17,31,36,33)(21,39,23,40)(24,38,34,41)(26,42,35,29);(12,16)(13,14)(15,30)(17,24)(18,19)(20,25)(21,35)(22,27)(23,26)(28,43)(29,39)(31,38)(32,37)(33,41)(34,36)(40,42)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17450);