Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19014 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19029 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
824 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)(8,9,13,11)(10,16,18,23)(12,20,22,15)(14,21,17,19)(26,32)(27,34)(29,37)(30,35)(33,36)(38,39);(8,10,13,18)(9,14,11,17)(12,21,22,19)(15,23,20,16)(24,25,28,31)(26,29,33,38)(27,35,34,30)(32,39,36,37);(8,11,13,9)(10,17,18,14)(12,15,22,20)(16,21,23,19)(24,26)(25,29)(27,36)(28,33)(30,39)(31,38)(32,34)(35,37);(10,18)(14,17)(16,23)(19,21)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12017);