Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#21476 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×2−1+4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1322 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)(8,9,11,10)(12,13,17,21)(14,22,25,36)(15,19,26,34)(16,28,31,20)(18,29,33,24)(23,39,40,38)(27,37,30,35)(32,42,43,41);(12,14)(13,18)(15,23)(16,29)(17,25)(19,32)(20,36)(21,33)(22,28)(24,31)(26,40)(27,42)(30,41)(34,43)(35,38)(37,39);(12,15,17,26)(13,19,21,34)(14,23,25,40)(16,30,31,27)(18,32,33,43)(20,37,28,35)(22,38,36,39)(24,42,29,41);(8,10,11,9)(15,26)(19,34)(23,40)(27,30)(32,43)(35,37)(38,39)(41,42)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14464);