Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#24725 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,12)(10,14,15,13)(16,17,22,27,20,25,21,26)(18,28,37,39,30,23,31,43)(19,32,36,24,34,42,35,41)(29,45,47,44,46,40,33,38);(9,12)(13,14)(16,18)(17,23)(19,33)(20,30)(21,31)(22,37)(24,40)(25,28)(26,39)(27,43)(29,36)(32,44)(34,47)(35,46)(38,42)(41,45);(16,19,20,34)(17,24,25,41)(18,29,30,46)(21,36,22,35)(23,38,28,44)(26,42,27,32)(31,47,37,33)(39,45,43,40);(8,10,11,15)(9,13,12,14)(17,25)(23,28)(24,41)(26,27)(32,42)(38,44)(39,43)(40,45)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17713);