Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18941 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3548 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
914 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)(8,9,14,18)(10,19,11,16)(12,17,13,22)(15,21,23,20)(24,25)(26,32)(27,35)(28,30)(29,34)(31,36)(33,39)(37,38);(8,10,14,11)(9,15,18,23)(12,20,13,21)(16,22,19,17)(27,36)(31,35)(32,39)(34,37);(8,11,14,10)(9,16,18,19)(12,20,13,21)(15,22,23,17)(24,26)(25,29)(27,37)(28,33)(30,38)(31,39)(32,35)(34,36);(8,12,14,13)(9,17,18,22)(10,20,11,21)(15,16,23,19)(25,30)(29,38)(31,35)(32,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11929);