Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14715 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#15198 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(10,14)(13,15)(16,17)(18,20)(19,22)(21,23)(24,25,27,29)(26,30,31,28)(33,35)(37,38);(9,12)(13,15)(17,18)(21,22)(24,25,27,29)(26,28,31,30)(32,33,36,35)(34,37,39,38);(8,9)(10,13)(11,12)(14,15)(16,18,20,17)(19,22,23,21)(24,25)(26,28)(27,29)(30,31)(32,34,36,39)(33,37,35,38);(8,10,11,14)(9,13,12,15)(16,19,20,23)(17,21,18,22)(24,26,27,31)(25,28,29,30)(32,35,36,33)(34,38,39,37)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 8186);