Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#7975 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#95 |
| commutator | C2×C4 | C2×C42×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C24×C7 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C42×C7 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,14,16,27)(10,18)(11,22)(15,25,26,37)(17,31,30,38)(20,34)(21,33)(23,24)(28,29,39,35)(32,36);(8,9,11,17,13,16,24,30)(10,14,20,28,21,27,34,39)(12,15,23,29,19,26,22,35)(18,25,32,38,33,37,36,31);(9,15)(14,25)(16,26)(17,29)(27,37)(28,38)(30,35)(31,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 963);