Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18746 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18789 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C2×C7×#41 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
916 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,15)(10,16,18,23)(11,19,21,14)(13,20,22,17)(24,25,30,35)(26,32,37,38)(27,31,36,39)(28,34,29,33);(8,10,12,18)(9,13,15,22)(11,20,21,17)(14,23,19,16)(24,26,30,37)(25,31,35,39)(27,28,36,29)(32,33,38,34);(24,27)(25,32)(26,28)(29,37)(30,36)(31,33)(34,39)(35,38);(24,28,30,29)(25,33,35,34)(26,36,37,27)(31,38,39,32)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11777);