Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18562 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18617 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3506 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
930 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)(8,9,13,16)(10,17,20,22)(11,15,12,21)(14,19,23,18)(24,25,29,33)(26,34,35,38)(27,32,28,31)(30,37,39,36);(8,10,13,20)(9,14,16,23)(11,18,12,19)(15,22,21,17)(24,26,29,35)(25,30,33,39)(27,37,28,36)(31,38,32,34);(8,11,13,12)(9,15,16,21)(10,18,20,19)(14,22,23,17)(25,31)(27,28)(30,38)(32,33)(34,39)(36,37);(8,11,13,12)(9,15,16,21)(10,19,20,18)(14,17,23,22)(26,35)(30,39)(34,38)(36,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11605);