Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#32871 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,14,16,13,19,12,18)(10,20,21,28,24,30,23,15)(11,17,25,31,27,34,26,33)(22,35,36,32,37,39,38,29);(8,10,12,23,13,24,14,21)(9,15,16,20,19,28,18,30)(11,22,25,36,27,37,26,38)(17,32,33,35,34,29,31,39);(9,16)(10,21)(11,25)(12,14)(15,28)(18,19)(22,37)(23,24)(26,27)(29,35)(31,33)(32,39);(8,11)(9,17)(10,22)(12,26)(13,27)(14,25)(15,29)(16,31)(18,33)(19,34)(20,35)(21,36)(23,38)(24,37)(28,32)(30,39)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 25859);