Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18628 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3519 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,16)(11,19)(12,14)(13,18)(15,21)(17,23)(20,22)(24,25,29,32)(26,34,35,38)(27,33,28,31)(30,37,39,36);(8,10)(9,13)(11,20)(12,17)(14,22)(15,23)(16,19)(18,21)(24,26)(25,30)(27,37)(28,36)(29,35)(31,38)(32,39)(33,34);(25,31)(27,28)(30,38)(32,33)(34,39)(36,37);(9,14)(10,17)(15,19)(18,20)(25,32)(26,35)(31,33)(36,37)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11616);